THE UNIVERSITY OF MICHIGAN COLLEGE OF ENGINEERING Simulation Center Technical Report ARTIFICIAL GENETIC BREEDING PROCEDURES FOR PARAMETER OPTIMIZATION Roy B. Hollstien with assistance from: NATIONAL SCIENCE FOUNDATION GRANT NO. GJ-36115 WASHINGTON, D. C. administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR September 1973

ABSTRACT This report describes a method of applying the breeding procedures of agriculture to optimization problems in computer science and/or engineering. A direct search in parameter space is guided by an artificial breeding program, so mathematical relationships between the parameters and the objective are not required. Artificial organisms are represented by diploid genotypes composed of chromosome-like arrays of binary bits. Each genotype controls the synthesis of a trial point in parameter space, and the phenotypic worth of each individual is determined by a measure of the search objective evaluated at that point. Gene action algorithms employ intra-allelic additivity, intra-allelic interaction with dominance at the gene level controlled by modifier loci, interallelic additivity of multiple factors, and epistatic control of different steps in synthetic pathways. Agricultural breeding methods are used to select and mate parents in successive generations, starting with heterozygous populations that simulate wide crosses of genetically dissimilar varieties. Offspring are produced by meiotic division of parental genotypes and the union of two gametic sets of chromosomes. Genetic recombination is induced by independent segregation of chromosomes and crossing-over of nonsister chromatids during gametogenisis; recombination is suppressed by inhibiting crossing-over within inverted or translocated chromosome segments. Background variation is maintained by point mutations that transform the diallelic genes into their opposite conformation. Mathematical functions of numerical parameters are used to test combinations of artificial species and breeding methods for rates and limits of progress on objective surfaces with topological features such as ridges, plateaus, and multiple peaks that are nemeses of general methods of optimization.

FORWARD This report covers research partially supported by the National Science Foundation Office of Computing Activities under Grant No. GJ-36115. The project, entitled "Artificial Genetic Breeding Procedures for Parameter Optimization," was conducted at the University of Michigan College of Engineering Simulation Center while the author was an Associate Research Engineer in the Department of Aerospace Engineering. The grant was effective from October 1, 1972 to March 31, 1974. National Science Foundation support during this period is greatfully acknowledged. Basic concepts of the ARTIFICIAL BREEDING method of optimization were developed at the University of Michigan prior to the NSF assisted study. I especially thank Professors Robert M. Howe, Chairman of the Department of Aerospace Engineering, and Laurence E. Fogarty, Director of the Simulation Center, for the opportunity to pursue this study. I am also very greatful to Dr. R. W. Allard, Department of Genetics, University of California at Davis for his personal critique of the fundamental concepts of ARTIFICIAL BREEDING in simulating the genetic search process involved in agricultural breeding programs and as a method of optimization in computer science and/or engineering. The breeding methods used in this study are based on the techniques lucidly described in his book: Principles of Plant Breeding. ROY B. HOLLSTIEN California Polytechnic State University February 1974

CONTENTS FOREWORD ABSTRACT LIST OF FIGURES 1 INTRODUCTION 1.1 Parameter Search Problems in Computer Science 1.2 Genetic Search Problems in Agricultural Plant Breeding 1.3 An Artificial Breeding Approach to Direct Search Optimization 1.4 Background and Objectives 2 METHOD 2.1 Artificial Breeding for Parameter Optimization 2.2 Genetic Composition of Artificial Organisms 2.3 Reproduction 2.4 Parameter Synthesis 2.5 Objective Characters 2.6 Breeding Methods 3 RESULTS 3.1 Comparison of Gene Action/Breeding Method Combinations 3.2 Pedigree Method 1 Experiments 3.3 Bulk Population Breeding 1 Experiments 3.4 Mass Selection 1 Experiments 3.5 Simple Recurrent Selection 1 Experiments 3.6 Pedigree Method 2 Experiments 3.7 Simple Recurrent Selection 2 Experiments 4 CONCLUSIONS REFERENCES APPENDIX Computer Programs Used in Experimental Investigations of Artificial Breeding Procedures

LIST OF FIGURES Figure Page 1 Genotype of an artificial organism 2 Close-up views of an artificial chromosome 3 Synthetic pathway model of Gene Action 2 4 Synthetic pathway model of Gene Action 3 5 Transformation used in Gene Actions 4, 5 and 6 6 Synthetic pathway model of Gene Action 5 7 Synthetic pathway model of Gene Action 6 8 Synthetic pathway model of Gene Action 2A 9 Transformation used in Gene Actions 5A and 11A 10 Synthetic pathway model of Gene Action 5A 11 Objective characters Plane, Ridge, Peak NE, Peak W, Peak S and Hypersphere plotted in 2-dimensional parameter space 12a-h Comparison of gene action/breeding method combinations: Gene Actions 1 - 12, 2A, 5A, 8A and 11A with pedigree, bulk population, mass selection, simple recurrent selection and reciprocal recurrent selction breeding methods 13a-c Pedigree breeding for 2-parameter Plane using Gene Action 3 and the selection schedule of Section 3.1 14a-b Phenotypic and parameter values of individuals during pedigree breeding for 2-parameter Plane using Gene Action 3 15 Effect of artificial selection intensity in bulk population breeding for 8-parameter Plane using Gene Action 4 16 Effect of population size in bulk population breeding for 8-parameter Plane using Gene Action 4 17 Effect of cross-fertilization in bulk population breeding for 8-parameter Plane using Gene Action 4 18 Parameter values of individuals produced in bulk population breeding for 8-parameter Plane using Gene Action 4 19a-b Phenotypic and parameter values of individuals during bulk population breeding for 8-parameter Plane using Gene Action 4 20a-b Phenotypic and parameter values of individuals during bulk population breeding for 8-parameter Plane using Gene Action 4 with linkage 21a-b Five replications of bulk population breeding for 8-parameter Plane: Averaged results and parameter values of individuals with increasing phenotypic values 22a-b Phenotypic and parameter values of individuals during bulk population breeding for 8-parameter Ridge using Gene Action 4

Figure Page 23a-b Five replications of bulk population breeding for 8-parameter Ridge: Averaged results and parameter values of individuals with increasing phenotypic values 24a-b Phenotypi.c and parameter values of individuals during mass selection for 8-parameter Plane using Gene Action 4 25a-b Phenotypic and parameter values of individuals during mass selection for 8-parameter Plane using Gene Action 10 26a-b Phenotypic and parameter values of individuals during mass selection for 8-parameter Plane using Gene Action 3 27a-b Phenotypic and parameter values of individuals during mass selection for 8-parameter Plane using Gene Action 9 28a-d Effect of population size of five replications of mass selection for 8-parameter Ridge using Gene Action 3: Averaged results and parameter values of individuals with increasing phenotypic values for populations of 16, 32 and 64 29a-c Simple recurrent selection for 8-parameter Plane using Gene Action 4 30a-c Extended pedigree breeding for 8-parameter Plane using Gene Action 4 31a-c Extended simple recurrent selection for 8-parameter Plane using Gene Action 4 32a-c Extended simple recurrent selection for 8-parameter Ridge using Gene Action 4 33a-c Extended simple recurrent selection for 8-parameter Peak NE using Gene Action 4 34a-c Extended simple recurrent selection for 8-parameter Peak W using Gene Action 4 35a-c Extended simple recurrent selection for 8-parameter Hypersphere using Gene Action 4 36a-c Extended simple recurrent selection for 8-parameter Plane using Gene Action 4 with random inversion, translocation and mutation 37a-c Extended simple recurrent selection for 8-parameter Ridge using Gene Action 4 with random inversion, translocation and mutation 38a-c Extended simple recurrent selection for 8-parameter Peak NE using Gene Action 4 with random inversion, translocation and mutation 39a-c Extended simple recurrent selection for 8-parameter Peak W using Gene Action 4 with random inversion, translocation and mutation 40a-c Extended simple recurrent selection for 8-parameter Peak S using Gene Action 4 with random inversion, translocation and mutation

1 INTRODUCTION 1.1 PARAMETER SEARCH PROBLEMS IN COMPUTER SCIENCE The mathematical programming approach to parameter optimization is based on the mathematical expression of cause-and-effect relationships between the adjustable parameters and a quantitative measure of the objective to be either maximized or minimized. When they are not known, or when the mathematical models are so complex that the programming approach is impractical, direct search methods of optimization may be the only available method of attack. The direct search approach determines experimentally how parameters are related to the objective. The objective is evaluated at trial points in parameter space and the results are used to deduce what new trials are to be made. If successful, the search progresses surely and rapidly to optimal parameter values. Algorithms for direct search optimization have a wide range of applications and are of great practical interest in computer science. How objective values of trial points are obtained is not particularly important in developing direct search algorithms; it may be assumed that they are determined by an unknown mathematical function V(X) that is to be maximized by adjusting the components x, x2,..., xN of the N-dimensional parameter vector X. Minimization problems can always be transformed into an equivalent maximization problem. In practical search problems, there are always bounds on the range of individual parameter values. There may also be constraints that define admissible domains within the larger space bounded by the individual parameter ranges. These constraints are usually expressed on the form of mathematical relations among the parameters X. It is usually desireable to find the optimal parameters in as few trials as possible. This may not be particularly important when the effects of parameters are evaluated by computer simulation. However, charges for computing time are

seldom negligible. Minimizing the number of trial:s required to find optimal parameter values may be very important in on-line control applications where losses are suffered while operating at suboptimal conditions. Most direct search algorithms move incrementally through parameter space along paths of progressive improvement in the objective value (McMurtry, 1970; Swann, 1972). These algorithms are locally exploratory and may progress very slowly or stall on ridges, or wander aimlessly on plateaus in an objective surface. The possibility of multiple peaks makes search problems insolvable, in general, except by exhaustive trial of all admissible points. Some risk of missing optimal peaks must be accepted. But the risk can be reduced by continuing the search at additional cost; for example, incremental searches can be started at many points throughout the parameter space if the cost of repeatedly returning to suboptimapeaks is not too great. The most useful search procedures are those that minimize the cost of reliability for a broad range of problems. It appears that general search algorithms should begin with globally random trials and progressively narrow the exploration to the most promising regions of the parameter space. The question is how to infer from previous trials what new trials should be made. 1.2 GENETIC SEARCH PROBLEMS IN AGRICULTURAL PLANT BREEDING Breeding for improvement in quantitative characteristics of agricultural plants can be viewed as a direct search for genotypic parameters that maximize a phenotypic objective character. The genotypic parameters of the search affect the objective at various levels of gene action, by means of extremely complex biochemical reactions that for practical purposes are unknown to the breeder. The quantitative objective characters of an agricultural breeding program are analogous to continuous functions of parameters in a computer search. Qualitative characters are similar to discontinuous functions of search parameters. To develop improved plant varieties, explorations of genetic parameter space are first induced by crossing two or more source varieties. If the breeder crosses varieties that are homozygous but differ genetically at loci having a major effect on the objective character, there will be a large phenotypic variation 2

in the hybrid F1 generation produced by the cross. The breeder's job is to select and propagate (either by self- or cross-fertilization) specific plants in the F1 and subsequent F2, F3,... generations until a new, true-breeding variety is developed. Specialized breeding methods for self- or cross-pollination, for diploid or polyploid genotypes, and for additive or epistatic gene action have been developed by agricultural geneticists. Selecting plants to be propagated entirely on the basis of individual merit will not always produce the best results. The varietal development methods of agricultural plant breeding are actually random searches in genetic parameter space that start with global explorations and end with incremental explorations in the most promising regions of the parameter space. In the early generations, while there is still a large amount of genetic variation in the population, offspring are apt to have new combinations of genes that are unlike those of their predecessors. In later generations, as the population approaches homozygosity, there is a transition from a global to an incremental random search because the offspring of nearly homozygous parents are less variable. Trial points in genetic parameter space are only indirectly controlled by the breeder. Once plants have been selected and pollinated, genotypes in the next generation are determined by the random mechanisms of inheritance. Nature, therefore, deserves much of the credit for success in agricultural breeding programs, for it has been through natural selection over countless generations that the remarkably adaptive capability of sexually reproductive populations has evolved (Mettler, 1969). 1.3 AN ARTIFICIAL BREEDING APPROACH TO DIRECT SEARCH OPTIMIZATION The adaptive mechanisms of sexually reproductive populations and the breeding methods of agriculture can, by means of simulation, be applied to optimization problems in computer science. This report describes a direct search method in which trial points in parameter space are synthesized by artificial gene action and information stored in the genotypes of artificial organisms. Parameter values simulate intermediate products of gene action, and the phenotypic value of an 5

individual in a population of artificial organisms is represented by the search objective value at the corresponding trial point. Wide crosses of genetically dissimilar varieties are simulated by assigning heterozygous alleles with random coupling/repulsion phase relationship in the genotypes of F1 populations of artificial breeding programs. The hybrids are bred for improvement in the simulated character of interest (search objective) using the selection and propagation techniques of agricultural plant breeding. After improved varieties have been developed from completely heterozygous first-cross populations, crosses among the improved varieties can be used to continue the artificial breeding process of parameter optimization. 1.4 BACKGROUND AND OBJECTIVES The artificial breeding method of direct search optimization was first envisioned as a means of providing adaptive capability in computer-controlled systems (Hollstien, 1971). Prior to this study, emphasis had been placed on the use of cross-fertilizing species and random mating because the ability to store partial descriptions of parameters in recessive form appeared to be genetically best fulfilled by outbreeding. In late 1971 and early 1972 I began to reconsider methods of plant breeding, having earlier rejected the use of self-fertilizing organisms because latent information can not be stored in homozygotes. Many plants are self-fertilizing and these species rapidly approach homozygosity under almost any breeding plan. I now believe that plant reproductive systems offer a powerful repertoire of adaptive mechanisms, and, in this study, apply the breeding methods described by Allard (1960) to completely self-fertilizing, partially cross-fertilizing, and completely cross-fertilizing populations of artificial species. Partial support of this study from November 1972 to August 1973 was provided by National Science Foundation Grant No. GJ-36115. This portion of the study was devoted to static and deterministic parameter optimization —where the dynamic performance of the breeding population does not affect the stability of the overall system, and there are no probabilistic phenomena involved in determining the objective value of trial points in parameter space. 4

The specific objectives of the project were to (1) Determine the relative effectiveness of additive vs. epistatic gene action (2) Model and investigate the effects of intra-allelic dominance at the genotypic level (3) Develop artificial breeding systems (computer programs) for direct search optimization in up to 32-dimensional parameter spaces. 5

2 METHOD 2.1 ARTIFICIAL BREEDING FOR PARAMETER OPTIMIZATION Let X represent a parameter vector with components xl, x2,..., xN and V(X) the scalar measure of an objective to be maximized by finding the optimal parameter * values X. Only maximization problems are considered because minimization problems can easily be converted to equivalent maximization problems. Cause-and-effect relationships between the parameters and the objective are represented by a function V(X), but it will be assumed that these relationships are either not known, are not expressible in mathematical form, or are not amenable to the "mathematical programming" approach to parameter optimization. The ARTIFICIAL BREEDING procedure described here is a "direct search" method based on simulation of agricultural plant-breeding programs. Contrived functions V(X) will be used to test the method, but the mathematical form of these objective functions are not used in any other way. The method is summarized as follows: Artificial organisms are represented by diploid genotypes composed of chromosomelike arrays of binary bits. Each bit corresponds to a diallelic locus at which there may reside either a "0" or a "1" allele. Offspring are produced by the union of gametic sets of chromosomes obtained by meiotic division of parental genotypes. Chromosomes segregate independently during gametogenesis. Crossing-over between nonsister chromatids occurs randomly along the chromosomes. Random translocations and inversions of chromosome segments occur during interphase. Suppression of recombination is simulated by producing only functional gametes in which there are no duplications or deficiencies of loci due to 6

crossing-over within inverted or translocated segments. Background variation is provided by random mutation from one allelic conformation of genes to the other. Numerical values of parameters are synthesized by gene action algorithms that incorporate a) intra-allelic additivity, b) intra-allelic interaction with dominance at the gene level controlled by modifier loci, c) inter-allelic additivity of multiple factors, and d) epistatic effects of genes that control different steps in synthetic pathways. The parameter values correspond to intermediate effects of gene action, such as concentrations or activity levels of enzymes synthesized by the combined effects of several genes in living organisms. Quantitative characters of artificial organisms are simulated by evaluating the search problem objective at trial points in parameter space corresponding to the individual genotypes. Plant breeding methods for varietal or hybrid development are applied to populations of artificial organisms. Initial hybrids formed by wide crosses of genetically dissimilar varieties are simulated by random assignment of heterozygous alleles with random coupling/repulsion phase relationship. Improved varieties developed from random source populations are later crossed to continue long-term searches in the most promising regions of the parameter space. Achievement of maximum theoretical genetic gain in a simulated breeding program corresponds to the optimal solution of the underlying parameter search problem. 2.2 GENETIC COMPOSITION OF ARTIFICIAL ORGANISMS The artificial organisms are diploids with genotypes composed of two homologous sets of chromosomes as shown schematically in Fig. 1. A particular artificial species may have from 1 to 32 chromosomes, depending on the number of parameters involved in the search problem and the type of gene action used to synthesize the numerical values of parameters. Genes are located in complexes of 16 adjacent loci and occur in either of two allelic conformations: "0" or "1". The complement of genes in a species does not change during the course of a breeding program, 7

however, the relative positions of complexes in the chromosomes may be altered by inversions and/or translocations. Up to 4096 genes in 256 complexes segregate in present artificial breeding programs, but the maximum number is limited only by the digital computer memory available. In Fig. 2, which shows how a typical artificial chromosome might appear under three degrees of magnification, we see that the complexes are on one arm of the chromosomes, and that the positions of complexes within the chromosomes are numbered from left to right, starting with the position nearest a hypothetical centromere. Separation of gene complexes is represented by PCROS, the probability that gametes will be produced with an odd number of cross-overs between any two adjacent complexes, or between the centromere and the first position. Numerals above the left end of each complex identify the function of the complex in the artificial gene action algorithm. Loci within complexes are numbered from left to right, and their separation is represented by PCROL, the probability that an odd number of cross-overs will occur between any two adjacent loci within a complex. The relative positions of loci within gene complexes are fixed, so the function of every locus in the genome is uniquely identified by 1) a number indicating its gene complex, and 2) the position of the locus within the complex. At the bottom of the figure, under the highest magnification, the "0" and "1" alleles at individual loci may be seen. The basic elements of artificial genotypes are genes, and the binary alleles of each gene simulate two conformations of chromosome segments that in living organisms control the synthesis of either two functionally distinguishable products (enzymes) or one functional and one nonfunctional product. In living organisms, distinguishable effects of alleles are sometimes due to a difference in only one nucleotide base pair, even though a long sequence of nucleotides may be required to specify the amino acid sequence of the polypeptide chains. Based on experiments with the bacterial virus T4, Watson (1970) estimates that the average gene contains from 900 to 1500 nucleotide pairs! Gene action in artificial organisms then begins with the interaction of intermediate products of individual gene action rather than the primary genetic code that translates DNA base-pair sequences into amino acid sequences of polypeptide chains. 8

2.3 REPRODUCTION During the reproduction of artificial organisms, the genotypes of two parents and their offspring are stored in two, 3-dimensional arrays CP(I,J,K) and 9(I,J,K). Subscript I identifies a gene complex by its function in the gene action algorithm, J identifies the parental genome, and K identifies one of the two parents or the offspring. The organisms are monoecious, so the order of parent genotypes may be interchanged. They are also capable of self-fertilization, so the parent genotypes may be identical. Numbers indicating the chromosome and position of complexes I are packed into integer locations of array CP. The binary alleles in the complexes are contained in the corresponding elements of array S. Inversion and translocation of chromosome segments during interphase are programmed by calling subroutines INVER(CP,NSEG,PINV) and TRANS(CP,NSEG,PTRA), where argument NSEG is the number of gene complexes in the genome, PINV is the probability of chromosome breakage between any two adjacent loci and subsequent fusion with a chromosome segment in an inverted position, and PTRA is the probability of chromosome breakage between any two adjacent loci and subsequent fusion with a translocated segment from a different chromosome. Independent segregation of chromosomes, crossing-over of nonsister chromatids, and the union of gametic sets of chromosomes to form zygote genotypes is programmed by calling subroutine FZYGO(CP,S,NSEG,PCROS,PCROL). Crossing-over occurs with uniform probabilities PCROS and PCROL as defined previously. Crossing-over between complexes is inhibited whenever duplications or deficiencies of loci would occur in the resultant gametic sets of chromosomes. This eliminates the need for time-consuming test for nonfunctional gametes and the repeated matings that would otherwise be required to obtain a chance union of functional gametes. FZYGO returns with the offspring genotype in array locations CP(I,J,3) and S(I,J,3). Independent mutation of zygote alleles with probability PMUT of transformation from "0" to "1" or "1" to "O" is programmed by calling subroutine MUTAT(S,NSEG, PMUT). One record of a direct-access file is used to store the genotype of each artificial organism. Parent genotypes are read from the file and offspring genotypes 9

are written into the file as illustrated in the tollowing sequence of instructions. Artificial organisms with genotypes in records K1 and K2 of file Fl are mated and the offspring genotype is stored in record K3 of the same file. READ(Fl'Kl)((CP(I,J,1),S(I,J,1),I=,NSEG),J=l,2) READ(F1'K2)((CP(I,J,2),S(I,J,2),I=1,NSEG),J=1,2) CALL INVER(CP,NSEG,PINV) CALL TRANS(CP,NSEG,PTRA) CALL FZYGO(CP,S,NSEG,PCROS,PCROL) CALL MUTAT(S,NSEG,PMUT) WRITE(Fl'K3)((CP(I,J,3),S(I,J,3),I=l,NSEG),J=1,2) 2.4 PARAMETER SYNTHESIS Agricultural breeders try to anticipate the effects of various breeding methods on the genetic composition of populations when the phenotypic characters of interest exhibit a) intra-allelic additivity, b) dominance interaction, c) cumulative effects of multiple factors, and/or d) epistatic interaction. These phenomena must also occur at an intermediate level of biochemical products (enzymes) that interact in the final phases of gene action to produce observable effects. In the ARTIFICIAL BREEDING method, the search-problem parameters play the role of the postulated intermediate products of gene action. Numerical values of the parameters are synthesized by artificial gene action algorithms that exhibit each of the properties mentioned above; i.e., additivity, dominance, cumulative effect, and epistasis. The following gene action algorithms have been investigated in artificial breeding programs. 2.4.1 Gene Action 1 Individual parameters are controlled by the cumulative action of four complexes containing a total of 64 genes. The number of "1" alleles in each complex is multiplied by a weighting factor and the results are summed to form the numerical value of the parameter. The parameter range under this gene action algorithm is [0,65535]. If all loci are homozygous 0/0, the minimum value is synthesized. And if all loci are homozygous 1/1, the maximum value is synthesized; this is obtained by summing the maximum contributions of the four complexes given in the right-hand column below. 10

weighting complex factor 1 15/32 15 2 15/2 240 3 120 3840 4 1920 61440 maximum value 65535 The algorithm is additive at the intermediate (parameter) level because the effect of heterozygous genotype 0/1 is midway between those of the two homozygous genotypes 0/0 and 1/1. 2.4.2 Gene Action 2 Individual parameters are controlled by the cumulative action of 16 genes in a single complex. Each gene has a different level of effect equal to an integral 15 14 0 power of 2: 2 = 32768, 2 = 16384,.., 2 = 1. The effects of all loci are summed to form the numerical value of the parameter. The parameter range is [0,65535] since genotypes 0/0 at all loci are equivalent to the binary number 0000000000000000 = 010 and genotypes 1/1 at all loci are equivalent to 11111111111111112 = 6553510. This algorithm is also additive at the intermediate (parameter) level because homozygous genotypes 1/1 contribute the full effect of the binary-weighted loci, heterozygous genotypes 0/1 contribute half that amount, and homozygous genotypes 0/0 contribute nothing to the parameter value. The algorithm can be viewed as though the parameter value is produced by a sequence of reactions that transform a hypothetical substrate into one of 65535 possible intermediate products or activity levels. In Fig. 3, the substrate is shown on the left and alternate pathways at each reaction step appear as branching points. Each gene in the complex controls one step in the reaction sequence: gene 1 controls the first step, gene 2 the second step, etc. Homozygous genotypes 0/0 route the pathway along the lower branches, and homozygous genotypes 1/1 route the pathway along the upper branches at each step in the simulated reaction 11

sequence. When heterozygous genotypes occur, both of the possible reactions are activated, creating alternate pathways through which two or more numerical products are synthesized. Two are produced if any one of the loci are heterozygous, four if any two loci are heterozygous, etc. The composite value of the parameter is the average of values produced along the alternate pathways. This simulates additive products of intermediate gene action. A disadvantage of the binary number system as a basis for simulated gene action is that the alleles at many loci must sometimes change simultaneously to produce small changes in the numerical values of parameters. We can see from Fig. 3, for example, that the alleles at every locus must change to transform the genotype for the numerical value 32767 to that for 32768. All but one of the loci must change to transform 16383 to 16384 or 49151 to 49152. To the breeder these genotypes represent barriers in genetic parameter space that are very difficult to transcend by random recombination of genes. If biochemical pathways have a similar structure, this mechanism could explain the existence of suboptimal limits to selection for quantitative characters in agricultural breeding. 2.4.3 Gene Action 3 Individual parameters are controlled by a single complex of 16 genes that determi the numerical parameter values according to the synthetic pathway model in Fig. 4 Each gene controls one of a sequence of hypothetical reactions that transform a substrate into one of 65535 possible intermediate products. In the group of reaction steps controlled by a particular gene, the directions are reversed for every other branch point as compared with the model in Fig. 3. These directions are based on a permutation of the binary number system (the "Gray" code) in which contiguous numerical values are encoded by changing only one bit in the binary representation. In Fig. 3, changing the genotype at a locus controlling one of the first few reactions will always have a large effect, whereas, in Fig. 4 the effect may be large or small depending on the genotypes that control subsequent reactions. In this algorithm, therefore, the genes in each complex are epistatic at the intermediate (parameter) level. 12

The average of values produced along all pathways described by heterozygous genotypes will always be the median of the possible values associated with the branch point corresponding to the first heterozygous locus. To avoid this cancellation of the effects of several heterozygous loci, an additional interallelic interaction is introduced to make all heterozygous loci act simultaneously as either 0/0 or 1/1 genotypes. The products of two alternate pathways are then averaged to obtain the final parameter value corresponding to each gene complex. If one locus is heterozygous, this will produce the median value associated with the corresponding branch point. If two or more loci are heterozygous, various end product interactions will be produced depending on the genotypes at the homozygous loci. 2.4.4 Gene Action 4 In Gene Action 1, genotypes containing all "O" or all "1" alleles are required to develop extreme values of parameters. Many genotypes produce intermediate values in the parameter range, but there is no genetic redundancy at the extreme values. To provide genetic redundancy over the complete range of parameter values, this algorithm uses a subroutine PGA4(S1,S2,M) that returns a primary value M as in Gene Action 1 and a subroutine SGA4(NSEG,S,NPAR,X) that transforms M into a secondary value X as shown in Fig. 5. This increases the number of genotypes that represent parameter values near the extremes of the parameter range. Resolution is sacrificed to obtain this redundancy. Now only even values of parameters in the range [0,65535] are synthesized. The transformation from M into X is a discrete mapping of integers into integers and is only represented approximately in Fig. 5 by what appears to be a continuous function. 2.4.5 Gene Action 5 The transformation of Fig. 5 is used in conjunction with the primary algorithm of Gene Action 2. The effect, as shown by the synthetic pathway model in Fig. 6, 15

is better distribution of genetic redundancy, for there are now alternate pathways to all of the intermediate products represented by numerical parameter values. 2.4.6 Gene Action 6 The transformation of Fig. 5 is used in conjunction with the primary algorithm of Gene Action 3. This is the approach used to obtain Gene Action 4 from 1 and Gene Action 5 from 2. After several experiments had been run, it was discovered that there is in fact no increase in genetic redundancy provided by this schene. This is a result of the reflected nature of the Gray code (Fig. 7). The folding effect of the secondary transformation very nearly eliminates the influence of gene 2 on the numerical product, because the fold lines of the secondary transformation pass through the pathway branch points associated with gene 2. Gene 2 does have a small residual effect, however, due to the integer arithmatic involved in the folding operation of the secondary transformation. We should expect only slight differences in the average performance of artificial populations that use Gene Actions 3 and 6, even though there may be considerable differences in particular breeding experiments in which the two algorithms are used. 2.4.7 Gene Action 7 Intra-allelic interaction is simulated by associating a dominance modifier locus with each of the functional loci in the genome. Even-numbered complexes contain functional genes whose dominance modifiers are found in corresponding positions within the next, odd-numbered complex. Parameter values are synthesized by the cumulative effect of four complexes containing polygenes weighted as in Gene Action 1. If the functional loci are all homozygous, the modifier loci have no effect and the parameter values will be the same as those determined by Gene Action 1. When functional loci are heterozygous and the associated dominance modifier loci are homozygous, dominance of the alleles present at the modifier loci is imposed at the functional loci. When functional loci and the corresponding modifier loci are both heterozygous, dominance at the functional loci is determined randomly. This simulated dominance at the gene level is programmed by modification of the primary gene action algorithm of Gene Action 1. Similar modifications of 14

Gene Actions 2 through 6 are used to obtain additional algorithms as follows: 2.4.8 Gene Action 8 Dominance modifier loci are added to the primary algorithm of Gene Action 2. There is now a single pathway in Fig. 3 along which the parameter values are synthesized; the direction at each reaction branch point is determined by the combined effects of a functional gene and its associated dominance modifier. 2.4.9 Gene Action 9 Dominance modifier loci are added to the primary algorithm of Gene Action 3. 2.4.10 Gene Action 10 Dominance modifier loci are added to the primary algorithm of Gene Action 4. 2.4.11 Gene Action 11 Dominance modifier loci are added to the primary algorithm of Gene Action 5. 2.4.12 Gene Action 12 Dominance modifier loci are added to the primary algorithm of Gene Action 6. 2.4.13 Gene Action 2A A modification of the binary encoding scheme of Gene Action 2 is used in this algorithm. Each parameter is controlled by a single complex of 16 genes. The left-most gene acts as a regulator that controls the function of all the other genes in the complex. If the regulator is homozygous 0/0, the arrays of alleles in the two homologous chromosome segments are read separately as binary numbers in the range [0,32767] and their values are summed to form the numerical value of the parameter controlled by the complex. If either of the regulatory alleles are "1", the alleles on the same chromosome are complemented before the value is read and used in the parameter computation. For example, the genotypes 15

1111111111111000 1111111111111000 0000000000000111 an 1111111111111000 are "equivalent" to the homozygous genotype 0000000000000111 0000000000000111 which represents the numerical parameter value 14, obtained by summing the two gametic values of 7. A single crossover between the 12th and 13th loci of the heterozygous genotype above will produce two gametic arrays having numerical value 7 as illustrated below 111111111111 1000 - 0000000000001000 000000000000 0111 --- 11111111110111 A synthetic pathway interpretation of the algorithm is illustrated in Fig. 8. As in the previous diagrams, the pathways shown are those determined by a completely homozygous gene complex. In this algorithm, a complex heterozygous at any loci will produce alternate products that are summed (not averaged) to form the final parameter value. This corresponds to a cumulative effect of intermediate products. This algorithm was developed with two objectives in mind. The first is to reduce the chance of stalling at suboptimal selection limits. To do this, it provides a mechanism by which crossing-over, a "normal" event that occurs frequently in short-term breeding programs, is capable of producing small variations in parameter values throughout the parameter range. This should dimish the effects of the barriers in genetic parameter space that are a result of the cyclic properties of the binary number system. The second objective is to slow down the approach to homozygosity. There are polymorphic genotypes that encode the same parameter values throughout the parameter range, so the selection intensity for a particular allele at any locus should be reduced. Maintaining genetic variation as long as possible helps avoid premature fixation of undesireable alleles. The algorithm might also be viewed as a model of multi-allelic gene action with 16

the arrays of O's and l's in the homologous chromosome segments representing different functional conformations of a single gene. Parameter values would then correspond to distinct enzymes with structural compositions controlled by specific genes. 2.4.14 Gene Action 5A The primary gene action algorithm is the same as that used in Gene Action 2A. A secondary gene action subroutine transforms the primary value M into the parameter value X as in Gene Action 4, but in this case the transformation is discontinuous as shown in Fig. 9. The intent was to increase the genetic redundancy of the algorithm. Fig. 10 shows this transformation also nullifies the effect of gene 2. 2.4.15 Gene Action 8A Dominance modifier loci are added to the primary algorithm of Gene Action 2A. 2.4.16 Gene Action 11A Dominance modifier loci are added to the primary algorithm of Gene Action 5A. 2.5 OBJECTIVE CHARACTERS Objective characters may be any process that transforms trial sets of parameter values into corresponding objective values. The objective characters may be evaluated either within or outside the computer used to simulate the artificial population and breeding program. In the experiments described in this report, objective characters were evaluated internally by subroutines that evaluate mathematical functions of the parameters in simulated direct-search problems. Two-dimensional contour plots of six objective functions used in the experiments are shown in Fig. 11. These objective characters are identified by names that refer to their main topological feature. Functions of more than two parameters are obtained by summing evaluations of 17

2-parameter functions. For example, if a 2-parameter objective character is defined by V(X1,X2), the 8-parameter character of the same type is V(X1,X2,X3, X4,X5,X6,X7,X8) = V(X1,X2) + V(X3,X4) + V(X5,X6) + V(X7,X8). 2.5.1 Plane A hyperplane is inclined in parameter space in such a way that the maximum phenotypic value of 100 units is achieved at the lower bound (0) of the oddnumbered parameters and the upper bound (65535) of the even-numbered parameters. 2.5.2 Ridge A curved, knife-edged ridge passes through the origin and upper-right-hand corner of each 2-parameter plane. The phenotypic value increases gradually along the ridge to a maximum value of 100 units at the upper bound (65535) of all parameters. The objective value decreases rapidly in directions away from the ridge line. 2.5.3 Peak NE Three peaks —the highest of which is located in the North East quadrant —rise out of each 2-parameter plane. The peaks have the form of normal probability density functions and are therefore characterized by the means (locations of peaks), standard deviations (sharpness of the peaks), and the correlation coefficients (interaction of the two parameters) of the three probability density functions. The functions are multiplied by weighting factors and summed to form the phenotypic value of the objective character. When the peaks are sharp (small standard deviations) and widely separated (differences in mean values large compared to the standard deviations), the objective value at each peak is determined primarily by the three weighting factors. The maximum value of this objective function is achieved when all parameters have the value 49151, corresponding to the location of the North East peak in each 2-parameter plane. The objective value is 60 at the West peak (coordinates 0,32767 in the 2-parameter plane) and 40 at the South peak (coordinates 26214,6553), The parameters interact (correlation coefficient 0.95) in the neighborhood of the 18

NE peak but do not interact (correlation coefficients 0.0) in the vicinity of the other two peaks. The standard deviations that characterize the sharpness of the peaks are all equal to 10 percent of the parameter range. The peaks are, therefore, quite sharp and isolated. As may be seen in Fig. 11, the phenotypic objective value is less than 10 units over a large part of the 2-parameter plane. 2.5.4 Peak W This objective character is similar to Peak NE with the weighting factors of the North Ease and West peaks interchanged to make the West peak the highestvalued of the three peaks in each 2-parameter plane. 2.5.5 Peak S This objective character is also similar to Peak NE except that the weighting factors of all three functions are interchanged to make the South peak the highest valued, West peak the second, and North East peak the third highest of the three. 2.5.6 Hypersphere A hyperspherical surface is centered in the range of parameter values so that the objective character has a maximum value of 100 units when all parameters are equal to 32767. The character has a phenotypic value of 0 if all parameters are either 0 or 65535, i.e., they are all at the extemes of the parameter range. 2.6 BREEDING METHODS There are basically two different approaches to agricultural plant breeding. One is to develop new, improved, true-breeding varieties. The other is to improve the hybrid offspring of two or more established varieties. To develop improved varieties, two or more source varieties are first crossed 19

to obtain a hybrid F1 generation. The breeder then selects and propagates (by self- or cross-pollination) individuals in successive generations of the hybrid population until a new variety is established. If 1) the original varieties are complementary, 2) the variation needed for improvement in the characteristics of interest is present in the F1 generation, and 3) the necessary recombinations of alleles occur and are not lost by genetic drift or too intense selection, then the breeding program may succeed in producing an improved variety having greater phenotypic value than the source varieties. The second approach is used when the hybrids produced by the first cross of two varieties are superior to either of the parents, but lose their superiority when propagated in an effort to establish an improved, true-breeding variety. Selection and mating of individuals within the two parental populations according to the phenotypic value of their cross-bred progeny, rather than on the basis of their own characteristics, has become a standard plant-breeding procedure. Methods of selection and propagation differ for self- and cross-pollinated plant species, but a surprisingly few basic methods are applied successfully to many different species and characteristics. While these agricultural breeding methods do not guarantee success, they often do produce significant improvement in the characters of interest in only a few breeding generations. What makes these relatively simple breeding algorithms for selection and mating as reliable and robust as they are? One reason is that there is an intrinsically adaptive capability of sexually reproductive populations under artificial or natural selection. Another reason is that the mechanisms of reproduction and gene action are fundamentally the same in all species of plants and animals (Stahl, 1964). The basic idea of ARTIFICIAL BREEDING is that, if the mechanisms of reproduction and gene action are accurately simulated, the genetic principles of agricultural breeding should also be effective in breeding for improvement in direct-search objective characters of artificial organisms. The practical value of the method can only be established by experimental investigations using realistic objective functions and specific breeding methods. 20

The artificial breeding methods used in this study are based on the agricultural methods of plant breeding described by Allard (1960). Main programs, subroutines, input data and PDP-9 CHAIN/EXECUTE systems for all of the artificial breeding systems are included in the Appendix. 2.6.1 Pedigree Method 1 In pedigree breeding, the procedure most widely used to improve characteristics of self-pollinated species, two or more well established varieties are crossed to form a large, hybrid F1 generation. Families are started in the F2 generation by growing several plants from self-pollinated seeds of F individuals selected for general appearance, but without particular regard to the objective of the breeding program. Selection for the objective character is started within families in the F2 generation. As family differences appear in later generations, selection among families is introduced until finally the entire population is produced by the single, most valuable individual selected from the previous generation. Pedigree Method 1 (PM1) simulates an ideal F1 population formed by a cross of parental varieties that differ at all loci contributing to the objective character. F1 alleles are randomly assigned to one genome and the complement alleles are assigned to the other. Although the virtual F1 population is large, completely heterozygous, and in gametic phase equilibrium, only a sample of the F1 generation is used to produce the F2 generation. Therefore, the original genetic variation needed to optimize the objective character in subsequent generations of pedigree breeding may not be present in the F2 generation. Trial points in the direct-search parameter space are first produced in the F2 generation. The S2 highest-valued individuals selected from the F generation are selfed N3/S2 times to produce N3 individuals in the F3 generation. Thereafter, commensurate population sizes N. and numbers of families Si are specified for successive generations in which families are propagated by selfing the single, highest-valued member of the family in the previous generation. 21

2.6.2 Pedigree Method 2 The pedigree method of PM1 is used to obtain a sequence of improved varieties starting with an initial cross of random, dissimilar varieties. In the second cross, the first improved variety replaces one of the random parental varieties. The third variety is bred from a cross of the first two improved varieties. Subsequent varieties are derived from crosses between the two, highest-valued varieties previously developed. 2.6.3 Bulk Population Breeding 1 Characters positively correlated witn natural ritness are sometimes improved Dy propagating the entire (bulk) population. The breeder assumes (or knows from previous experience with the species) that the fittest plants will also be the most desireable with respect to the character of interest. In Bulk Population Breeding 1 (BPB1), fitness is made proportional to the direct-search objective value of each individual. The breeder may also impose artificial selection by specifying some number NSEL of the highest-valued individuals in each generation among which the competition for producing offspring occurs. The artificial species may be completely self-fertilizing, partially cross-fertilizing, or completely cross-fertilizing as specified by a probability POUCR of outcrossing in producing each offspring organism. 2.6.4 Mass Selection 1 A procedure used to improve characteristics of outcrossing species is simply to select individuals from each generation entirely on the basis of their own merit and then mate the selected individuals randomly to produce the next generation. Genetic variation in the original population can be produced by crossing two or more varieties, or, as is often the case, there may be enough variation in populations that have not previously been under selection for the character of interest to the breeder. In Mass Selection 1 (MS1), a completely heterozygous first generation is formed with random alleles in one genome and the complement alleles in the other. 22

The population size and number of individuals selected in each generation remain fixed throughout the breeding program. The artificial organisms are considered monoecious and have equal probabilities of self-fertilization or cross-fertilization with any other selected individual. 2.6.5 Simple Recurrent Selection 1 Hybrid populations of outcrossing but self-compatible species are sometimes selfand cross-pollinated in alternate generations; two such consecutive generations are called a selection cycle. Simple recurrent selection is started by selecting the most desireable individuals in a hybrid population. These selected individuals are selfed to produce progeny that, on the average, are homozygous at half of the loci contributing to the character of interest to the breeder. The third generation (first generation of the second recurrent selection cycle) is formed by making all possible crosses of offspring from individuals selected in the first generation. This process of selection in alternate generations is continued until a new, true-breeding variety is obtained. In Simple Recurrent Selection 1 (SRS1), the population size is made an integer multiple of the N(N - 1)/2 possible crosses of offspring from N individuals selected in each cross-bred generation. Trial points are evaluated in only the cross-bred generations, so the method is no more costly in terms of trial point evaluations than the mass selection method. Time is required to simulate the intermediate generations, but, because the progeny of selfed individuals can be produced as they are needed and do not have to be stored in disk memory, the total time required for a recurrent selection cycle is less than twice that of a mass selection generation of equivalent population size. The additional memory required to simulate the intermediate generations is negligible. 2.6.6 Simple Recurrent Selection 2 The simple recurrent selection method of SRS1 is used to obtain a sequence of improved varieties starting with an initial cross of random, dissimilar varieties. The first improved variety replaces one of the random varieties, and the third 23

is bred from a cross of the first two improved varieties. Subsequent varieties are derived from crosses between the two, highest-valued varieties previously developed. 2.6.7 Reciprocal Recurrent Selection 1 Reciprocal Recurrent Selection 1 (RRS1) improves the hybrid offspring of two parental varieties. Two completely heterozygous source populations, A and B, are formed by randomly assigning alleles and their complements to homologous chromosomes as described earlier. Each individual in population A is crossed with a sample chosen randomly from B, and each individual in B is crossed with a sample chosen randomly from A. The recurrent parents in each population having progeny with highest individual value are selected and selfed to propagate populations A and B. The objective values of A and B individuals are never required, so trial points in direct-search parameter space are evaluated for only the hybrids in each selection cycle. The entire A and B populations must be stored in disk memory because any particular individual may be required in determining the combining ability of individuals in the opposite population. There is no need to store the hybrid individuals, however, once their objective value has been determined. In RRS1, populations A and B are the same size and equal numbers of trial crosses are used in determining individual combining abilities. The number of hybrid offspring in each reciprocal recurrent selection cycle is therefore 2Nn, where N is the size of populations A and B, and n is the number of trial crosses of each recurrent parent. Initially, populations A and B are completely heterozygous. After several selection cycles, the two populations approach homozygosity. Individuals in the final A and B populations may themselves have low phenotypic value, but, if the breeding program is successful, they will have high combining ability with the opposite population. The recurrent selection procedure was originally developed to test simultaneously for general and specific combining ability. General combining ability is measured by an individual's progeny when crossed with a heterozygous population; specific combining ability is measured by an individual's progeny when crossed with a particular homozygous population. 24

set i centromere chromosom i ~ //l 1:W i't II-IIIUIIII +IN1 t II fIhhI set 2 chromosome -i - OWHI- 1MW-m1-1W MUM -Yin...............IN 1...ulK 4 uu AIim III...41ui i..il".Iim.. 2 U — floll lllt, W- mIU - 1 Wii ( 1 i -tlIII.IIf-A __IlU VlIItIIIrI III1 111 [I11 lHN Jll M(f ll uS - Figure 1 Genotype of an artificial organism centromere 1 2 / 6 7 8 PCROS- - PCROS- PCROS6 i t,11'111 - 6'1pCRoL 61 i 2 3 4* 5 G 7 *$ 10 9 j i 1to 9 i 0 I Figure 2 Close-up views of an artificial chromosome 25

II On substraCte c \r ~~~E' 1 Figure 3 Synthetic pathway model of Gene Action 2 C c ^^<^ H~ ^s 4q151 substrate / 34 0 Figure 4 Synthetic pathway model of Gene Action 3 26 P^^~~~~~~~~~~~~~6 or^ 26

uo) >1 in inO I 05 \ Figure 5 Secondary transformation of Gene Action 4, 5 and 6 I'0~~~~~~)~ \0 co.32768 00 substrcate I 6 X 276555 27 Figure 6 Syntheti c pathway model of ~.'..4-, S Sn ^^ ^^ ^^<^ i^ I. 27

? c) 1 o 32768 s.bstrcxa. e- ~ "3,*276 6' ) SobtrA d --- ---— G 5 X 0\ i Figure 7 Synthetic pathway model of Gene Action 6 u e) ~ @ / <327e 63276 sulbstrraee ___ (fold >32766 Figure 8 Synthetic pathway model of Gene Action 2A 28

u3 In'' It)'0 1o / 0 56583 32767 4q151 65555 prLmary value Figure 9 Secondary transformation of Gene Action 5A and 11A e if~~~~~~~~~)~Q) Q4 c C 0l 0 sutbstrae (fl --------- 0I 675555 Figure 10 Synthetic pathway model of Gene Action 5A 29 ^ 61534~E Suttstriatel._of. Gee4 Action L 29

Ioplm.m 0 0 0 0 oK' oP. *'.*.' *.-iS *':.* r R:: UL 2.'..:L.-U 4 O..: l..- Plane / Rid,":..::'|:'a:':.. 20.*,.* 40~.'..:.' / *:.'.'.' xK CU.*.' ** **.x ru / R.. *..,-:...:::I.':/.' 2..**.** / 0 1U.., -1.-. k S: |:': *''.. 10 -4 -'' s..':'.':.-:.''.';_'.'....: ~;^ " S-..;' 2CL.'.-..' -':.'.?-.'-'-': *.;:~ *:~ ** _^ o;.... * *'optimu.m (i...... ~..'....:..'....................".."..'.: - *.:-.*:-.:: *'.*.. *.. -. O ~-. ~..- ----— r —- o o o ~ ~W~ W 1t6383 3767 9 1 5 l 6d5535 16383 3 767 49 1 1 S3 XI X1 Fig, r.11 t i c t I R i P N P W P S ti. ti.C Figure 11 Objective characters Plane, Ridge Pa NE, Pekak W Peak S and ~:'...::'... O..." -'...-0"'' ~ ~ ~ ~ ~ ~'.. ]~ - — ~3,'.,:-..,. Zo~~'...:.: ~o.'".:'C.~o ~ ~ ~~ ~ ~ r::;''::':' r ~ ~~~ ~rr I ~~~~~ ~ ~ ~ ~ ~ ~ ~ ~~':.:.:: ~~ ~~ in~~ ~~~.40.~~~::.. V.:,:,o. J.'':" ~" P'':'...-k - ~ ~ ~ ~ ~!i:-:.:' "::": f' "'"'" ~ ~ r ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~ I ~ ~'"''' "' "' ~~ O,''' ~ ~ ~ O ~ 6 1G8 3~~ &1l b'SS O 13~ 2/7 41! E-S Xl~~~~~ r ~ ~ ~ ~~~~X Fiur1 Ojciv chrctr Pln, Ride ekNE ekW Pa n Hyeshr plote in 2- i mnioa p aaetrspc ~~~ ~ ~ ~~~~5o

3 RESULTS Experimental studies of ARTIFICIAL BREEDING for parameter optimization were run on a Digital Equipment Corporation PDP-9 computer at the University of Michigan Simulation Center. The programs are documented in the Appendix. 3.1 COMPARISON OF GENE ACTION/BREEDING METHOD COMBINATIONS All combinations of 16 gene action algorithms and five breeding methods were first compared for general performance using an 8-parameter version of objective character Plane. Genotypes with eight complexes per chromosome were used in each case. Polygenic complexes were arranged in descending order of effect and in normal order of parameter indeces. When using Gene Action 1, for example, each chromosome contained two sets of four complexes and controlled the synthesis of one odd- and one even-numbered parameter. When using Gene Action 2, the genome consisted of one chromosome containing the eight complexes for all of the parameters. This structural arrangement of genes on the chromosomes was fixed by setting the probabilities of inversion and translocation to zero. Free recombination was simulated by setting crossover probabilities PCROS and PCROL to 0.5, so the genes were effectively unlinked and the structural arrangement is immaterial. The probability of mutation was also set to zero. Initial populations were completely heterozygous, simulating an ideal cross of source varieties that differ genetically at all loci contributing to the character of interest to the breeder. Alleles in one genome were chosen randomly and the complementary alleles were assigned to the homologous genome. The solution of the underlying direct-search problem is at the lower bound (O) of the odd parameters Xl, X3, X5 and X7, and at the upper bound (65535) of the 51

even parameters X2, X4, X6 and X8. Notice that the parameters do not interact in the objective character Plane; the optimal value of each parameter can be determined with the others fixed at any value. Even though the parameters do not interact, the search problem is somewhat more difficult than it might appear at first glance. Consider a very crude exhaustive search. Suppose we divide each parameter range into ten equal intervals and make trial evaluations at the centers of the 100 million subdivisions of the parameter space. At a rate of one trial evaluation per second, this would require more than 30,000 hours. Let us obtain a rough estimate of the number of trials required for a sequential search of the parameter space. This will of course depend on the starting point and increment step size used. Starting at the midpoint of each parameter range and incrementing by say five percent (10 steps to either extreme parameter value) will require 80 trial points. This is the average number for randomly chosen starting points. If five replications of the sequential search are made to be reasonably sure a global optimum is found, 400 trial points are required. The populations for each breeding method were sized to obtain approximately the same number of trial points in each experiment —about 300 —which is somewhat less than the estimated number of trials required to make a sequential search of the 8-dimensional space. The objective of this preliminary comparison of gene action/breeding method combinations was to determine whether marked differences in performance could be used to narrow the study to those most promising combinations. It seemed essential to base this decision on ARTIFICIAL BREEDING experiments that use an encouraging number of trials. Pedigree Method 1. An F2 population was formed by selfing completely heterozygous individuals drawn from a large, virtual F1 population. In the following generations the highest-valued individuals in each family were compared, and the highest-valued individuals among these family representatives were selected and selfed to propagate their families into the next generation. The population size was held constant after the F3 generation by increasing the family size as the number of selected families was reduced according to the following schedule: 52

Population Families Family Generation size selected size 2 64 32 3 32 16 1 4 32 16 2 5 32 8 2 6 32 4 4 7 32 2 8 8 32 1 16 9 32 1 32 10 32 1 32 Bulk Population Breeding 1. Populations of 32 self-fertilized individuals were propagated in bulk for ten generations with simulated artificial selection of the highest-valued half of each generation. The probability of outcrossing, POUCR, was set to zero. Mass Selection 1. Populations of 32 cross-fertilized individuals were bred for ten generations with mass selection of the highest-valued half of each generation. The selected individuals were mated randomly to produce each individual in the next generation. Simple Recurrent Selection 1. Populations were bred for ten simple recurrent selection cycles. The eight, highest-valued individuals in each cross-bred generation were selected and selfed to produce the intermediate generations. A diallel cross of eight individuals in each intermediate generation was used to produce (8)(7)/2 = 28 individuals in each cross-bred generation. The diallel cross of eight individuals numbered 1 to 8 is illustrated by the following diagram: 1 2 3 4 5 6 7 8 1 x x x x x x 2 x x x x x x 3 x x x x x 4 X x x x 5 x x x 6 x x 7 x 8 33

Reciprocal Recurrent Selection 1. Two populations of eighlt individuals were bred for ten reciprocal recurrent selection cycles. Four individuals were selected from each population on the basis of the highest-valued offspring produced by crossing each individual with a random sample of two individuals from the opposite population. There were, therefore, (4)(2)(2) = 32 individuals in the hybrid generation of each selection cycle. The selected individuals were selfed to propagate the two parental lines. A single breeding experiment was run for each gene action/breeding method combination. Graphical results of the experiments are shown in Fig. 12a-h. In each part of the figure the phenotypic values of all individuals are shown in the order that they are produced in the simulated breeding program. The sequential order of individuals within a particular generation is not significant from the genetic or breeding viewpoint, but the progressive improvement of the objective character is of principal interest in evaluating the direct-search algorithm performance. The best overall performance was obtained using Gene Actions 4 and 6 in combination with simple recurrent selection. These combinations achieved approximately 90 percent of the maximum theoretical genetic gain within 280 trials. In each experiment, however, there was evidence that major genes reached fixation prematurely. Without mutation, there was no way to break through the resulting selection limits. Gene action/breeding method combinations that reached at least 80 percent of the maximum theoretical genetic gain were considered promising for use in ARTIFICIAL BREEDING. A list of these prospects is given below in descending order of phenotypic value achieved by the end of a single breeding experiment: Gene Action 4/simple recurrent selection Gene Action 6/simple recurrent selection Gene Action 3/simple recurrent selection Gene Action 9/simple recurrent selection Gene Action 6/mass selection Gene Action 6/pedigree method Gene Action 8/simple recurrent selection Gene Action 8/mass selection 54

Gene Action 2A/pedigree method Gene Action 1A/simple recurrent selection Gene Action 4/mass selection It was of course impossible to draw firm conclusions on the basis of single experiments with each gene action/breeding method combination. Therefore, several of the most promising gene action models and breeding methods were investigated in further experiments. 3.2 PEDIGREE METHOD 1 EXPERIMENTS Definite progress was observed in pedigree breeding for the 8-parameter objective character Plane during the preliminary comparison of gene action/ breeding method combinations described in Section 3.1. However, in every case fixation of undesireable alleles prevented genetic advance beyond suboptimal selection limits of approximately 75 to 85 phenotypic units. The maximum possible objective value for Plane is 100 phenotypic units. 3.2.1 Breeding for 2-Parameter Plane To verify that this problem is related to the number of segregating loci, the Gene Action 3/Pedigree Method 1 combination was used in ARTIFICIAL BREEDING for a 2-parameter version of Plane. The results of this experiment are shown in Figs. 13a-c. The population reached a limit of 96.77 in the 8th generation with final parameter values of Xl = 2078 and X2 = 63379. This is greater than the genetic advance observed in any of the experiments using the 8-parameter version; it shows that the chances of finding optimal values are greatest when there are fewer loci (parameters) affecting the objective character. The results of ARTIFICIAL BREEDING experiments are averaged over replications of the experiment. The AVERAGE VALUES are printed at the bottom of the output as shown in Fig. 13c. When the experiment is not replicated, the AVERAGE VALUES are the actual values of the single experiment, as in the case of Fig. 13c. The column headings for the AVERAGE VALUES are defined as follows: EFF Efficiency of the breeding program; the ratio of the total phenotypic value of all individuals to the maximum possible total value 35

AVG Average phenotypic value of the population in the current generat i on STD Standard deviation of phenotypic values for the population in the current generation AVGS Average phenotypic value of selected individuals in the current generation STDS Standard deviation of phenotypic values of selected individuals in the current generation NIZ Number of inviable zygotes in the current generation NTR Number of trial evaluations of the objective function in the current generation PM1A in the input data of Fig. 13c indicates that Gene Actions 2A, 5A, 8A and 11A had been compiled on disk at the time the experiment was run. 3.2.2 No Selection Among Families After the F3 Generation If fixation of undesireable alleles was caused by too intense a selection among families in the early generations of the last experiment, reducing that pressure might improve the breeding performance. So the experiment was repeated with 32 individuals selected from the Fo generation as before, but 16 families were kept in the remaining generations. There were two members in each family. These results are shown in Fig. 14a,b. The average value of the late generations decreased, but the maximum individual value remained about the same as in the previous experiment —96.201 compared with the previous value of 96.770. The population did not reach genetic fixation, but the average value changed very slowly after the 7th generation. Other experiments, in which no selection among families was practiced after the F3 generation, were also run using Gene Action 3 and Gene Action 4 in conjunction with the 8-parameter Plane. The results were similar to those of Fig. 14. Eliminating selection among families, therefore, did not have an appreciable effect on the pedigree method performance. 56

3.3 BULK POPULATION BREEDING 1 EXPERIMENTS In the preliminary experiments of Section 3.1, bulk population breeding also produced definite genetic advance in the 8-parameter objective character Plane. Several populations reached phenotypic values of 75 to 80 units, but in all cases progress was limited by fixation of undesireable alleles. The following additional experiments were run using Gene Action 4/Bulk Population Breeding 1. 33.31 Effect of Selection Intensity Figure 15 shows the results of three experiments in which 4,8 and 16 individuals were artificially selected from populations of 32. Increasing the artificial selection intensity increased the initial rate of response with little effect on the final selection limit. 3.3.2 Effect of Population Size Bulk population breeding of these extremely small populations can not be compared with agricultural programs where hundreds or thousands of individual plants are bulked in each generation. However, large populations can not be used in ARTIFICIAL BREEDING for parameter optimization if it is important to keep the number of trials at a minimum. We must be concerned with the performance of the bulk population method when applied to very small populations even though the results will be subject to "small sample errors." Effects of population size were explored briefly in experiments using populations of 16 and 64 individuals. These results are shown in Fig. 16. In each case one-fourth of the population was artificially selected. The small population reached fixation in approximately five generations (after 160 trials). The larger population did not reach fixation during the 10-generation breeding program, but the total genetic advance was only slightly greater than the selection limit of the smaller population. There appeared to be no reason to use populations of more than 32 individuals in ARTIFICIAL BREEDING by the bulk population method. 37

3.3.3 Effect of Cross-fertilization Performance improved wllen the probability of outcrossing, POUCR, was increased from zero to 0.5 and 1.0. Results olbtained using Gene Action 4/ Bulk Population Breeding 1 and artificially selecting four individuals from a population of 16 are shown in Fig. 17. A greater initial rate of response and a higher final selection limit were observed when using the completely outcrossing species. The eight parameter values of each individual produced during that experiment are shown in Fig. 18. The selection limit is clearly due to fixation of genes that control parameters X3 and X8. Increasing the population size to 32 with artificial selection of eight individuals in each generation produced further improvement in the parameter optimization performance. These results are shown in Fig. 19a,b. Progress was steady over the ten generations, and genetic variation remained in the population throughout the breeding program. The selection limit was increased to above 90 phenotypic units. 3.3.4 Effect of Linkage In the last experiment all eight of the parameters approached the optimal values individually, but the performance would have been greatly improved if the values nearest the optimal values had occurred in the same individuals. This raises a question as to whether linkage would improve the parameter optimization performance of the ARTIFICIAL BREEDING program. The experiment was repeated with 0.05 probability of crossover between adjacent loci within complexes (PCROL) and 0.1 probability of crossover between adjacent complexes (PCROS). Results are shown in Fig. 20a,b. The rate of response is slightly lower, but steady. Genetic variation is maintained, but there is now evidence of fixation of many genes that control parameters X2 and X4. The other parameters also exhibited slower convergence. It appears that linkage impedes the performance of bulk population breeding of cross-fertilized species. 58

3.3.5 Replicated Breeding for 8-Parameter Plane Five replications of a bulk population breeding program for 8-parameter Plane were run using Gene Action 4, no linkage, completely cross-fertilizing organisms, populations of 32 individuals, artificial selection of eight individuals and 20 generations. In Fig. 21a are plotted the generation mean and standard deviation when averaged over the five replications. The printed results of the replicated experiment are shown in Fig. 21b. With the print control IPBP set to 1, only parameter values with corresponding objective values that exceed the values at previous trial points are printed. The AVERAGE, MAXIMUM, and MINIMUM VALUES of "generation" information are printed following the parameter values for the five experiments. The lowest mean phenotypic value for the 20th generation in the five replications was 93.259, so the bulk population breeding method appears to be reliable. The maximum individual phenotypic values that occurred in each of the five replications of the breeding program are listed below: Experiment Maximum value Trial 1 97.871 611 2 97.870 586 3 96.684 575 4 97.037 457 5 97.606 589 3.3.6 Breeding for 8-Parameter Ridge The same bulk population breeding program was applied to the 8-parameter objective character Ridge with the results shown in Fig. 22a,b. Genetic progress was slow but steady over the 20 generations. Parameters X1 and X2 became stalled along the ridge line in the 2-dimensional subspace, but the other parameters were driven close to the optimal values at the upper bound of the parameter range, 65535. 59

3.3.7 Replicated Breeding for 8-Parameter Ridge Five replications of the same experiment were run with the results shown in Fig. 23a,b. The population mean of the 20th generation, averaged over the five replications, was 80.795 phenotypic units. Robustness of the ARTIFICIAL BREEDING system should not be judged on the basis of averaged phenotypic values, since these values may vary widely depending on the features of the objective character. A distance measure of how close trial points come to the optimal point would be more appropriate. A numerical measure of this sort was not computed, however, Fig. 22 gives an indication of the parameter "miss distance" in one particular experiment. The 605th trial of the first replication came closest to the optimal parameters for Ridge during the replicated experiments. The parameter values for this individual are 55388, 48452, 64206, 62950, 63086, 61146, 63160, and 63564 for X1 to X8 respectively. The phenotypic value is 94.023 phenotypic units, quite close to the maximum theoretical gain considering the complexity and degree of interaction among the parameters in this objective character. 3.4 MASS SELECTION 1 EXPERIMENTS Bulk population breeding of cross-fertilized species with artificial selection is actually a form of mass selection with random matings biased in favor of mating the highest-valued individuals among those selected artificially. Mass selection with uniform random mating was also investigated in experiments described here. 3.4.1 Effect of Selection Intensity Half of the population was selected for random mating in the preliminary comparison of gene action/breeding method combinations described in Section 3.1. Increasing the selection intensity by selecting eight of the 32 individuals in each generation produced the results shown in Fig. 24a,b. The objective 40

character is 8-parameter Plane with parameter synthesis by Gene Action 4. Progress was steady during the first ten generations (320 trials). Considerable genetic variation was maintained throughout the breeding program even though there was no mutation of individual genes. All parameters approached the optimal values at about the same rate. The final selection limit was at approximately 90 to 95 phenotypic units. 3.4.2 Effect of Dominance in Polygene Action Repeating the experiment in breeding for 8-parameter Plane using Gene Action 10 instead of Gene Action 4 produced the results shown in Fig. 25a,b. Recall that Gene Action 10 has functional polygenes as in Gene Action 4, and also dominance modifier loci that determine intra-allelic interaction at the level of parameter synthesis. The most noticeable effect of the dominance is an increase in phenotypic variation during the early generations. The overall performance is about the same as in the previous experiment using Gene Action 4. Parameters X6 and X8 show loss of genetic variation in the later generations. 3.4.3 Effect of Epistatic Gene Action Using Gene Action 3 in the mass selection program for 8-parameter Plane produced rapid convergence of some parameters with nearly complete elimination of genetic variation in later generations. These results are shown in Fig. 26a,b. Parameters X1, X5, X6 and X7 are driven very close to the optimal values, but the others are stalled by premature fixation of genes having major effect in the parameter synthesis. 3.4.4 Effect of Dominance in Epistatic Gene Action The results in Fig. 27a,b were obtained by repeating the experiment using Gene Action 9, which incorporates dominance modifier loci in the primary algorithm of Gene Action 3. The most noticeable effect here too was a marked increase in parameter variation, especially during the early generations. 41

Sustained variation at the most silgniflicant locus controlling parameter X8 caused X8 excursions from one extreme of the parameter range to the other even during the later generations when the less significant loci had become fixed. 3.4.5 Breeding for 8-Parameter Ridge Experiments in ARTIFICIAL BREEDING for 8-parameter Ridge using Gene Actions 4, 10, 3 and 9 were also run. Slow progress was observed in all cases. Greater variation in parameters occurred when using Gene Actions 10 and 9, which employ intra-allelic dominance. 3.4.6 Effect of Gene Number Rapid convergence to within a small neighborhood of the optimum was observed in breeding by mass selection for 2-parameter Ridge using Gene Action 3. When Gene Action 9 was used, however, the population converged rapidly to a point along the ridge line below the optimum. 3.4.7 Effect of Population Size Only slight differences in averaged performance were observed in five replications of mass selection for 8-parameter Ridge using populations of 16, 32 and 64 individuals. The results are shown in Fig. 28a,d. The initial rate of average response is the same for all three cases, but the larger populations reached slightly higher average phenotypic values. The highest-valued individual in the replicated experiments was the 1004th trial in the second replication of the largest population. Its parameter values are 56623, 49183, 61423, 55421, 56850, 52249, 49951 and 38511 for Xl to X8 respectively, and its phenotypic value is 87.508. 3.5 SIMPLE RECURRENT SELECTION 1 EXPERIMENTS In the experiments of Section 3.1, populations bred by simple recurrent selection had not reached a definite selection limit by the tenth cycle. 42

The method was continued for 20 cycles in the experiments described here, with results that indicate species capable of self- and cross-fertilization are probably the most versatile organisms for use in ARTIFICIAL BREEDING. 3.5.1 Effects of Selection Intensity and Population Size Figure 29a,c shows the results of a single experiment in breeding by simple recurrent selection for 8-parameter Plane using Gene Action 4 with free recombination, no inversion or translocation and no mutation of alleles. Eight individuals were selected from 32 in each cross-bred generation, the selected individuals were selfed, and their offspring were crossed in all possible combinations to complete a selection cycle. The breeding program was run for 20 cycles. The mean phenotypic value increased from 50.00 in the first cycle to 93.169 in the last cycle. Genetic variation was maintained throughout the 20 cycles,'and individual parameter converged to the neighborhood of optimal values more rapidly than in previous experiments using other breeding methods. The initial rate of response increased when higher selection intensity and smaller populations were used, but fixation of alleles caused selection limits below the total genetic advance indicated in Fig. 29. 3.5.2 Effect of Epistatic Gene Action The use of Gene Action 9 instead of Gene Action 4 caused even greater variation of parameter values than that shown in Fig. 29b. Fixation of undesireable alleles also caused lower selection limits. 3.5.3 Effect of Gene Number Experiments were also run using Gene Action 4 and simple recurrent selection for 8- and 2-parameter Ridge. These results show less dependence on the number of interacting genes than had previously been observed using Gene Action 3 and mass selection. This can not be definitely attributed to 1) differences in the epistatic effects of the two gene action algorithms, 43

or to 2) differences in the effectiveness in breeding for epistatic characters by the two methods. 3.5.4 Effect of Linkage Additional experiments were run using Gene Action 9 and simple recurrent selection for 8-parameter Plane, first with free recombination and then with gene linkage defined by probabilities 0.1 of crossing-over between adjacent segments and 0.05 of crossing-over between loci within complexes. A large amount of parameter variation was observed in the experiment using free recombination, as had been the experience using other breeding methods with this gene action algorithm. Parameter values converged more rapidly when gene linkage was introduced, and there was evidence that the linkage inhibited the dismantling of desireable complexes. But the linkage also had the effect of accelerating the fixation of undesireable alleles, so the population with linked genes stalled at a selection limit below that of the population with unlinked genes. 3.6 PEDIGREE METHOD 2 EXPERIMENTS So far, initial populations have been either completely heterozygous or they have been formed by selfing completely heterozygous individuals. This can be viewed as simulating either of two situations in plant breeding: 1) the development of new varieties from wild populations in which there is a large amount of genetic variation, or 2) the development of improved varieties from a cross of parental lines that differ genetically at all loci contributing to the character of interest to the breeder. In either case, these ARTIFICIAL BREEDING experiments have simulated only the first step of what in agricultural plant development may require a protracted series of breeding programs. The results of extended ARTIFICIAL BREEDING for 8-parameter Plane using Gene Action 4 and the pedigree method are described here. The "extended" means that after two varieties have been developed from completely heterozygous source populations, further search of the genetic parameter space is based on simulating the development of improved varieties. There are, of course, many ways varieties could be crossed to obtain the hybrids. In this case, 44

the two previous varieties that produced the highest individual phenotypic value were used. Six varieties were developed in all, including the first two derived from completely heterozygous source populations. Ten generations of pedigree breeding were used to develop each new variety. The population size was decreased in the later generations of each varietal development program to avoid repeated trials as the populations reached homozygosity. A total of 102 individuals were produced during each varietal development program. Inversion, translocation and mutation were prevented by setting the probabilities of occurrence to zero. Free recombination was simulated by using 0.5 probability of crossover,between adjacent loci. The results in Fig. 30a,c illustrate the importance of the extended breeding program. The first two varieties reached phenotypic values of 72.929 and 76.489 respectively; the third variety, developed from a cross of the first two, reached 85.371. The succeeding varieties improved steadily as. shown in the following list: Highest Variety individual value 1 72.929 2 76.489 3 85.371 4 87.262 5 90.066 6 93.219 The highest phenotypic value of the sixth variety exceeds that of the fifth by 2.804 units. This improvement exceeds the standard deviation of the F population from which the sixth variety was derived, indicating that the fourth and fifth varieties have complementary genotypes even though they are descendents of the same parental lines. Moreover, the pedigree method is capable of fixing favorable combinations of the complementary genes in an improved, true-breeding variety. 45

The standard deviations of phenotypic value in the first two F generations are 7.366 and 7.518 respectively. The last four F1 generations have either zero or very small variance, since they are obtained by crossing parental lines that are homozygous at nearly all loci. The effect of each varietal cross and the ensuing pedigree breeding process can be followed closely in Fig. 30b. The complementary effects of crossing previously improved varieties are strongest in the synthesis of parameter X7 and weakest in the synthesis of parameter X8. 3.7 SIMPLE RECURRENT SELECTION 2 EXPERIMENTS Extended breeding experiments were also run using simple recurrent selection for 8-parameter Plane, Ridge, Peak NE, Peak W, Peak S and Hypersphere. Five varieties were developed in each composite breeding program. The first two were developed from completely heterozygous source populations, the third from a cross of the first two, the fourth and fifth from crosses of the two previous varieties that produced the highest individual phenotypic values. Ten selection cycles were used in each varietal development program. In each cycle, eight individuals were selected from 32 members of a cross-bred generation and their self-bred offspring were crossed in all possible combinations to produce the cross-bred generation of the next cycle. The intermediate, self-bred individuals were not evaluated phenotypically, so the number of trial points in parameter space was equal to the number of cross-bred individuals. Free recombination was simulated by setting the probability of crossing over between any adjacent loci to 0.5. Inversions, translocations and mutations were first inhibited by setting their probabilities to zero. In later experiments random chromosome aberrations were simulated and were found to have a surprisingly advantageous effect on the performance of the ARTIFICIAL BREEDING system. Gene Action 4 was used in the first sequence of experiments described below. The epistatic Gene Action 6 was also tried but did not perform as well as 46

Gene Action 4, which was then used again in the final experiments. 3.7.1 Breeding for 8-parameter Objective Characters Using Gene Action 4 Without Inversion, Translocation or Mutation Plane. The phenotypic values and parameters for each individual are shown in parts a and b of Fig. 31a,c. Each tic mark on the horizontal axis represents the beginning or end of a varietal development program. The generation statistics for the five varieties are shown in part c of the figure. The first two varieties reached phenotypic values of 80.967 and 86.886 respectively. Further improvement to a value of 93.798 was obtained in the third variety. The mean value of the crossbred generations reached a limit of approximately 94.5 during the fourth variety and, thereafter, remained nearly constant. The improvement obtained in the third variety of the extended breeding program illustrates the importance of crossing "improved" varieties rather than starting from completely heterozygous source populations. In this case, the improvement was due primarily to complementary effects in the synthesis of parameter X6 (Fig. 31b). Ridge. The results of this experiment (Fig. 32a,c) also exhibit the advantage of extending the ARTIFICIAL BREEDING program. The first two varieties reached mean phenotypic values of 67.914 and 70.632 with only one individual phenotypic value greater than 80 units. The population means reached 74.877, 79.078 and 89.683 in the last three varietal development programs, with maximum phenotypic values exceeding 93 units during the last program. In this case the complementary effects that produced the improvement during the development of the last three varieties are most evident in the plots of parameters X5, X6 and X8 (Fig. 32b). The 2-dimensional Ridge functions V(X1,X2), V(X5,X6) and V(X7,X8) are nearly optimized by the end of the sequence of five varieties. However, the function V(X3,X4) was further from its optimal value at the end of the fifth varietal development than at the end of the first. 47

Peak NE. Each of the four, 2-dimensional Peak NE functions have three local peaks at parameter-pair values: (49151,49151), (0,32767) and (26214,6553). The North East peak at (49151,49151) is the optimum. There are three locally 4 optimal values of the four pairs of parameters, so there are 3 = 81 local peaks. The results of the experiment are shown in Fig. 33a,c. The first two varieties reached mean phenotypic values of 17.988 and 10.502 with only two individual phenotypic values greater than 40 units. Definite improvement was obtained in the last three varieties, but the mean values reached only 18.173, 22.134 and 27.146. Several individuals in the fifth varietal development program had phenotypic values just under 60 units. The extended breeding program converged in parameter values toward the suboptimal peak with (X1,X2) and (X5,X6) at (0,32767) and (X3,X4) and (X7,X8) at the optimal values (49151,49151). The optimal values of (X3,X4) were determined as a result of complementary effects of crossing the first two varieties (Fig. 33b). The optimal values of (X7,X8) were determined during the first two varietal development programs. Parameters (X5,X6) converged toward (0,32767) in both of the first two programs and remained in the neighborhood of these values throughout the last three programs. Parameters (X1,X2) converged rapidly to the same values in the first program, but failed to converge to any of the local peak values during the second, third or fourth development programs. Finally, during the last program, (X1,X2) were drawn again to the false peak at (0,32767). The breeding program determined the optimal values of four of the eight parameters, but converged to a false peak. It seems unlikely that the system would be able to move off the false peak in the development of additional varieties. Peak W. This objective function has local peaks at the same parameter-pair values as Peak NE: (49151,49151), (0,32767) and (26214,6553), but the optimum is at West peak values (0,32767). Results of the experiment are shown in Fig. 34a,c. Mean phenotypic values of 24.274 and 17.176 were reached in the first two varietal development 48

programs. Means of 42.989, 46.315 and 56.491 were reached in the last three. From Fig. 34a, complementary effects in crossing the first two varieties were obtained in the starting population for the third. However, the cross used to develop the fourth variety was a poor one and no further improvement was obtained in the fourth or fifth variety as compared with the third. The breeding program found the optimal values of parameters X1-X6, but failed to find the optimal values for X7 and X8. At the end of the fifth varietal development program, parameters X7 and X8 are near but are not precisely at values corresponding to the false peak at (26214,6553). So there is some possibility that the system would find the optimal values of X7 and X8 if the program had been continued. yper sphere. This objective function has a smooth, hyperspherical peak at parameter-pair values (32767,32767). When using additive Gene Action 4, the parameters of every individual in the completely heterozygous F1 populations used to develop the first two improved varieties are precisely at the optimal values. The amount that the F mean value drops below the optimal value of 100.00 units is a measure of the average parameter error at the beginning of the breeding program, and may be used to compare the parameter dispersion produced by the use of completely heterozygous source populations with various gene action algorithms. Results of the experiment are shown in Fig. 35a,c. For the reasons explained above, the mean values of the F1 generations in the first two varietal development programs are 100.00 units. The means drop to 88.182 and 88.132 in the F2 generations but increase to 94.475 and 94.929 by the end of the first two programs. Mean values of 97.053, 97.236 and 98.940 are achieved in the last three varieties. By the end of the fifth program, the average value of individuals selected from the cross-bred generations reached 99.515. 3.7.2 Effect of Epistatic Gene Action Similar experiments in breeding for 2- and 8-parameter versions of the objective characters were also run using Gene Action 6. 49

Rapid convergence to the optimal parameter values was observed in breeding for 2-parameter Plane and Ridge. The system converged rapidly but to false peaks in breeding for 2-parameter Peak NE and Peak W. Optimum parameter values were found in the third and fourth varieties while breeding for 2-parameter Peak S; but the fifth variety reverted to lower mean phenotypic values, as had been observed in earlier experiments. Rapid convergence was also observed in breeding for 2-parameter Hypersphere. Gene Action 6 was effective in breeding for 8-parameter Plane. However, poor performance was observed in breeding for 8-parameter Ridge; some parameters failed to converge, and some became prematurely fixed with undesireable alleles at loci having major effect. Further experiments using Gene Action 6 were then suspended in order to explore the effects of chromosomal aberrations while using Gene Action 4. 3.7.3 Effect of Inversions, Translocations and Mutations in Breeding for 8-Parameter Objective Characters Using Gene Action 4 The experiments described in Section 3.7.1 were repeated with the probabilities of inversion (PINV), translocation (PTRA) and mutation (PMUT) all set at 0.0010. This means that, on the average, one chromosome in a thousand will rupture between any two specific, adjacent loci and then re-fuse with a chromosome segment in either an inverted or translocated configuration. It means also that, on the average, one zygote in a thousand will have an allele at a specific locus that is a mutant of the one transmitted by the normal processes of inheritance. Plane. Results are shown in Fig. 36a,c. The differences in parts a and b of Figs. 31 and 36 are not pronounced, however, an improvement in performance can be seen by comparing part c. The random aberrations of chromosome structure and gene conformation increased the mean phenotypic value of the fifth variety from 94.551 to 97.201. Many individuals in the last generation of the fifth varietal development program (Fig. 36c) have phenotypic values greater than 97.0, while only one individual in the last generation exceeds this value in the previous experiment. One individual in this experiment 50

reached a phenotypic value of 98.082 units. The parameter values X1 to X8 of this individual are respectively: 416, 64156, 1082, 64774, 1096, 63724, 2182 and 64206. 1Ridge. Results are shown in Fig. 37a-c. In the previous experiment (Fig.32), a mean phenotypic value of 89.683 was reached in the last generation of the fifth varietial development program; the corresponding value in this case was 87.407. The final phenotypic values in Fig. 32c are higher than those of Fig. 37c. The general performance was, however, quite similar, and the small differences observed in these two experiments do not indicate a decrease in performance due to the use of simulated inversion, translocation and mutation; performance variations of this amount would be expected in replicated tests. Peak NE. Results are shown in Fig. 38a-c. In this experiment, parameter pairs (X1,X2), (X5,X6) and (X7,X8) converged toward the optimal values (49151,49151) of the 2-parameter Peak NE objective function. The parameters (X3,X4) converged to false peak values (26214,6553). Although the system again converged to a false peak, six of the eight parameters were optimized here compared to four in the previous experiment where inversion, translocation and mutation were inhibited. Peak W. Results are shown in Fig. 39a-c. Mean phenotypic values of 18.865 and 16.769 were reached in the first two varietal development programs with only three individuals exceeding phenotypic values of 40 units. In the last three programs, mean values reached 41.403, 50.990 and 78.063 units with many individual values in the fifth variety exceeding 80 units; one individual in the fifth variety reached a phenotypic value of 94.855 units. All four of the parameter-pairs (X1,X2), (X3,X4), (X5,X6) and (X7,X8) converged toward the optimal values (0,32767). Individuals with desireable combinations of alleles at loci controlling parameter-pairs (X3,X4), (X5,X6) and (X7,X8) were produced in the first varietal development (see Fig. 39b), and it appears that some of these combinations were preserved in the cross of the first and second varieties used to develop the third. Crossing the first and third varieties to develop the fourth must have produced many homozygous loci that control (X3,X4), (X5,X6) and (X7,X8) because these parameter-pairs were near 51

the optimal values in the earliest generations and remained there throughout the fourth varietal development. Parameter-pairs (Xl,X2), on the other hand, moved toward the false peak at (26214,6553) during the fourth program. In the fifth program (XI,X2) too were driven rapidly to the optimal values (0,32767). By the end of the fifth varietal development, the system had definitely found the optimal peak among the 81 local peaks of the objective function. Continued breeding would have undoubtedly refined the adjustment of the parameters. Peak S. Results are shown in Fig. 40a-c. The first two varieties reached mean phenotypic values of 35.802 and 34.721 units; the third, fourth and fifth varieties reached means of 71.129, 64.784 and 76.083 respectively. The third variety reached a higher mean,value than the fourth, and the highest-valued individual was in fact produced in at the end of the third program. The setback in the fourth variety was overcome in the fifth variety which reached the highest mean phenotypic value. From Fig. 40b, it appears that desireable combinations of alleles for parameter-pairs (X1,X2), (X3,X4) and (X5,X6) were found in the first varietal development program. The pair (X7,X8) converged to the optimal values (26214,6553) in the third program, but the cross used to develop the fourth variety appears to have been heterozygous at many of the loci controlling this pair of parameters. This would explain the setback at the beginning of the fourth program observed in Fig. 40a. The populations had not reached complete homozygosity by the ei breeding program, so, strictly speaking, they should not have been referred to as "varieties". However, the genetic variance does decrease within and over successive programs, and it is incorrect to infer from the increasing phenotypic variance that the genetic variance also increased. Increasing phenotypic variance is brought about by the greater steepness of the objective function in the vicinity of the optimal parameter values. A population with small genetic variance but nearly optimal genotype may, therefore, have larger phenotypic variance than a population with large genetic variance but far from optimal genotypes. 52

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gene action #5 gene action #2 0 ~ ~ o 0 0 80 160 z40 380 0 so 160 140 320 INDIVIDUAL INDIVIDUAL Figure 12c Compatison of gene action/breeding method combinations: Gene Action 2 and Gene Action 5 in combination with five breeding methods 55 0 all rrr r s4 Iri r ri ID! V! A! N[3! V I []LJAL o0~~~~~~~~~~~~~~~~~~~~~~~1 ~ ~ ~ ~ C ~~~~~~~~~tcr ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~nL IS 20 200 0 SO 24 W INIIUA NIVEA

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gene action #9 gene action #12 a i - I 3 i t oH0 0 j 1 H oo Hoo _ 0_| j |o o oQ zX so 840 3)0 ~ ao 1BO s4o 380 INDIVIDUAL INDIV IOUA Figure 12h Comparison of gene action/breeding method combinations: Gene Action 9 and Gene Action 12 in combination with five breeding methods 60

9, 0 Figure 13a Phenotypic value of individuals during pedigree breeding for 2-parameter Plane using Gene Action 3 and the schedule of selection described in Section 3.1 in J * 16 0 160 540 320 INDIVIDUAL 1 _L___i ____l x l ~1 _ _ "0 0 160 2~0 e30 INDIVIDUAL Figure 13b Parameter values of individuals during pedigree breeding for 2 parameter Plane using Gene Action 3 and the schedule of selection described in Section 3.1 61

10017 PMIA 6/26/73/ NDVLP 3 NVALU I PINV 0, 000 PTRA 0 0,0o PCROS 0 5000 PCROL.. 0 500 PMUT 0.0000 NPOP 64 32 32 32 32 32.32 32 32 NSEL... - 32 - - 16 -....-.. 8. 4...... 2..... 1........ NPAR 2 NSEG _..-.... 2-. NREP i.I X.t.- ~.. -..1 - IPAP t IPBP..... 0 IPAF 0.IPCS _........ 0 STOP 4 —A 5, 447 -2590 _ 1 99 3 32 53,536 33570 38204 __ __.79,265 2191 40549_... 4 31,885 50151 26408 ___.5...... 42, 112 36403. 26064. 6 34 483 59436 39098 -_J__.. 61,425. 19132 34107._. 8 70,900 23159 50553 n9.... - 38,698 54686 39873 10 53,925 24839 29984._.._-.. 55, 456.24674 3 R"' 12 64,913 3A-'' _.1 3 6.7- - ", d 63379 4.- __2078 __63379._ 6,770 2078 63379 31_ 12.. 96,770... 2078 63379 313 96 770 2078 63379 314__ 4 96,770._2078 63379 _ 315 96,770 207C 63379 ___316__ 96 770.__2078._ 63379_. 317 96.770 2078 63379 __318 _._._6,770.__2078 63379 319 96,770 2078 63379 __.320 _._96 770 __2078 _ 3379__ — AVER A G E_Y.AL UE S ____ _ GEN EFF AVG STD AVGS STDS NIZ NTR... 0000 I 0I00 0 000 ~,0 0 V0 0,000.0. 0,0 0,00 2 48,855 48,855 14 537 60 387 8,732 0 P00 64, 00.___ 5 4, 054 _. 644 53. 1 930 43 3 68 926 1 3 1 _ 0..00 32 01 4 57,125 66,338 13 786 69 037 13 189 0, 00 32. 03 _ 5.__ 6 1 3 1 2_ _78 058..__.5, 8 1 _ _81 3_ __5 523 _0,. 0 0 32,00 _ 6 65 118 84 148 4,816 90 181 6,369 0, 00 32,000.._ 7_.. 69,476 95,627 1,162 95,667 _ 1,560. 0,000 32,*00 8 72,888 96,770 0,000 96,770 0,000 0, 00'32, 00 _ 9...-._....75,542 96.770, 0 000. 96,770.... 0 00._. 0,00 32,030 10 77,664 96,770 0,000 96*770 0,000 0,000 32, 00 -Figure 13c Input data, parameter values and generation statistics during pedigree breeding for 2-parameter Plane using Gene Action 3 and the schedule of selection described in Section 3.1 62

O 8O 160 240 aeo INDIVIDUAL (a) 2-parameter Plane using Gene Action 3 II 0 0 1 40 360 01 im i6 o bo 1a0 aeo IND IV IUAL (b) Figure 14b Parameter values of individuals during pedigree breeding for 2-parameter Plane using Gene Action 3 65

16 selected r -, - i r ati~urr "' to.-..:.I ND I V IDUAL Figure 15 Effect of artificial selection intensity in bulk population breeding for 8-parameter Plane using Gene Action 4 8 selected > co.J0 0 - 0 80 I 0o 240 3P0 INDIVI DUAL Figure 16 Effect of population size in bulk population breeding for 8-parameter Plane using Gene Action 4 64

8 J *lr 0.5 probability of > i j Uv1l cross-fertilization'j 0 -O 80 160 240 380 INDIVIDUAL 0D 04 o - i 1.0 probability of J ll* r^ cross-fertilization -J 0 OP* 00 8 160 240 320 I NO V IDUAL Figure 17 Effect of cross-fertilization in bulk population breeding for 8-parameter Plane using Gene Action 4 65

mI LflD l l O *I.n m ni (Ul 0 0 80 160 240 320 0 80 10 240 320 INDIVIDUAL INDIVIDUAL uf' o to 0,sC~~~~~~~~~ce a.0 j n a. n o 80 160 240 320 0 so 160 240 NDI V I DUAL I ND I V IDUAL 0, N 1CI1~~~~~~~~~~~~I a I 0 0 80 160 240 320 0 0 160 240 30 INtDIVI DUAL INDIVIDUAL w Figure 18 Parameter values of individuals produced in bulk population breeding for 8-parameter Plane using Gene Action 4 66

0 ".0 z 0 0 80 )60 240 320 INDIVIDUAL Figure 19a Phenotypic value of individuals during bulk population breeding for 8-parameter Plane using Gene Action 4 67

00 8o 160 240:3; ~O a I 140 a4e IJDIVIDJAL INDIVIUIAL X4: ~O m IC~eio~o1*3 0 BO 160 Z 0 3 0 INDIVIDUAL INDIV IUAL at i. LA W W 0i1~~~~0 0 80 160...40 3.. 160 eVO 320 ~Q8~~~~~~~~~~~~~~~~ B ISO e~ 5 o MO &1 3 -NJAL 3a it nIJAI IND VI DUAL VIDUAL O 8e 160 240 320 oNdiVI0UAL i NDivroUAL iNDIVIDUAL for 8parameter Plane using Gene Action 4I 68 0)rl o so 160 240 320 INDIVIDUAL INDIVIDUAL a so ISO e0 320 0 GO B60 240 30No IIVIVII(:AL 68 W) 14e, ~~~~~~~~~~~~~~~~~~I 04-~~~~~~e

-. a In 160 24_0 _3 IOI VIDUAL Figure 20a Phenotypic value of individuals during bulk population breeding for 8-parameter Plane using Gene Action 4 with linkage 69

LA 0, t~~~~~~~-~~,,,~1~~~~~~~-~~~~~I~ -— ~rs~~~~~~~~~~~,, 0 0o 160 240 3M 0 80 160 240 320 INDIVIDUAL INDIVIDUAL u's R tst' Lnrn~~~~~~~~~~~~~~~iJ a 0o O 80 160 40O 30O 0 80 160 240 320 INDIVIDUAL INDIVIDUAL I N IVI ULN K I NDIlV I lAL 7L u~~~~~~~~~~~~~~~rl~~fu j ru~ O 90 160 GO 140 3I0 0 8O 360 240 320 INOIV IMUAL INDIVIDUAL Ln ~4 ~ ru INDIVIDUAL I ND V DUAL 70

MEAN VALUE 00 o 40 0 80 100 Ur w I 3 5 la 15 z STANDARD DEVI AT ION Figure 21a Averaged results of five replications of bulk population breeding for 8-parameter Plane 71

BPB1A 6/26/73 NOVLP 4 NVALU 1 PINV 0 000 PTRA o.e0rA PCROS 0.5000 PCROL 0. 5000 PMUT 0. P P POUCR 1,0000 CV0 0. 000 NPOP 32 NSEL 8 LGEN 20 NPAR 8 NSEG 32 NREP 5 Ix I IPAP 0 IPBP 1 IPAF 0 PCS 0 STOP 1 43,275 37836 36646 37100 17678 35828 28564 36598 29214 2 53,071 13514 21984 48080 25490 16928 28204 27996 46942 3 53.112 40220 39766 23660 47122 34610 31548 32796 29166 7 56,377 17106 32556 21262 24382 36546 51484 32572 32496 10 657,922 14468 48560 32766 47644 29446 59602 25368 40202 77 70,348 17348 47888 26s86 32074 18126 48394 17450 59936 99 70.621 8436 43790 27970 24860 33680 60366 13840 63024 111 71,822 17030 59662 36878 44570 32962 51976 14618 59690 117 74.593 1984 44464 10718 48108 13382 48290 25100 39258 130 76,032 1728 48048 29660 48904 21966 51696 13612 54798 134 81,681 9632 51950 13838 40720 5868 60532 17680 59914 161 82,508 2194 64910 13852 56066 17614 53120 21520 51516 173 86,757 5528 62946 10068 63486 26356 47616 2394 63006 202 88,677 t296i 63698 6288 63712 6440 47824 9534 62770 205 89,178 5510 55040 12960 63038 11236 58826 982 59388 227 91,063 2634 63020 5832 63742 10756 47572 2064 62238 234 92.064 1742 59946 1686 60622 6422 56224 4882 58474 267 92,663 5776 56076 1478 64010 6648 63632 8470 62326 295 93,414 9390 61868 1272 63710 4916 63454 6500 60656 321 95,218 5736 63730 2184 63800 3002 63550 6862 63774 324 95,731 5764 64748 1596 62990 1588 63182' 2390 60178 342 96,177 1190 60670 890 62780 2806 63438 4884 64978 391 97,1 3 1904 62720 1894 62768 1734 63586 970 64434 470 97,503 2126 64030 1878 63500 1876 63392 728 64736 611 97.871 1460 63710 996 64012 1092 63358 772 64216 I 44,831 37322 20872 40280 56002 24556 12352 35624 21456 2 52.697 32344 24616 32068 25850 32252 49596 26046.37578 6 64,473 40536 25336 25110 59650 9440 47648 37550 55880 66 64,515 25148 25360 18408 56556 35858 46686 28732 55644 69 64,969 27724 25264 18348 52448 21650 51994 25342 41840 70 66,310 37386 28718 17154 64238 23862 39964 33438 64432 75 67.855 20780 58006 20778 28580 6786 48320 33786 40834 78 70.009 14812 14316 13836 56558 24636 47642 24120 63792 99 72,352 12602 49596 13896 32482 6500 47858 32838 53086 126 73.027 6424 64060 13820 56318 10382 44750 35692 21918 133 77,202 14032 25622 13582 51972 1338 59406 25562 61t28 161 78,152 P998 33796 13416 59924 9526 44060 17868 60622 162 78,959 9996 36650 5898 51746 14018 58160 28950 64130 169 80,643 3546 30366 13820 59168 14256 63186 21048 60606 Figure 21b Parameter values of individuals with increasing phenotypic values during five replications of bulk population breeding for 8-parameter Plane (Sheet 1 of 4) 72

195 82,566 18368 51464 1816 56936 10206 60832 20818 52714 196 83,540 11466 40940 2230 44022 232a 64494 9978 52412 235 83,666 14828 40670 1670 43828 1984 59122 9484 60830 239 86.583 6680 48156 2184 63746 6126 44032 13606 64460 265 87,607 1584 40156 5672s 63446 200 63054 16530 56298 271 88,312 2736 62744 6084 64658 12636 63518 25124 56522 297 91,452 860 62940 1596 62570 5180 63472 21042 57020 309 93,411 594 59614 1944 55526 6740 62990 5946 64688 353 93,905 7372 63648 5962 63672 10144 63022 1368 64688 366 95,801 400 63436 1464 59814 864 64462 9034 64178 424 95,970 6396 62956 998 63546 2764 63486 3206 64386 444 96,438 2780 62522 1900 63544 1318 63714 2684 62366 457 97,602 1284 62958 1192 63544 342 83984 2982 64880 476 97,781 280 63468 2350 63928 2220 64192 902 64670 586 97.870 520 63694 1464 63914 1334 63982 372 63072 1 47,238 56348 56270 32078 28850 36354 25270 36876 36786 2 54,746 35226 37598 16896 3688 20780 37564 40292 26028 11 55,908 25070 29392 40956 42860 25522 26030 20768 45008 14 58,080 48368 28372 20738 35650 25056 41362 25820 56960 33 60,272 20976 35870 36650 51770 16820 40402 36366 36624 43 60,827 33250 33416 25292 39908 21726 33260 13582 44028 4-4 61299 25356 37782 233q4 40176 25326 25116 13594 43836 52 62,384 43582 55748 20918 44532 32060 42064 36394 55536 67 67,279 20998 31972 17480 53842 5348 39966 36384 45020 76 719279 19838 51428 9216 59920 17318 49748 47690 44528 100 729208 31806 52386 5584 59632 24322 50000 39982 56106 120 73,427 21008 47796 8718 51712 5110 45170 27946 40926 131 73,959 40238 56468 6544 56314 13266 49506 32720 56090 132 75500 32510 51878 1924 55822 12864 53358 36084 56016 139 75,943 14260 55432 12784 48356 9666 41530 27426 54830 159 77,932 22492 47856 2194 56498 6096 42110 28192 58952 168 78.561 24160 55460 9170 30894 5942 59870 16944 59732 182 79,184 32960 48262 8930 59860 21230 60764 9010 56252 191 82.112 26272 47736 5298 52630 1284 57618 19760 602986 193 82 615 1.988 58372 6050 44494 1310 42052 16386 60812 197 84,033 33758 51620 6502 59586 5168 49816 1088 63920 198 84,276 28894 51348 17300 60098 8736 64114 5200 64274 203 84,526 29676 55190 8630 50994 2316 60770 8764 63446 212 85,159 17182 639.80 990" 63934 4990 52924 28146 63720 240 85,623 22012 55448 7940 59604 1806 56228 15934 63178 941 87,870 17678 59930 5378 63716 2018 49266 9426 60132 257 89,135 13042 64432 9456 59884 4942 64834 20736 64202 267 90,932 14544 55750 9638 63938 1056 61490 5108 63764 290 91.366 6862 55416 12486 59478 1402 65106 2318 59944 295 91,499 16930 55006 1430 63092 4626 60020 1296 63736 306 91705 22926 64810 4776 60i74 2500 62154 2060 63774 307 91,869 14316 62436 1492 60098 2224 53108 2524 64426 325 92,252 17410 55728 1942 63176 830 60558 1506 63746 335 92,971 7068 63592 5256 63200 4940 58588 6100 63274 366 93,937 2766 55490 2124 59140 2602 65346 5390 63258 400 94,283 5210 63850 1476 62998 10438 60754 1750 63438 401 94,702 4674 64340 2168 59602 802 64356 1598 55306 405 96,135 2766 64344 1970 63684 800 65090 1056 55348 575 96,684 1386 62748 1646 63414 4430 64596 2528 63988 1 55.425 21290 37098 40420 41346 35930 55764 44282 36154 9 55953 21920 25416 33096 44226 27756 29632 44260 58970 21 59,474 24622 39490 14060 36532 32738 10494 9936 44510 22 59,987 40248 40182 21724 44268 26076 36530 35798 55224 32 65,712 8766 43596 6786 36290 17378 28776 37176 43820 34 68,275 23900 54864 22714 35826 7358 36592 21262 43782 67 71.382 5166 47166 14716 39680 8780 36218 29722 47422 68 74,479 5406 59488 22936 40386 25566 51680 21248 51938 102 74,790 9470 47232 15228 27918 10656 40492 13598 63278 Figure 21b Parameter values of individuals with increasing phenotypic values during five replications of bulk population breeding for 8-parameter Plane (Sheet 2 of 4) 73

112 75,932 12876 47934 14278 40894 15470 48218 13792 55328 125 76.004 13610 53590 17360 43366 17946 51534 22408 591t8 132 77.610 11676 63924 19054 51180 15260 39728 12610 48620 138 78340 13186 53380 29320 55114 14552 47408 13496 63232 143 78,670 8540 63038 9930 32986 4896 44074 25796 59376 159 80,346 9050 63940 29646 43130 14732 55536 140l18 63936 162 80.452 1128 64194 26498 62810 18378 43572 20728 55806 174 818.59 1340 59124 10626 47928 14062 44798 22124 62286 179 82.526 6182 60130 25268 55116 17866 59166 17592 d3022 198 83,885 1722 55090 24982 59434 22186 62508 13528 63040 203 83.891 2086 63472 21664 47418 15018 51968 10676 64270 210 85s,19 5928 60356 18112 39500 1046 59450 1 4062 63428 220 85*337 1098 63038 14450 59192 11390 47934 21192 63230 223 87,003 Q244 59226 6048 51662 3708 52432 14512 64192 242 87,691 9710 55356 5090 52114 3730 52418 6800 63050 259 88,243 p146 62528 13492 5218 1116 16 58700 6060 59902 265 88.786 9978 64388 2958 55082 8028 44766 3506 63582 266 89,139 2298 59168 1492 63690 11406 52446 18368 63458 270 90.940 1832 64928 6290 51230 6588 58928 6106 a0368 286 92,027 1548 59198 13986 63200 7098 63440 5874 63008 322 93q069 2006 63758 9156 55310 7356 64748 2742 63248 347 93,087 9182 59628 9936 58938 598 64208 828 63666 359 93,100 5920 64432 5826 64044 3226 55790 6832 63502 361 94,244 2296 63696 9618 54364 552 62750 606 64222 384 94.270 1766 59122 6068 63456 3004 64452 664 56572 385 94.593 1552 63514 5724 59616 4882 60878 t590 63530 429 94,602 1586 60400 2420 63504 3424 56574 2738 63530 435 95,494 1774 63500 1462 59868 4660 84462 1338 59918 436 95.777 1794 64688 1390 64254 170 60428 1596d 5552 457 97.037 2016 63982 1642 63482 3038 64272 1848 63414 1 54.433 25548 44256 36770 29108 24876 37794 33504 32782 5 55,051 16698 36816 32540 51080 51666 40654 40866.39702. 56,i65 28700 36878 44330 37104 28510 36874 25610 48618 12 60,275 27708 44238 36918 28326 9992 28a06 21936 49356 2.7 60,624 24622 51970 16926 40686 9936 20046 433:.26 37806 31 61,350 29404 59138 21426 40432 32288 36412 32588 39230 44 62,356 21020 45488 37582 32556 17916 45044 21800 40012 54 63,479 8736 56958 39548 47196 37536 48588 32378 36124 57 63,904 21188 47172 13340 32544 13612 36338 38808 43790 67 72,856 2258 55492 29210 40612 3220 35200 18162 41376 t08 734494 3240 51706 21064 31012 5676 51758 2820. 44496 109 81.826 5628 55522 21316 44198 2724 50544 10464 56724 t87 81,974 1344 63186 18374 47860 13818 38782 13570 64912 190 82,552 6850 55836 1370 28390 1286 47436 7086 55596 198 90,270 1596 64272 2330 54762 2762 54880 18176 62076 257 90,755 6882 63732 1288 58088 11012 s9166 11424 63290 263 91*634 1266 63740 666 55568 5942 62270 10738 55314 293 91.971 13296 56756 2100 64120 790 59436 4416 60338 294 93.032 8928 60610 2524 63190 2024 58700 7596 64178 308 95,476 800 63732 2074 60S32 3288 630s0 1 097e 63744 380 95 830 1712 59864 2360 63670 1542 63980 1 06 59886 391 96.570 2350 64708 1876 59800 2468 62750 588 64182 455 97,496 1884 62624 504 64086 1722 63730 106 863744. 506 97,599 1374 64184 264 S6359 214 63936 2786 64478 589 97, 606 1358 63256 1302 63736 1718 62784 544 64734 AVERAGE VALUES GEN EFF AVG STO AVGS STDS NZZ NTR.t 49,680 49,680 5,903 57,092 3*285 0000,e 32.00 2 53,497 57,313 4.163 62,140 1,467 0,000 32.000 3 56,460 62.387 4,187 67.704 2,258 08o00 32,000 4 59.141 67.181 3,886 71.850 1.960.000 32,000.5 61,592 71.397 3,636 76,097 1,666 0,000 32,000 Figure 21b Parameter values of individuals with increasing phenotypic values during five replications of bulk population breeding for 8-parameter Plane (Sheet 3 of 4) 74

6 64,005 76,069 3.522 80.271 1,388 0.000 32,000 7 66.277 7g9911 3.229 83,892 1.714 0000 32,000 8 68,352 82.875 3,213 86.511 1.102 0.000 32.000 9 70,286 85,762 2.606 89.940 1.336 0.000 32000 10 72052 87945 2*671 91,247 1.041 0000E 32,000 11 73 655 89.684 2,490 92.652 0,908 00000 32.000 12 75,127 91,318 2.031 93.666 0772 0,000 32,000 13 76,453 92,362 1,956 94.757 0.741 0.000 32.000 14 77 646 93. 15 1.564 95.044 0 637 0000 32,000 15 78.708 93.566 1,815 95,748 0.803 0.000 32,000 16 79,.668 94.077 1.469 95.749 0.549 0000 32,000.17 80520 94.154 1.446 95,907 0.464 0,000 32.000 18 8-1288 94.34 1.484 96.071 0,579 0,000 32,000 19 81,995 94.727 1 301 96.106 0,494 0,00 32,000 20 82.633 94.756 1,379 96,397 0.429 0000 32,000 MAXIMUM VALUES GEN EFF AVG STO AVGS STOD NI! NTR 1 50.513 50.513 6,637 57.918 4,814 0 32 2 54,344 58,460 5.286 63,793 2.740 0 32 3 57.234 64.281 4.801 70.44 2*926 0 32 4 60.218 69.169 4851 74.337 3,778 0 32 5 63.021 74.232 4,457 77.710 2,233 0 32 6 65.371 77.120 4.228 81.939 2.348 0 32 7 67.540 81.017 3,668 85.542 2992 0 32 8 69.488 85.109 3,795 89.286 1.668 P 32 9 71.376 87.956 3,252 90.411 1.687 0 32 10 72.956 89.801 3181t 92,514 1,797 0 32 11 74,480 91.480 2.965 94.735 1.306 0 32 12 75.843 92,373 2.274 94.656 1.269 0 32 13 77.139 93,473 2.564 95594 1156 0 32 14 78.333 94.011 1.911 95,530,0969 32 15 79.409 94.484 2.058 96.428 0.930 0 32 16 8,0350 94.664 1,678 96.319 0,730 0 32 17 81.182 94.931 1.692 96.783 0.710 0 32 18 81,924 95,535 1.790 96.951 0,749 0 32 19 82,624 95,749 1.648 97.103 a,68e e 32 20 83,260 95, 904 1833 97, 75 00661 0 32 MINIMUM VALUES GEN EFF AVG $TO AVGS STDO NIZ NTR 1 48,961 4 8.961 5.191 56.406 1287 0 32 2 53,018 56,394 3.278 60.553 0,993 0 32 3 55,487 6?.244 3.718 65.885 1.553 0 32 4 57.987 65,668 2,669 70.049 1,071 0 32 5 60.247 69.286 2.925 74.429 1,263 0 32 6 62.692 74*918 2.844 78.688 0,924 0 32 7 65.179 77.640 2.805 81.241 0,464 0 32 8 67,331 80,599 2 661 83.876 0.788 0 32 9 69,384 83,353 2.077 86.612 1.100 0 32 10 71.132 85,824 2,312 89.900 0,568 0 32 11 72.645 87.781 2,131 91,557 0,653 0 32 12 74.167 90.371 1,777 92.963 0,486 e 32 13 75.552 91.143 1.581 94,126 0.416 0 32 14 76,802 92*443 1.101 94.567 0,461 0 32 15 77,864 92.297 1.439 94.423 0.626 0 32 16 78,812 93.046 1,232 94.831 0.420 0 32 17 79,657 93,174 1.213 94.981 0.359 0 32 18 80.417 93.339 1.136 95,86 0.347 0 32 19 81.122 93,804 1081 95.414 0.317 0 32 20 81,729 93,259 0,967 95.409 0,275 0 32 Figure 21b Parameter values of individuals with increasing phenotypic values during five replications of bulk population breeding for 8-parameter Plane (Sheet 4 of 4) 75

8 O loni a 80 160 240 3W0 400 400 560 640 INDIVIDUAL IND O I V AI.. Figure 22a Phenotypic value of individuals during bulk population breeding for 8-parameter Ridge using Gene Action 4 76

IIVI*DUAL -*DIVI-AL INDIVIDUAL INDIVIDUAL INDTVIDUAL JNDIVIDUAL INDIVIDUAL INDIVIDUAL mW t- 0 80 1_0 240 3iQ o 10 400S 6 INDI V IDUAL. INOIDUAL Mx n-._. 0% _ ao G o e 30 40 240:50 400 S INDIV! DAL INDIVIDUAL Figure 22b Parameter values of individuals during bulk population breeding for 8-parameter ridge using Gene Action 4 (Sheet 1 of 2) 77

4 IL, U'l O e0 1 b0 240- 32 400 480 560 640 INDIVIDUAL INOIVIDUAL ED 0 80 160 240 320 400 490 560 640 INDIVIDUAL INDIVIDUAL L f U1 rn a. 0 80 160 240 320 400 480 560 640 INDI V IDUAL IN I V IDUAL Figure 22b Parameter values of individuals during bulk population breeding II or 8-parameter Ridge using Gene Action 4 (Sheet 2 of 2) 78 rNO VI!DUAL NOIV'I:UAL IX O: Fiue2bPrmtrvlusoindiiul uigblouainbedn fo 8-aaee ig sigGnAcon4(he2of) WQT ~ ~ ~ ~ ~ 7

MEAN VALUE 0 O0 40 sO 80 100 )o. 0. -----—.I'i a0 5 0 S1 20 STANDARD DEVIATION Figure 23a Averaged results of five replications of bulk population breeding for 8-parameter Ridge 79

2 031. BP 1A 6/26/73 NDVLP 4 NVALU 2 PINV 0 000 PTRA 0C000 PCROS 0 8,500 PCROL 05000 PMUT 0000 POUCR 1.ee00 cv 0.000 NPOP 32 NSEL 8 LGEN 20 NPAR 8 NSEG 32 NREP 5 IX I IPAP0 I.PB 1 IPAF PCS 0 STOP 1 60,860 37836 36646 37100 17878 35828 28564 36598 29214 8 62 091 24606 21518 40238 37106 40476 24756 37116 17588 17 63, 83 49100 36110 32236 25026 47256 37026 36140 49954 41 70 135 48836 31458 45948 21978 47828 40160 44812 28714 102 71,118 45066 27588 44298 25572 44200 36398 41616 25354 105 72,844 43854 32180 49116 33534 43734 36876 41406 28712 119 73 452 55776 39574 48396 32062 59514 49128 36798 27962 174 73,728 43564 23506 56598 44620 59062 45246 37786 214 187 75 377 48146 35778 46026 28436 58842 40474 48798 36376 197 80,589 44076 31622 56310 44094 59540 53178 42392 28626 265 82, 54 47932 35942 52776 36384 63384 60920 49098 40906 333 83,626 55356 36408 56782 51520 64312 60874 53942 43518 355 86,436 51486 40234 52716 44800 59286 49610 61384 58864 417 86 650 51576 39782 61070 48852 59996 56556 60182 55730 433 86,661 51516 39512 56782 51700 59230 52686 57576 55806 488 87,850 51546 39556 59840 51208 59468 52206 60198 56226 497 88,370 48158 44790 56586 47892 63564 60860 65016 64016 499 88,514 51308 43846 57036 50980 59472 60394 64760 64284 39 89,346 55356 47474 60592 51220 63340 59900 64504 59358 550 91,088 51530 40756 56316 52422 63114 60874 65270 64044 551 92 762 58716 51796 63710 55512 63610 62274 64760 64400 605 94 023 5538. 48452 64206 62950 63086 61146 63160 63564 1. 5.9048 37322 20672 40280 56002 24556 12352 35624 21456 17 62,520 35380 24606 26046 24878 43564 29680 43790 43116 23 65,366 25312 21230 4'4272 35888 44296 37146 47904 29404 36 66,097 39662 25336 40898 25298 33272 25086 37088 33340 53 69,636 40012 28958 48400 39460 48156 37146 35628 35690 91 75.873 44064 33072 44560 27698 54180 44872 35854 19116 1S95.79.075 56736 47978 39996 24100 46500 33562 47898 39682 292 80,306 44976 40478 51216 38488 61112 56108 49176 39968 A43. 8.3070 60638 55692 52222 36850 57992 48670 48410 39982 549 83,085 56768 48172 52206 44484 64756 57344 48154 39714.565 895.330 59890 55374 48110 36324 57914 49452 52234 39250 1 63,389 56348 56270 32078 28850 36354 25270 36876 38786 4 8.33s3 51968 32596 47915 28920 39486 32028 44106 40732 41 68.434 48588 29538 48138 32764 35946 24602 45012 44610 42 69.285 52192 47690 47872 36380 44240 36108 38946 45546 45 70.515 36676 21214 52204 44296 44268 25356 44226 45260 S7 71. 957 56720. 6014 4958 32494 39684 25778 37070 26014 Figure 23b Parameter values of individuals with increasing phenotypic values during five replications of bulk population breeding for 8-parameter Ridge (Sheet 1 of 3) 80

8 7.1,986 52448 40934 4835m 37296 5099.0... 20704 51494..4.774 95 73 118 28896 16624 52908 47420 43656 28236 44426 33210 102 75*,957 56960 52652 45288 28154 35844 19098 418.4.- 2a68 3 159 76.038 51888 36812 53388 40442 39892 21528 51248 37346 232- 7.9-543 60336 53462 51966 39932 38946 28602 48^A4 344s6 275 81*973 63966 62852 57260 45800 44420 33082 48352 41630 326 82.675 63754 60824 53210 44804 94 3 29180 52446 44800 394 82,694 63476 61326 58522 48842 43446 20780 62e58 45620 436 83 304 59838 55094 57980 48632 39158 25276 52026 40266 441 85,504 64466 64414 57756 52216 50690 36336 51730 48394 5-41 86,*451 63048 58722 5678..2174 43460 3114 4359618,6944 545 87,308 64722 62292 59930 52444 47316 38962 59078 56222 5.78 89. 151 64678 64668 56092 47898 50960 43310 56240 48378 638 89,391 64662 64430 60170 56t16 50706 43266 59588 59834 1 45,288 21290 37098 40420 41346 35930 55764 44262: 36154 2 56,226 40130 28898 33022 44736 41000 40282 37598 32316.3- 64. 661 47140 47210 25296 28504 45260 32838 4.4508 28220 31 76,403 40730 24698 52656 39574 48786 37338 37180 20810 184 76.824 48152 35484 56286 51542 45496 28370 36248 2316 310 77.036 55754 47048 63804 58906 33092 16610 32094 11902 363 77 230 56010 46822 59838 51268 33046 16150 32124. 1.710 389 77*398 55772 46808 59598 54854 36694 16134 31642 t5726 390 77*814 56282 46824 59650 51508 36932 20212 32124 15.292 418 77,969 49292 38862 60124 55574 32820 16132 36680 19372 451 78,621 53146 43168 64188 59386 36614 20210 31136 15534 509 78,884 55534 46808 63264 58934 32852 16120 32618 15488 582 80.130 55548 47048 63506 58980 37156 20168 35242 18652 1 41 820 25548 44256 38770 29108 24876 37794 33504 32782 3 46837 28906 36846 36816 26270 21770 39526 51678 a2865 4 52,471 28178 28418 40156 35890 44510 25082 20046 29166 1 65 159 33440 21230 39968 35466 32706 17632 51892 32498 17 65 453 44784 28442 36828 43582 52206 29930 49352 39022 26 67 939 37100 28032 47808 33740 40910 20994 28926 14778 70 69.944 45262 22066 36850 17110 48528 37360 44522 28860.102 70 892 48096 33784 32962 26694 52 172 40732 39932 33166 116 71 217 59388 43186 33888 19262 40358 25326 48766 44962 147 71.840 52402 41720 32044 26062 44,016 26048 48408 32690 160 72.708 55036 43934 36992 15694 44480 36668 55980 60334 162 72.969 62972 51108 37474 19024 40416 28690 5190_.4 48832 168 74.456 47824 37662 28384 16910 48548 36638 63722 52610 220 75.011 51422 51794 29598 16144 490056 327906. 962-1 586461 239 779740 51962 44390 40848 27436 49040 44526 55746 44466.292 81.070 51660 36694 33228 24540 56420 48232 6441.4 63188 336 82 805 55322 44118 33212 20460 56418 48426 63438 59600 373 83,030 59776 48198 37072 20672 55712 48170 063720 59332 419 835338 51228 43906 41104 24046 52610 44030 63918 62510 439 84,833 52412 47956 40656 27846 60e28 5.585. 6a3.94 86174 489 85,206 55516 47688 32960 16610 55926 48140 6334262762 527 88,267 59146 54900 36290 20194 80274 55610 640.30 63244 AVERAGE VALUES GEN EFF AVG STD AVGS STD8 N12 NTR 1 48186...48.186 9,728 60,176 4,t760 0.000 32.000 2 52,393 56,599 7,143 65.110 2.632 0,00 32.000 3 54.751 59.468 6.801 67,683 2,216 0000 32 10008 4 56,206 68,572 7,023 69 013 2,367 0,001 32 000 5 57 183 61,0b9 6,245 68,589 2s258 a0, 000 32,000 6 58,377 64 347 6,079 71384 2.044 0,000 32,000 7 59,346 65. 163 5.777 72.032 2.448 0., 000 32.000 8 60,3109 67 044 5,262 73.380 1 959 0 000 32,000 9 61,249 68.771 5,502 75,410 2 101 0,008 32,000 10 62,174 70,497 4.85Q 76 373 1,937 0e000 32000 11 63,062 71,949 4 756 77*739 1t718 0,000 32,000 Figure 23b Parameter values of individuals with increasing phenotypic values during five replications of bulk population breeding for 8-parameter Ridge (Sheet 2 of 3) 81

12 639.51 73.725 4,860 79.245 1,624 08100 32,000 13 64,766 74.553 4,059 790421 1 348 0000p 32,000 14 65*512 75.209 4,275 80.507 1 477 09000 321000 15' 66,182 75.553 3,926 80.275 t1491 0,000e 32000 16 66.831 76.577 4'124 4 81 2 6260 2 0E000 32,e00 17 67.454 77.407 30789 821t1 1.622 0,000 32,000 18 68,061 78.389 4,154 83 132 1I509 00 00 32000O 19 68,721 80,603 3,028 84.054 1.t88 0.000 32,000 20 69.325 80.795 3,209 84*456 1.320 0,000 32,000.MAXIMUM VALUES GEN EFF AVG STD AVGS STOS N12 NTR 1 49.311 49.311 10.808 60.466 7,200 0 32 2 530599 58 850 8,250 68.884 3.175 0 32 3 56 255 61 568 7,462 69,595 3,313 0 32 4 58.123 63,728 8,092 71t.62 3,050 0 32 5 59,104 63.026 8,406 72,328 2,487 0 32 6 59,984 65,286 7,213 720343 2.952 0 32 7 60.736 660474 6,961 7307186 3681 0 3; 8 61.783 69 110 5,753 74.820 2,366 0 32 9 62,538 70 574 7 216 78 131 2,523 0 32 10 63.291 720314 5s839 77.533 2.753 0 32 11 64 150 74,239 6.329 80 649 2,144 0 32 12 65 157 76.229 5,983 82. 81 2,278 0 32 13 65,888 78.678 49753 83032 1.428 0 32 14 66.,93 77 891 5063 84 035 2,023 0 32 15 67,544 79,453 4.483 830985 1,874 0 32 16 68,359 89 587 5 632 85.782 2,308 0 32 17 69.111 81.144 40642 86.522 2,072 0 38 18 69,960 84.384 4,894 90.067 2.416 0 32 19 70.785 85,641 30865 90,180 1,795 0 32 20 71.607 87,231 3.671 90.872 1.705 0 3t MINIMUM VALUES GEN EFF AVG STO AVGS 8TDS NIZ NTR 1 46,517 468517.0966 59,804 2.417 0 32 2 50,978 5.5298 6 359 63 684 1,859 0 32 3 53,711 57 727 6249 66 574 1,2386 32 4 54,912 58,130 50664 67.473 10348 0 32 5 565248 59,950 5 133 66.960 2 080 0 32 6 57,489 62 303 5.091 68.948 1.523 0 32 7 58,421 64.012 4.774 70374 1,404 0 32 8 59 496 63.228 4 244 70 526 1 673 0 32 9 60 570 67 650 40512 73.441 1 563 0 32 10 61 477 69*636 3.718 75.127 1487 0 32 1 62,266 69 283 3,974 73.808 0,956 0 32 12 62,975 70,66,6 3,422 75,618 1,074 0 32 13 63,643 71 661 3.563 76.177 1.226 0 32 14 640278 72 155 3,724 76e728 0e621 0 32 15 64,863 72e967 3.073 76,007 1313 0 32 16 65,407 72,872 2,076 76.904 0846 0 32 17 65,928 73,516 2*697 76.776 1,085 0 32 18 66,382 74.101 3.111 77,182 0.713 0 32 19 66,889 76 018 2,497 780538 0647 0 32 20 67,361 76,333 2,062 78,743 0,729' e 32 Figure 23b Parameter values of individuals with increasing phenotypic values during five replications of bulk population breeding for 8-parameter Ridge (Sheet 3 of 3) 82

0ISO1 ~ 240 3 0 40~ 480 660 640 ~tN-T V!-JUAxL INDIVILUUAL Figure 24a Phenotypic value of individuals during mass selection for 8-parameter Plane using Gene Action 4 85 a~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 853

IL 0 80 160 20 30 400'80 560 640 INDIV AI.. INDIVIVUAI. 00 80 6 240 1a6 s 30 00 90 5660 6:.0 INOIVIMDJAL INIVInUAL I 0 0 X 180 240 320 400 480 560 640 INDIVIDUAL INDIVIDUAL II U IR 0 80 160 240 320 400 480 56 640 INDIVIDUAL INDIVIDUAL Figure 24b Parameter values of individuals during mass selection for 8-parameter Plane using Gene Action 4 (Sheet 1 of 2) 84

INDIVIDIAL INDIVIDUAL I' ain xP 0 30 16U 240:3IO0 400 480 560 640 INDIVI UAL INDIVIDUAL To I o 8. 60 240:3.0 00 1 seo 0 tNO I v I OU Io~tIOL I INDIVIDUAL u r IINDIVIDUAL Figure 24b Parameter values of individuals during mass selection for 8-parameter Plane using Gene Action 4 (Sheet 2 of 2) 85 r1 a INOIVIOUAL INDIVICLAL Figure 24b Parameter values of individualq durinc Ma4z eleciin fnr A-parrnmt-a PlneusngGee cio 4(See 85f2

- 10 o Ii iSO 24O 3M ow MO Mo. a~ INO IVI DUAL INDIVIDUAL Figure 25a Phenotypic value of individuals during mass selection for 8-parameter Plane using Gene Action 10 86

I NIVIUAL INDIVIDUAL cU x'. 80 160 240 3a0 400 0o0 5B0' O INDIVIDUAL tNDIVUiAL *"4o I. 0 90 160 B40 30 400 480 S0 640 Figure 25b Parameter values of individuals during mass selection for 8-parameter Plane using Gene Action 10 (Shet 1 of 2) 87 87

0 80 160 240 320 400 480 560 540 INDO! V IDUAL IND I DUAL xI. La 00- I I'...... 0 80 160 240 320 400 4O0 560 640 N IVI EUAL INDIVIDUAL C I 2 0 0o 160 240 320 400 4o40 GO 640 INDIVIDUAL INDI VIDLAL M]u0 0 oa _, Figure 25b Parameter values of individuals during mass selection for 8-parameter Plane using Gene Action 10 (Sheet 2 of 2) 88

t-0 Cso N8 O O — I, — ___ i ___,!! _;;,_ r. 0 8W' 160 240 3O 400 480 S60,40 INDIVIOUAL I ND IVIDUAL Figure 26a Phenotypic value of individuals during mass selection for 8-parameter Plane using Gene Action 3 89

INO1VI':AL INDIVIDAL In, Cfl 0 80 iSo 2r40 320 400 4O 560 640 INDIVDIDUAL INDIVI DUAL ru INDIVIDUAL INDIVIDUAL Figure 26b Parameter values of individuals during mass selection for 8-parameter Plane using Gene Action 3 (Sheet 1 of 2) NIV 90DUAL N V A o 80 1o I 2l0 3 0 4 4w 800 INDIVIDUAL INODIVIfDAL Figure 26b Parameter values of individuals during mass selection for 8-parameter Plane using Gene Action 3 (Sheet 1 of 2) 9o

o 80 160 240 30 4.00 ~'00 560 640 ur 0 80 160 240 3a0 400 40 860 640 INDIVIDUAL ]IND IVIDUAL u~,t (.... x t C. 0 80 160 240 3I0 400 480 Soo 640 INDIVIDUAL INDIVIDUAL ~..i,;...., I.......," a i l O 80 B 160 24 3 00 0 3D0 560 0 IND V I DUAL INIVI UAL 91'..n. OO -~IWAW x gre 0 8C X t6Q Z~Q ~ ~OC~ 8An O 40 640 I N 1 DVlAL INDIVIDUAL Figure 26b Parameter values of individuals during mass selection for 8-parameter Plane using Gene Action 3 (Sheet 2 of-2) 91

.0 to a'1 3 ) 0 0 0 80 160 230 O 400'.480 660 640 INDI V IDU JAL I N IVIDUAL Figure 27a Phenotypic value of individuals during mass selection for 8-paraneter Plane using Gene Action 9 92

0 ou 160 o40 3X. 0 o bO 60 INDI V IDUAL INXDIVIDUAL In In C, r "LInVIIUAL AL IL 0 80 160 240 320 400 400 560 640 INDIVIDUAL INDIV IOUAL 0 80 160I 240 320 00 m m 40 INDIVIDUAL INDIVIDUAL Figure 27b Parameter values of individuals during mass selection for 8parameter Plane using Gene Action 9 (Sheet 1 of 2) 95

oBl~~~~~~~~~:~~~ o I NO IVIDUAL IND VI)nUAI.. LVUAL INIVIDUA 00 s I160 30 400 240 560 640 INDIVIDUAL INDIVIDUAL Iq by~ I,. I.., 0 80 160 240 3W 400.400 560 640 INDIVICKAL INDIVIDUAL 0 811o ISO 240 320 400 40 560 640 NOIV IUJAL INDIVIDUAL Figure 27b Parameter values of individuals during mass selection for 8-parameter Plane using Gene Action 9 (Sheet 2 of 2) 94

0 16 0 32 it 64 06Zi e 0 f 1 l Z 0 S 10 1S 80 GENERAT ION Figure 28a Averaged population mean and standard deviation of phenotypic values for five replications of mass selection for 8-parameter Ridge using Gene Action 3 and three population sizes: 16, 32 and 64 95

30028 NDVLP 3 NVALU 2 P-INV 0,0000 PCR0S 0.b000 PCRL_ __0.5_00 __ PMUT 0.0000 NPOP 16 NSEL _..__.___ LGEN 20 JNP.AR- 8_ NSEQ' 8 NREP_. 5 IX I IPAP_ ____ IPBP' 1AE__ __A __0 IPC8 0 3029_a_.~,,....~.... _ 1 41,606 58976 25258 11077 49266 39450 22494 34951 ~ 25-403 __.47_. _5.1....4...2836_ 3238..7 48630 20589.1830 305086 _ 21491 3 50,046 21952 34525 51038 52512 25394 30198 24330 11162 2__2.z...___S2 2.-.. 47.053:_i.38976..._21A.429... 26844 2.,.2_44_17 32671 26971.1.4206. 6 62,901 38445 28951 18120 25380 49353 48225 60994 49458 _ 6 _56.e_949 49_27.._4._ _._..0... 1_~.E_47... _3..P_.2.e..._2...5._...... _M0i__-63^9119_492 7 4-5425-.a36.4 2A-473..^222 6329_4 ^597 40 49.67,431 52518 51827 12303 12221 32239 24395 63936 59267 69_ -..___.965_.._52646........50 42.44122_5 _6S. 5929_2.... 93 5 6.........4.9 63., a.4. 8 8.... 63 159 79,048 52519 36863. 57054 51085 32767 24503 63487 59160 i..e16_6___ 8._ 38...57... 41__. 37.9 55 3_ 3723..5_7_0. 5.1.__40908..24495 63487..9_ 57599 207 81,671 52735 37253 57101 51077 40959 24503 63487 57599 3 1 3.1,73 L.. 52_5._7 2_ _ 2_Z..9_. _ _523 59_,_....9_9__4 _749_ 229 81.972 52525 37252 57024 50170 40959 24503 63487 57599 _2_47....7.... __2, 0506....._,_~25.._.3.7.52 57..2.4... 51077 ~ 40959 24503 62994 575_99 249 82,194 52525 37252 57024 51077 40959 24503 62994 57831 _-28. __8....... 263.. 5_2525-....... 25_... 5 57-089..5.7...5.. 77. 40908 24503 62994. 5S7831._ 316 82,286 52525 37252 57149 51077 40959 24503 62994 57831 3A2802 8529752_7-__1-s>58....5 7077 4.0909. 453 62994. 83 I 55,200 31338 10644 42964 20148 37819 28407 16201 22554 4..__._22 1 626...-.35302_0052 30522...9292 33938 29241 3 0800. 184333 6 64,733 35567 31372 48981 29467 33549 10691 56648 59655 2_0... 0 _6.~,06.57 3.....:5583_....2.a9.7.L...2.97J.. L....21 3463 327.. 43519.. 27644.0173 4_0727 37 66,769 34687. 39413 53410 52347' 53441 31189 53248 46908 49 70 7t.8...356_ 4122 6. 34 _09___48._3.9 3276 932 1 2 99_5_49 97 74,221 34306 33807 6067'1 53222 54016 59951 57311 53596 12..1..._,e8 -8_4.....34_9._..3.4314.. 5673 -S__._0.5.4527.5991....608i.9..._:.. 53375 130 75,091 34r812 34314 57506 53029 54377 60031 60416 53375 _4A1L._..7_5_ 3481_5 3.._43_14 567.._._ 6 67... -_8~_~9082.5._..45267 5.9595.1 60290 55679 144 78,532 35169 17914 56738. 53247' 54271 59903 57373 50939 1i __9_7.26 1iZA 2_9120 1403 3693 558908 22438 22450 6464 3 43,135 47263 25113 2750 21257 17706 28854 20769 13399 4 A__ 43347- i793L._7_L34 _3977 50492 42263 23201 16948 21982 10 50,836 51773 314.53 31411 27905 34391 1'9374 50036 5272 2~6 _ 5.27_, 3641?7__3_.82._ _3.2255 20883 344955 19489 41980 5230 34 62,859. 30191 4056 61052 49937 32331 28'558 35830 20350 55a. 64,077__ 37 6 _95I 142 5___50___ 4452 _38915 32578 49151 A9S888e 87 65,859 45368 14321 51074 43505 41535 32347 42623' 24611. 98 a_____6 4_3__9 3308_0 15_349 518 18 L._..._ 43423__.33191 82376 49263 279551. 109 67,683 37119 16343 50433 4341,1 42627 26500 32767.27e84 __117. 6,_39.8_ 4 _055___ 20_L 9 4351 41383 _32767 4273_ 24511 Figure 28b Parameter values of individuals with increasing phenotypic values during five replications of mass selection for 8-parameter Ridge using Gene Action 3 and population size 16 (Sheet 1 of 3) 96

118 71,404 385071 16343 51413 44032 40995 26432 46831 27696 143 74,273 34806 18721 51408 43409 42584 32580 42735 28767 153 74,798 33272 18173 52482 43409 40999 26683 45055 28799 17L 75,396 34815 18109 SS550 43885 40956 25600 42735 28751 2007 76.,280 3481 t 181 10 53709 43885 42584 26564 42735 28671 216 76,391 34615 18110i 52735 43885 40995 25530 45055 31743 228 76,391 34823 18110 53487 43885 40956 25530 42735 28671 243 76.453 34623 18110 53694 43885 40956 25599 42735 28784 261 76,492 34823 18114 53679 43885 40956 25599 42735 28671 295 76,493 34823 1811 53680 43885 40959 25599 42735 28671 1 38,742 21478 53362 11192 29068 29511 22112 50475 50131 2 42s915 16597 32135 49089 22887 26290 34517 15164 5125 3 56.518 11712 5082 61786 63612 26683- 39982 38608 13268 tI 57,4i5 2,P33 22082 28169 15173 29259 25683 34761 21395 36 60,1t32 7891 5301 30683 19360 50270 32830 31309 22668 65 64,469 5612 12159 63319 65019 45636 39424 40262 20304 88 66.0f77 5564 12178 6t319 64941 43003 39458 47103 32767 107 66,564 5624 8978 603308 64945 45124 39458 46406 28671 J14 68,853 57b t 8841 6M33 65099 46719 39457 47103 31919 122 69.22 59 88 595 8 60331 65099 46591 39457 47103 32943 131 69.411 6531 8831 60331 65097 46380 39457 46406 32943 132 69P.69 9704 8850 641319 65019 46508 39457 47103 33791 148 69.691 5705 8813 60331 65099 46803 39457 46406 32943 153 69,835 5708 8850 60331 65099 46803 39457 47103 33967 169 69,839 573 8631 60331 65099 46803 39457 47103 33791 179 69.870 5706 8031 6i331 65019 46803 39457 47103 33967 193 69.895 57r5 8 831 6 33 64950 46803 39457 47103 33967 246 69,898 5705 8831 60331 64943 46803 39457 47103 33967 269 69,99070 I75 8831 60331 64937 46803 39457 47103 33967 277 69,905 P7Ps5 8813 60331 64937 46803 39457 47103 33967 i 3,4315 l1113 33189 27041 30923 14952 45929 22429 10839 3 57,815 53338 22094 33516 10064 29792 22521 49197 41923 4 58.534 24631 17167 28929 13546 26173 20267 50486 57250 24 50,919 44274 48629 32807 1867 49121 45057 46290 41167 48 61.699 4880o 32904 26482 7344 38598 31651 27794 23692.51 63,301 5s451 608001 1514o( 2971 45549 41974 38373 23543 52 63,320 5(340a 62556 8283 187 45295 38507 52065 35581 55 65.337 5I5P2 53361 15286 1994 47107 39636 38598' 29495 85 68.239 54l7 5319d 15363 1168 45543 40414 54491 49095 87 70,742 56206 57393 15391 1199 47091 40960 54471 42239 92 71.192 56674 54143 15329 2954 47106 37887 40959 31542 98 74,364 56674 54143 15333 2954 48665 37195 46726 31542 124 74.984 56674 54111 15332 2955 48665 37195 46726 32767 135 75,552 52P95 54111 15237 2939 48665 37908 54975 45055 136 76,848 56674 54143 15230 2954 4866i 38580 54918 46281 146 76,848 56674 54321 15236 2960 48665 37908 55041 47103 160 77,245 56674 54143 15233 2944 48665 37215 54975 46281 171 77,264 58674 54111 15233 2954 48665 37195 54975 46281 AVERAGE VALUES GEN EFF AVG STO AVGS STU8 NIZ NTR 1 429,13 42*813,1 093 55 003 3,532 00 00 16,000 2 43,593 44.373 9.137 54,739 2,885 0,000 16e000 3 46,290 5. 66f 6 676 5.9 269 3,254 00 00 16,000 4 48,477 5.0~39 6,877 63. 90 i,816 0,0000 t1000 5 50, 66 1 59171 4,902 64.855 2,693 00 00 16,000 6 52.383 61.218 5 694 67,751 1,4888 0.e 0e 000 7 54,313 65*896 3.893 70,486 1.162 0 002 16,000 8 56.e62 68.299 3, 560 72 431 0,789 0,.00 16,000m 9 57.618 7?.067 3.297 73.550 1,265 0 000 16,000 1 58,986 7193,1 2,547 74.244 0,906 0, 00 16,000 11 6,179 72.17 2.590 74.802 10817 0,000 16,000 12 61,211 72 2 7",5( 2,148 75 113 0,710 0 000 16,000 Figure 28b Parameter values of individuals with increasing phenotypic values during five replications of mass selection for 8-parameter Ridge using Gene Action 3 and population size 16 (Sheet 2 of 3) 97

Al 62.210 74.205 1,483 75*909 0,484 0.000 16.000 14 63,1 03 74 712 1,565 76 349 0,204 0 00 16 00.0 15 63.875 74 676 1 584 76 296 0 236, 000 16.000 16 64,574 7,05 5 1.445 76.466 0 175 0,000 16,000.Z. 65,.['17 9 74ad,9 1 574 76 520 0 117 010, 1.6. 000 18 65,713 74.765 1 685 76,462 0 145 0,000 16e000 19 66.202 76.014 1,341 76,380 0*259 0,000 16,000 20.66,649 75 1.45 1209 76,402 0,173 00000 16,000 MAXIMUM VALUES..'GEN EFF AVG $TO AVGS STOS NIZ NTR I 46,454 46.454 13.616 61.899 5,670 0 16 2 47,P41 47,676 11,066 61 320 4,447 e 16 3 50,381 5-7 768 9,094 64, 282 5862 0 16 4 539266 61 919 7.847 69 100 2.316 0 16 5 55,517 4 52 1 10,027 69,635 5,717 0 16 &. 56..397 63 966 7,441 72 349 1,866 0 16 7 57,968 69.21 4,331 74,271 2.189 0 16 8 59,343 70.856 4,920 75 178 1,95 0 16 9 60.783 72,304 4,275 75*756 2,039 016 10 61.s86 72 657 5,197 7M6888 1,914 0 16 11 63.58 73 772 4,683 77.750 3 073 0 16 12 64,098 75,547 4,127 77 951 2,245 0 16 13 64,984 7 122 2,670 80 530 1,104 0 16 14 65 713 872, 293 3 154 8 1558 4083 0 16 15 66 314 8. 12 2,453 81.846 0,535 0 16 1. 66 857 8C.609 2. 1S2 8 2027 0.329 0 16 17 67,408 8(.453 3.450 82.082 0,267 0 16 If 68, 159 8,0925 4,427 82 175 0 322 0 1.6. 19 68,823 80.769 2,804 82,235 0,764 0 16 20 69,422 80.11 2,184 82,269 0,662 0 16 IN.IM.UM VALUES GEN EFF AVG STD AVGS STDS NIZ NTR 1 3.3..7.90 36.790 8.472 46,665 1.239 0 16 2 38,9038 36808 6,356 50,468 11099 0 16 - 41..460 46,566 5,496 5549613 1 566 0 16 4 43,886 48,756 5.799 57.025 1.478 0 16 i 465-62 56, 117 3, 213 60 735 1,225 0 16 6 48,776 58,369 3,031 63,375 1l 72 16 -7 5-62,8 61 740 3.488 65.881 01 59 1 8 52,601 65 392 1 777 68. 890 0,295 e 6 -2.4418. 68,577 0,551 69,543 0,105 016 10 55,917 69.402 0.276 69,744 0,042 0 16 L 57 1.58 69,573 0,201 69 827 0 0140 16 12 58.198 69 641 0,215 69 855 0.013 0 16 -4 -.59,076 69.11 0*180 69.863 0,033 0 16 14 59,837 69.726 0,178 69.875 0.024 16 15 60,469 69.617 0,173 69,875 0.023 e 16 16 e61, 65 69,.7d9 0 194 69.884 0,015 0 16.17_ 61.576 69,749 0.148 69,897 0,08.2 0 16 18 62,o31 769 59 0 190 69 900 0,003 0 16 19 624.2 s69, 665,198 69,900,00 0 16 20 62.794 69. b9 0213 69.901 0,05 0 16 Figure 28b Parameter values of individuals with increasing phenoty, ues during five replications of mass selection for 8-parameter Ridge using Gene Action 3 and population size 16 (Sheet 3 of 3) 98

3(0WI29 MStA 6/26/73 NOVLP 3 NVALU 2 PINY 0,00Qm PTRA 0 0000 PCROS 0,5000 PCRQL. 5000 PMUT 0 6 91 CV.'0*000 NPOP 32 NSEL 8 LGEN 20 NPAR 8 NSEG 8 NREP IX 1 IPAP IPBP I IPAF 0 IPCS i 41 606 58976 25258 11077 49266 39450 22494 34951 25403 2 47.945 28^14 20356 32387 48630 20589 18130 30506 21491 3 50,046 215-2 34525 51038 52512 25394 30198 24330 11162 5 52,362 47053 3$976 21429 26844 24417 32671 26971 14206 6 6p,901 3R44b 2651 18120 25380 49353 48225 60994 49458 27 64 163 29092 30~10 55414 53587 47350 48246 31374 1.834 43 68 162 42477 28139 31769 33150 56855 49600 21966 8649 54 71.535 32742 16668 51236 51918 55835 47008 24655 12587 72 74,405 32663 16961 59415 56861 53786 48917 24588 12830 164 74,873 3255o 26879 53247 59647 57670 49151 55695 46709 1868 77,2506 35378 i6376 63807 57295 52413 46831 55026 47012 200 78,870 367fi 23443 57623 49263 57091 48367 49086 46713 233 79 403 3364d 16319 59378 49201 57595 46079 55070 491t1 240 84,785 36223 19451 63883 59676 56837 48390 57150 48761 428 85,233 32772 16383 61439 59648 59391 53247 55136 46759 480 85,369 3251d 1.6447 61439 59679 60415 55529 57342 48818 56? 85,629 3:2768 16384 63495 59789 59073 53247 55039 46767 1 388,76 31741 29120 1403 36938 55908 22438 22450 6464 3 43,135 47263 25113 2750 21257 17706 28854 20769 13399 4 43,547 17931 31l34 37977 50492 42263 23201 16948 21982 10 50,836 51773 31453 31411 27905 34391 19374' 50036 272 21 55o425 52003 50622 7073 25982 47818 33681 22252 22332 22 57 678 26.67 24934 34401 12327 37818 37638 48080 45199 27 63,132 5b669 38935 53366 26586 25414 18336 36189 22763 43 64,301 5^039 34259 22498 35015 31421 19300 57991 50281 86 64,575 47$1 35607 32735 16791 24707 24323 37384 17454 129 69,512 49779 38911 48957 58517 32445 18432 45156 32904 164 72,480 5798g3 44274 33945 21656 37628 24837 46280 32636 20? 72,540 A971? 36915 55489 61929 33224 27074 46944 33712 213 76,501 53314 40146 59383 46846 37664 19507 48320 34600 216 78,392 49167 34816 56326 53760 37899 24323 49137 36686 245 78 417 4910.3 34816 55281 52053 49138 37843 49697 32085 260 78,970 48144 32831 60609 $5061 37682 17541 51214 40783 371 78B990 50 116 47564 57345 49408 37902 24786 51592 40783 385 7P9713 56324 48063 53255 41449 37651 25643 49141 39376 420 80.152 57343 47116 53255 42241 37600 24786 52153 40522 475 80 181 56324 48127 51208 41493 37855 18477 51493 39936 477 80,563 56324 48063 55368 42241 38639 25363 52113 42927 499 81. 066 57343 49074 52431 42239 37864 25601 51664 42927 552 81,672 56324 48140 52023 42241 37916 24319 52207 42934 Figure 28c Parameter values of individuals with increasing phenotypic values during five replications of mass selection for 8-parameter Ridge using Gene Action 3 and population size 32 (Sheet 1 of 4) 99

6.03 82,009 57 43 49087 52431 41727 38620 2476 51640 41551 1 33,315 19113 33189 27041 30923 14952 45929 22429 10839 3 57,8e 1_5 53338 22094 335161.10064 29792 22521 49197 41923 4 58,534 24631 17167 28929 13546 26173 20267 50486 57250 19 6ib,-134 17512.12985 48001 36632 50.00 4751Z47 304 1195.3 53 67.5i5 26865 15021 42121 24550 60859 48240 23404 8319 98 67,536 46 526 249 53244 28591 47609 31139 48090 38531 143 69,91 42138 29308 55742 51327 36511 34404 42630 20819 178 70,582 34638 16966 47035 50537 57743 55265 41968 22803 193- 74602 33945 17151 57855 49408 40893 27941 40555 22889 209 77,.564 4009e 26715 54968 60381 61909 57040 42928 30678 353 77,973 32443 15330 55869 49151 55359 44933 38911 23211 3&65 79.166 31587 15612 63671 61056 52418 46843 40951 26495 421 80,758 32399 1490 61438 57513 59134 49151 44275 30671 447 8,4'23 32407 15384 61885 57344 57553 49151 44275 29728 548 81.719 3240 15366 63487 61014 57343 49247 40970 25599 I 40,291 3.018 6779 51.811 19459 19523 32435 24028 29811 3 50.279 32476 12491 22918 26284 28170 25592 21675 17647 5 51.981 P1251 31276 39251 21576 52634 51754 28287 33397 8 52,012 4552 29174 21759 28514 26961 32342 32187 26048 20 57.998 3 S195 21410 53430 31944 33290 29350 18115 18888 29 60,843 5535 53767 11189 18757 33204 17871 33423 25827 88 63,216 5108 38460 25088 26597 40886 24702 35667 34188 96 66'903 2874 1.3653 51873 37704 34915 19805 31999 26147 140 665,985 52225 4908g6 27023 30717 32790 18495 55103 43422 146 7O.623 53299 38861 32832 24459 41471 25343 60479 44960 498 71,633 52479 40650e 33727 24719 42492 18895 56287 45587 199 73,924 4s65 34561 32095 16391 41987 25327 57453 44964 5.4 76,921 535249 41055 33563.16439 41987 25357 57261 47635 296 77,115 54587 39420 40326 24000 41987 24927 56109 47607 305 77,796 5321 A40650 39999 24064 41831 24271 55473 45599 312 7'8,368 5~981 41i87 40351 24062 41979 24316 55295 45119 S33 78,485 5.25~4 40951 40764 23985 41984 29919 55391 47488 355 78,725 53^59 41303 40515 23999 42335 30172 55244 47519 AB6 78.765..51969 40578 39932 24049 42343 24383 5534 47487 403 79.186 54417 48247 39931 24051 42343 29919 57119 47488 A35 79.,266 5441b 48250 40447 23795 424965 3195 55281 47615 457 79.274 64637 45498 40575 24177 42496 24883 57t132 47599 465 79,484 54526 47173 40195 24000 42343 29935 57152 U.47663 476 80.042 54591 45253 40966 24255' 42344 29935 55314 47615 486 80.354 5e4539 4525.3 40194 242SA5.5 243495 299.16 852. 47799 498 80,546 54589 45567 40194 24191 42495 29916 55314 47431 s53 B,80605 54529. 45509 40192 24205 42643 29887 55295 47432 598 08,764 54642 45567 40067 24383 42647 29884 552915 47607 1 4A.,5172 33200 1881.3.241641 6269 24529 34132 9872 28466 2 56,217 479s19 54023 21818 1 5944 32246 356291 50176 277149 17 5.l73i 54506 38018 3041:7 15775 40936 22540 23725 34495 19 65,318 51500 22938 26853 16915 53848 39043 48148 38470 22 8 84.196 6127:9 55171 31414 35.058 50877 24002 48312 3i313 34 68.463 52459 43583 34418 17748 30994 24575 50736 55987 73 75.954 486383831 321.01 159344 40097 24387 54049 42376 118 76,579 57439 46884 33151 16367 45162 2828a 53551 41380 i 7ZZjSS 54.9A. 4 533.6 51.15362 4851 33303 48135 401671 223 78,223 66532 55054 32369 16268 46053 36803 53991 41343 23.7 1..6.08441 542 35 3.1238 14207 47114 37191 537289 41191 259 78.735 59364 59315 32160 15810 54378 40963 51677 38948 2.83 7,,96.5 60442 56484 30047 15756 49015 33212 51485 41743 323 79,146 578649 54059 30582 10236 53095 44483 52255 41751 26. 79g,31 573?_Z5 543Z7 5 354 16463 48274 4 3660 51498 41940 337 79,435 59390 53268 42889 22479 54362 40959 53301 40867 352 80,924 59.04.0 53017 3:193 15362 52232 44540 52191 40731 423 82,651 61567 57360 32672 16303 53359 44543 522-55 44099 470 83,225 6t951 58127 32886 16447 54275 44732 52223 43991 Figure 28c Parameter values of individuals with increasing phenotypic values during five replications of mass selection for 8-parameter Ridge using Gene Action 3 and population size 32 (Sheet 2 of 4) 100

520 83,348 611 59h2Y 41920 22925 53481 44287 54005 44031 597 83.442 6;34^ 593<4 4215 23154 54047 44799 53215 44095 602 83,^G3 t 3o1b t6062 41887 22530 54340 44731 52277 42004 607 83,780 63bl 6b3 3 a268 22335 54043 44551 52223 40956 AVERAGE VALk.S GEN FF AV STD AVGS STD$ NII NTR 1 43. A4?, P 8 10. 37 55 720 4 775 0,00 32,000 2 45.9yW 469, 2 9.18a 59,700 3,762 0,000 32,000 3 47, 74 1.244 4 421 61 251 4.167 0,00 32,000 4 49,30L3 5390 b,707 63.533 2 379 0,000 32,000 5 51.42 b5.797 b,8:? 67 871 2.424 0.00 32,000 6 53, 3':^ 3. 12, 693 70,733 1,762 0,000 32,000 7 5., 2 6 R3,387 73,073 2 385 0.000 32,000 8,56.75b s8a.5,0764 74.597 2.408 08000 32.000 9 -Ru12i LS 7-.4 1 4 6J3 75,999 1 635 0 00 32 8000 10 59665 72.304 4 100 77 005 1.288 0,00 32000 11 6S i47~:.~? 4 1df 77la 7:.. 77.711 1*093 9,00~ 32,000 12 62. 5 f 74 ^, 3,262 78,503 1,571 0 p0 32,000 13.63.rb 7 S'sr 3. 8 78 597 0,868 0.000 32.000 14 64,b62 77.13 2 769 80.313 0,957 0.000 32,000 15 b4-9. 77.349 ~.402 80.178 t,064 0,o00 32,000 16 65,71t2 77,9 2,331 80.717 0,677 0.000 32.000 17 b6,ti 7 78.5s 2 021 80.959 0,749 0,000 32,000 168 67. 2 79,?7, 2.39 1 81.375 0,569 0.00I0 32,00 19 67,8 jw 7.223 1 917 81,551 0,594 0,000 32,000 20 8. 423 79,2e 1.883 81.643 0 569,0 000 32000 MAXIMUM VAL.IES GE N EFF A VG STO AVGS STOS NIZ NTR 1 47,. 4 47. 4 1 1.59 58.18 5,5 5 0 32 2 47,856 5 9a I tl.03 64, 100 4565 0 32 3 50 415 Si, 3, 732 66 162 5,003 0 32 4 52,R78 57.770 12.128 70 196 39 239 0 32 5 54,736 65.370 7 586 73,062 3,880 0 32 6 56,9m3 67 734 8 715 74,944 2,560 0 32 7 58,664 70.71 10 608 76.323 3,874 0 32 8 60.0h4 7.,7g9 6 131 77.639 3 283 0 32 9 61 414 75. 1o. 6 376 80. 00 2,656 0 32 0 62,716 77 217 6 11Q 81 426 2,085 0 32 11 63.93 76 538 5,425 81 982 1 369 0 32 12 65.227 79 126 4,893 82.74 1,560 0 32 13 66.3,2 7,241 47t13 82 132 1,337 032 14 67,3;1 8.7o)6 3,841 83.712 1.562 0 32 15 68.171 7,0936 2,897 83, 34 1,324 0 32 16 68, 95 80 882 3,020 83,631 0,884 0 32 17 69.655 80.664 2.835 83.822 1 267 0 32 18 70.321 81.642 2.855 84 616 1,131 332 19 70,929 81,868 2.618 84,490 1,091 32 20 71,429 82.150 2,975 84*520 0,946 0 32 MINIMUM VALUES G~. E.~.PF AVG STO AVGS STDS NIZ NTR 1 40,660 4. 660 9,670 53.215 3,250 0 32 2 43*416 45,665 8,217 53,337 2,880 0 32 3 44 779 47 505 5 626 58.266 2 514 0 32 4 46,?89 5,.118 7,297 59.489 1,719 0 32 5 48 929 55, 045 6.277 62.698 1,749 32 6. SL,5_A l 5A7.-_99.4 4,A_146 67.269 0 532 032 7 52 341 59 011 4,449 71.430 1.414 0 32 8 54_.42 644,264 3,507 72,047 1 711 0 32 9 55,a8 64.922 2 583 71,448 0,880 0 32 10 56,93. 66, 80 2,700 73.054 0,565 0 32 Figure 28c Parameter values of individuals with increasing phenotypic values during five replications of mass selection for 8-parame.ter Ridge using Gene Action 3 and population size 32 (Sheet 3 of 4) 101

11 58, P7 6 47 a,376 74,733 0,911 0 32 12 59.22 7, 12 1,674 77 227 0,669 0 32 X3 6.60, 71 2 3 I.356 76 215 0.388 0 32 14 6.1 1 74,359, 504 78,664 0 333 0 32 15 62. 54 7?575 0 1 343 78,845 0,413 0 32 16 62.97 7. ^ 4 1.6 78,780 0 400 0 32 17 63,76 7 5 <,8~ 989 79.232 0 381 0 32 18 64,475 75,.67 ~,871 79.448 0, 181 32 19 65.79 7S 957 0 934 79,284 0,247 0 32 20 5 6 2 7.43,83.79 978 0,098 32 Figure 28c Parameter values of individuals with increasing phenotypic values during five replications of mass selection for 8-parameter Ridge using Gene Action 3 and population size 32 (Sheet 4 of 4) 102

MS1A 6/a2/76 NOVLP NVALU PINV 0, A PTRA 0. C PCROS 0I.50A PCROL' 0, 0 B PMUT 0r00 CV 0 0.M (l NPOP 3 NSEL L(~EN NPAR 8 NSE 8 NREP IX1 IPAP IP8P IPAF IPCS 1 41,606 5^76 5't58 X1077 49266 39450 22494 34951 25403 2 47.945 21l-v S05A66 32387 48630 20589 18130 30506 21491 3 5O v46 S!'2 64525 b1038 52512 25394 30198 24330 11162 52,362 47053 36976 21429 26844 24417 32671 26971 14206 6 6P. 91 ~34, 2bb 1 6120 25380 49353 48225 60994 49458 27 64,163 29P2 3O'10 55414 53587 47350 48246 31374 18334 43 68.162 49477 26139 31769 33150 56855 49600 21966 8649 54 71 535 3274 1b he$ b1236 51918 55835 47008 24655 12587 72 74, 45 3E6f3o t6i1 59415 56861 53786 48917 24588 12830 164 74 873 32550 P66/9 53247 59647 57670 49151 55695 46709 168 77,p26 3^376 3- 537 63867 57295 52413 46831 55026 47012 2e0 7.8870 3f7F 23443 57623 49263 57091 48367 49086 46713 233 79. 43 S364b 163l 9 59378 49201 57595 46079 55070 49151 240 84 785 3223 19451 63893 59676 56837 48390 57150 48761 428 85 233 P7772 1t6bO 61439 59648 59391 53247 55136 46759 480 85,369 3.P 1t 1.6447 61439 59679 60415 55529 57342 48818 560 8e,62 3P7? 163564 63495 59789 59073 53247 55039 46767 I 38,7P6 31741X 2912 1403 36938 55908 22438 22450 6464 3 43. 135 47263 25113 2750 21P57 17706 28854 20769 13399 4 43,547 17931 3 1T34 37977 50492 42263 23201 16948 21982 P 5P, 836 5177 3 31 43 31411 27905 34391 19374 50036 5272 21 55,425 5 50620? 7073 25982 47818 33681 22252 22332 22 57,678 26 67 24934 34401 12327 37818 37638 48080 45199 27 63,132 5 b6t 38935 53366 26586 25.414 18336 36189 22763 43 64,301 5f39 342b9 2249b 35015 31421 19300 57991 50281 86 64.575 479o1 35~07 32735 16791 24707 24323 37364 17454 129 69,512 4R77, 38911 48957 58517 32445 18432 45156 32904 164 72,480 5793 44274 33945 21666 37628 24837 46280 32636 2~ 72,540 a4716 36415 55489 61929 33224 27074 46944 33712 213,76.501 53314 4146 59383 46846 37664 19507 48320 34600 216 78,392 4Q16Y 34816 56326 53760 37899 24323 49137 36686 245 78.417 49103 34616 55281 52053 498 4918 7 49697 32085 260 78,970 4A144 32831 t6A609 55061 37682 17541 51214 40783 371 78,990 50116 47564 57345 49408 37902 24786 51592 40783 385 79,713 5634 480g3 53255 41449 37651 25643 49141 39376 420 b0.152 57343 471 16 53255 42241 37600 2478,6 52153 40522 475 80 181 56324 48127 5.128 41493 37855 18477 51493 39936 477 86,3563 5834 4863 5(0368 42241 38639 25363 52113 42927 499 81,66 57343 49074 52431 42239 37864 25601 51664 42927 552 81,672 5.634 4140 52023 42241 37916 24319 52207 42934 Figure 28d Parameter values of individuals with increasing phenotypic values during five replications of mass selection for 8-parameter Ridge using Gene Action 3 and population size 64 (Sheet 1 of 3) 103

2a6 73,813 35199 15090 55134 57772 49151 41015 48505 38179 269 75.302 35839 15438 57718 55735 47047 40089 54207 40974 3ji0 76.312 33163 8130 61342 57158 48987 39159 53999 51206 353 76. 550 35059 14900 57744 54143 51328 33271 53322 44035 35.7.98.Z1 4..30Z 3.3.44.5.9401 57491.53.25 1 40296 53438 42782 396 82,589 45251 31627 59005 53352 46233 37185 53598 43149 576 83..100 45633 32639 60428 55404 50059 35376 54089 42801 787 83,36 45823 3197 59914 53247 48143 34067 53792 45879 -8.0 844A40 45766 31777 58303 53575 52200 41173 53739 42993 816 84,926 45824 34503 58395 54298 55440 46743 53246 42847.L0A4 __ij53..47155 327262 58942 53226 56162 45527 55348 47388 1 49,928 33731 34169 33876 15224 26257 26081 22787 28334 3. 580.834 356?3 2255 35096 42242 14599 12898 26962 2279 6 55,283 25934 17619 33533 28061 29883 31670 46547 24571 27. 64,015 54453 38528 46266 13968 53647 58931 37821 23597 86 70,829 44841 32541 35986 27000 48113 37662 33541 20330 5-3 _-72,395 385a8 29 2s A326 3 7610.5 2845. 49561. 46 0747 26114 243 73.882 43936 34017 38701 22591 54242 42905 36278 23540 262 77,642 2517.130.66 45075 32473 58479 52527 54285 49090 539 77.881 41023 26111 42971 33032 57119 49038 52128 49183 98 79,467 42931.26044 42031 26438 57858 49052 48368 37438 840 79,504 45055 33692 42799 26877 54057 44945 49175 36469.a3 79.76446..32-.3248 A..4455. 2707?8 53556 44155_ 48522 37269 866 79,829 4592 33055 42815 32216 58363 49151 53226 40908 998 80.,368 46779 3291 2 43275 32366 58092 50995 54249 40830 1021 8,699 4b623 33279 43799 26431 58659 51091 49374 37305 i039 80,927 4607'9 33P21 42042. 26575 58087 51133 51069 37372 1101 80,999 46079 33283 42975 26408 60126 55381 48127 37441 1i26 81,152 414347 331..A4.L96 32446 58346 51005 53238 4099 1204 82.085 47872 37475 42981 26633 61160 57201 49188 37443 1235 82.137 a46s7 32991 43986 33071 61142 57235 49129 37370 1258 82.260 49e83 37903 43002 27392 59710 55298 50427 37446 I 44.458 21285 31651 35793 30942 9977 22015 59483 36111 4 49,631 37234 25648 25556 21046 18286 20449 22792 27691 7 58,927 58291 29.94 52733 24788 57890 29872 6155 55377 8 66,463 55094 37278 49085 53617 40994 24702 25161 7879 429 67,289 35831 14924 39812 22591 59156 49116 59928 35001 147 67.609 5$336 54272 46121 34261 52295 38051 59864 21595.169 74,140 56423 32845 39645 29227 57647 49904 55996 55062 202 74,251 57960 49660 33279 13437 50079 27853 52773 41998 3.1 77,007 61391 49229_ 32342 13977 58159 47100 59883 49652 394 78,232 58384 52955 19659 4672 48332 33315 56076 47396 409 79,301 57387 49189 39019 24674 53355 52876 56714 57617 630 80,382 49280 36599 40640 26785 51425 45503 56642 48123 757 80,516 46345 32775 39222 26880 55359 46631 60167 50653 794 81,122 46294 36656 40959 24207 53420 42701 59638 5115 &4A 8-1-+287. 433S 3353 40.833 26717 52833- 45057.. 5S62- -1221 855 82,191 46336 32767 40905 26993 53408 42544 59615 55855 901 83,7.02 4633. 327.51 40831 26878 55252 48127 61692 58276 1194 83,918 46372 32791 40450 24451 55319 47135 61427 57333 AVERAGE VALUES GEN EEF AVG aST AVGS STDS N Z NTR 1 42.538 4 2 536 109667 55382 5 099 0000 d4.000 2 45. 379 48.222 9,736 60.004 4,03.8 0,000 64.00 3 47,688 52 307 8 835 63,021 3,531 0,000 64,000 4 44 9 744 55.912 7.951 65,272 3,204 0, 00 6400 5 51.529 -58 668 7,980 68,393 2989 0,000 64,000 -6 5.3.2. 61.556 6.894 70?050 2..538 0,000 64,0I9 7 54,74 4,P88 6 933 72 371 2,400 0,000 64,098 8 6,294 6 06.8.60 5 661 73.571 1 931 0.0070 64,00e 9 57,841 7',224 4,984 76.302 1.986 0,00 64. e9 10 59 225 71 679 4.23A 76,750 1i707 0,000 64.,D 0 Figure 28d Parameter values of individuals with increasing phenotypic values during five replications of mass selection for 8-parameter Ridge using Gene Action 3 and population size 64 (Sheet 2 of 3) 104

11 6a0507 73.323 4, 020 78.053 l31a6 0.0 *4I000 12 d6,6.9 74458 4 221 79,156 1 277 0.000 64o000 13 62,777 768072 38087 80,, 352. 10, 0 64 0,, 14 63,791 76,975 3.137 80.745 1.215 0.000 64.000 A15 64.744 78.~75 3.227 81.661 1.06..2 000_ 64.000. 16 65.601 78,457 3.09 82el8 105 15 0 00e 64d 000 17 66 374 78?746 3.151 82 415 0.951 QI0 l00 64,000 18 67,15 79.532 2 573 82. 5 7 4,.804 0,0 00 64 000 19 67,778 7.,898 2.766 83.088 0,948 04000 64,000 20 68,41tS 8.511 2.52 83*422 0 674 0.0010 640000 MAXIMUM VALUES GEN E FF AVG STO AVGS STDS NIZ NTR 43 44,3695 4395 11.959 56.793 6,432 0 64 2 46.371 49,42 10 265 60.576 5.322 0 64 3 48,665 9,39 9.361 64 391 4.218 0 64 4... 51s01 58.416 9 008 68.651 3.513 0 64 5 53,286 1 61, 6 2 9,629 72321 4,080 0 64 6 55,574 67.015 8 691 74,200 3,938 0 64 7 57,744 7o,766 9.063 77,051 2.818 0 64 8 -59.6S27 7?.s85 627.0 77585 2,913 0 64 9 61,223 7 3,96 6.919 78 960 2.091 0 64 10.62 ^20 75 193 4 735 79 686 2.697 64 11 63,819 75.809 4.965 80.956 1.691 0 64 12.. 64.872 7.,753 6,965 81 275 2.145 0 64'13 65, t93 7 8.138 4.941 82 643 1,655 0 64 14 66.781 78.334 4 142 82.792 1.718 0 64 15 67,6.4 79.572 4,558 83.505 1965.0 64 16 68,340 79.348 4 139 83731 1. 910 64 17 88,967 79,773 4.492 83.535 1.513 0 64 18 69,539 81.319 3,945 83.781 1.105 _ 64 19 7,0092 8.455 3,792 84.600 1.663 0 64 20 70.622 82. 532 3 s 164 85338 0,805 80 64'. MI NI MU IM VALUES GEN EFF AVG STD AVG8 STDS NIZ TR I 40 315 4rM 315 9.695 52,788 4,497 0 64 2 43,444 46 593 9.354 59 181 2,707 0 64 3. 46 178 50.112 8,487 60.753 1,986 0. 64 4 48.226 53.7e4 6.583 62.990 2,789 0 64 5 50,267 55,273 6 458 65.005 2,478 0 64 6 51,412 57.136 5,477 67.629 1.464 0 64 7 5-2. 692 60.376 5.576 69.841 2.050 0 64 8 54A,071 63.725 3.974 71.272 1,498 0 64 9 55 S.57 6 67,392 4.95 73,413 1,814 950 64 10 56,953 69,346 3.462 74.553 1,206 0 64 11 58 13 70-159 3 418 7 5.896 1.1020 64 12 59,195 70.650 2.973 77.355 0914 64 13 60 368 74 143 2.697 77,493 0,644 0 64 14 61.381 74,537 2.164 78.426 0.812 0 64 15 2, 410 76,56 321.22 78,.81 0,604 0 64 16 63,429 756577 1.905 78,863 0,521 0 64 17 64 309 77 373. 918 79.873 0 631 0 64 18 65. 24 77 186 1.619 79.701 0,678 0 64 19 66, 106 78. 17 1,726 80.419 0,565 0 64 20 66,928 78,985 1 682 80.864 0,556 0 64 Figure 28d Parameter values of individuals with increasing phenotypic values during five replications of mass selection for 8-parameter Ridge using Gene Action 3 and population size 64 (Sheet 3 of 3) 105

o J. S. a:>ai;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~n 0 00 ICO 4O 3~0 400 480 560 643 INDJV tIDUAL INI V I DUAL Figure 29a Phenotypic value of individuals during simple recurrent selection for 8-parameter Plane using Gene Action 4 106

JI iini r - IL 0 8 I0 240 3o 400 480 560 640 INDIVIDUAL INDIVIDUAL it'I,,'yi,TlwNt I 0 0 0 80 160 P40 3e0 400 480 5S0 640 INDI V I[UAL INDTVIDUAL n-., _, X4 ~ Wm' I <r i o 80 160.40 3O0 400 40 560 640!NDIV IDUAL [NO]'VOOUAL INDIVIDUAL INDIVIDUAL Figure 29b Parameter values of individuals during simple recurrent selection for 8-parameter Plane using Gene Action 4 (Sheet.1 of 2) 107

U' w fro o so ISO 240 30 400 40 660 640 INIVIOUAL INOIVIDUAL I~ --,,~u -4 -I L.i -a o80 160 240 3O 400 0 s6s 640 INDIVIDUAL INDIVIDUAL 0 o 80 t60 240 320 400 460 560 6o INDIV DUAL INDIVIDUAL Figure 29b Parameter values of individuals during simple recurrent selection for 8-parameter Plane using Gene Action 4 (Sheet 2 of 2) 108

40024 SRSIA 7/4/73 NOVLP 4 NVALU -... —- -1 -.PINV 0 0000 PTRA.-... 0 000 PCROS 0. 500 PCROL.... 5000. PMUT o.000o.CV Y000 0-_ NPOP 32.NSEL -8LCYC 20 NPAR a8 NSEG 32 NREP 1 ~I1 IPAP t1IPBP 0 IPAF_ 0-_ IPCS 0 STOP —._ —.._.__...1 50,000 32766 32765 32766 32766 32766 32766 32766 32766 2- _.50,000... 32766 32 766 32766 32766 32766. 32766 32766 32766 3 50,000 32766 32766 32766 32766 32766 32766 32766 32764- 50,000_ 32766 32766 32766 32766 32766 _32766 37< 5 50,000 32766 32765 32766 32766 32766 8 "-' -e42.S. 50,000- 32766..32766 32766 32766 -"''- 5363 62330 7 50,000 32766 32766 327'c.^^3q 55442 1840 53350 8 510,000 32766 -_3597 u3?74 2328 59834 2826 60756 9 50,000 2328 63254 3256 63854 5900 65154..p1..... 55566 4958. 62804.1034 56130 2680 57414.,a35 3008 63486 2964 63240 3258 63614 2096 64948,. 94,127 2738 59888 52J8 63512 4934 63796 12088.8270 dj37 96,677 2020 62994 1384 60626 804 63778 1030. 62556 638 88.664 1o702 62752 10360 62S.L — 4316 56686 5560 61866 639 94,011 5166 63276 2424 62796 5690 59402 2316 60864 640 90,212 9246. 59888 5382 60824. 6860. 59252. 1_7.82. 54130.AVERAGE-V.ALUES __ GEN EFF AVG STO AVGS STY NDS NTR..- 50,000:50,000, 0 00- 50 000 0,000 0,000 32,000 2 49,491 48,983 6,034 56.483 2,401 0.000 32,000 -3 51,858 56,592 4.260. 62,227 2,088 0,00 32,000 4 54,055 60,646 4,081 65,732 3,106 0.00 32, 00 5. 56,155.64,554 4, 377 69 564.1 57g 0 P00 0 32.00 6 58,348 69,314 4,107 73,841 1 969 0.000 32,0p0.7 60,383 72.592 2 961 75,671.1, 634 0,00. 32,000 8 62,314 75,835 2,989 79,618 2,081 0,e00 32,000 9 64,096 78,350 3,632. 82,987 1,482 0. 00 32, 30 10 65,783 8(,967 2,832 84,267 0,937 0,0 P0 32, 0 11 67,308 82,561 2,951. 86,033 1l141.. 0 00..32, 0 12 68,858 85,893 2,472 88,861 0,907 0 000 32, 05 13 70,288 87,457 2 474 90,678 1284 0,000 32, 00 14 71,659 89,479 2 102 92.212 1,045 0,000 32,000 15 72,963 91,212 2,259 949065 0,776 0, 00 32,000 16 74,148 91,933 2,012 94,245 0,974 0,P00 32,000 17_ 75,242 92.740_ 1.726 94,747 0,500 0,00 32,000 18 76,219 92,831 1,398 94,464 0,363 0,000 32,000 19-. 77,103 93,013. 1,499.. 94,850 0 333 Oe P0 32 000 20 77,906 93,169 2.232 95.769 0,832 0,000 32.00a Figure 29c Input data, parameter values and generation statistics during simple recurrent selection for 8-parameter Plane using Gene Action 4 109

0'.. z s8IV \OUAL I NO 1! DUA -41 Li a 0 0 80 160 8*0 330 ~400 480 560 640 INDIVIDUAL INDIVIDUAL Figure 30a Phenotypic value of individuals during extended pedigree breeding for 8-parameter Plane using Gene Action 4 110

a-he I O 0 0 0 16 e40 30 400 480 560 640 INDI V IDUAL. INDIVIDUAL o 0 160 240 320 400 400 5S0 640 INDIVIDUAL INDIVIDUAL IL X4 0 o 0 i6 r40 30' o00 4 (0 5 640 INDIVIDUAL INDIVIDUAL Figure 30b Parameter values of individuals during extended pedigree breeding O. --- I... I r __\ L for 8-paraeter Plane using Gene Action 4 (Sheet 1 of 2)0 111

X U0 0 160 240 32S0 a00 40 560 640 INDIVIDUAL INDIVIDUAL a 80 160 240 3O 400 480 60 640 INDIVIDUAL INDIVIDUAL.M - fo 8- Pln usn Ge0 400 490 (See 2 o 0 WS ~~....,-1; Url a eo t 60 8eo 16 40 38 c400 4 o INII V 1I UAL Figure 30b Parameter values of individuals during extended pedigree breeding for 8-parameter Plane -using Gene Action 4 (Sheet 2 of 2) 112 Figue.30 Praetr vaus finiidas uin xtnedpdire redn

60005 PM2 7/9/73 NOVLP 4 NVALU- PINV 0.0100 PTRA 0.0000 PCRO. 0,5000 PCROL 0 5000 PMUT 0. 000 CV 0. 00_____....- _NPOP 32 32 16 8 4 2 2 2 2 2 NSEL 16 16 8 4 2 1 1t 1 1 LGEN 10 NPAR 8 NSEG 32 ALNVAR 6 Ix I IX 1.IPAP __ __ __ t___ _ IPBP 0 STOP... ____ 1 39,958 21262 36816 44348 17360 47416 26316 41136 21020 2 46.610 29138 20522 52146 13310 29516 28790 6384 36888 3 55.195 32302 33022 17330 21040 37086 60190 37096 36800 4 61.984 16686 3343S 32736 32196 9200 60122 36590 32316 5 47.010 33498 29658 12665 1790 36558 24846 37626 48380 3. 47,461 33002.. 39923 63i138 4046 __ 44468_ 28942 32.'0 7 38.946 29300 2002 28910 29406 33214 <. 8. 481t64 17628 28206 25056 28524 A/30 44848 9 57.799 21454 29434 2Q' ^-_ t 338 325o 44850 10 53.301 36130 s -...q 1654 56338 3250 44850 11 53,819P'-.-._.4 60214 1174 56336 3970 44850 12,uo410 2256 60184 1174 56336 3970 44850 i62 63410 1556 56344 1654 56338 10930 44850 90,832 162 63396 2284 56344 1414 56352 3010 44850 15 90.011. 162 63396 2268 60198 1174 56338 7570 41010 76 89,924 132 63408 2284 64038 1414 56338 11650 41012 77 89.508 132 63426 9250 60184 1414 56320 3010 41210 78 89.512 132 63426 9250 60184 1414 56338 30)0 41012.7-9 88.730 162 63396 16930 64R54 1174 56352 3490 41010 80 90,192 162 63396 9252 64h54 1174 56338 7330 44848 J __L 23 30_ 1.32 63426 1556 64024 11 74 56336 3490 48688 82 91.662 132 63426 9252 64024 1414 56336 3250 48688 83 90,0873 162 63396 1572 56374 1174 56308 3730 44848 84 91,559 162 63396 5412 64054 1414 56308 3730 44848 -85_ 691.566 146 63396 1554 60t84 1174 56336 3970 44853 86 91,432 162 63426 2270 60184 1174 56338 3970 44850 -87 -90-,93 132. 63396 1542 56344 1414 56338 3250 44850 88 90,976 132 63396 1542 56344 1414 5b338 3010 44850 89 93,219 132 63425 1572 64024 1174 56336 3010 48688 90 93.130 132 63426 1556 64C24 1174 56336 3490 48688 91. 91.563..146 63395 1.570 60184 1174 56336 3970 44853 92 90.834 146 63396 1554 56344 1174 56336 3970 44850 93. 93.219. 132 63426 1572 64024 1 74 56336 3010 48688 94 93.219 132 63426 1572 64024 1174 56336 3010 48688 95. 93219 132 63426 1572 6424 1174 56336 3010 46688 96 93,219 132 63426 1572 64c24 1174 56336 3010 48688.9t -93.219 132 63426 1572 64024 1174 56336 3010 48688 Figure 30c Input data, initial and final parameter values, and generation statistics for six varieties in extended pedigree breeding for 8-parameter Plane using Gene Action 4 (Sheet 1 of 3) 113

_ 98 93.219 132 63426 1572 64224 1174. 56336 3010 48688 99 93.219 132 63425 1572 64^24 1174 56336 3010 48688 _.100 93.219 132 63425 1572 6d424 1174 56336 3010 48688 t01 93.219 132 63426 1572 64024 1174 56336 3010 48688 -.1id2 93,219 132.63426.1572 65024 17Z4.4.56336__3010_A48688___ VARIETY I _GEN E F_ EFF __. AVG _. STO__ AVGS _.. STOS. __ NI__ NTR 1 49,425 49,425 7,366 55, 33 4.388 0 32 2 _ 52 176.. 7._54,.926._.4,99 _ 56 687 __4.497_ 0 32 3 53,717 59.881 5.307 61,672 5.211 0 16 __4 54.809 65.729 4,79_..66.m96 ~_ 4,970 _ 8_ 5 55,437 69,272 2.526 69,807 3,232 0 4.6.55,793 72,145. 0.,65 __72.191 ___0 0 _0__ 2 7 56,142 72.535 0,552 72.926 09000 0 2. 8__ 56 484_ 72.924_ ___,a 2 _72, 96_, 00__ 0_ 2 9 56,813 72.903 0 101 72.974 0,000 0 2 1a 5.7-129 7,9.29_2..0.03 __ 7-2,92.9 __'3. 0 2 VARIETY 2 _~ ENEV E.F. AV S.____._ A.. _..VGS SOTD S I N T. R 1 50,374 5i,374 7,518 56,453 5 196 0 32 2.,214_..5.6.,055 71___,J 5, 868 6.t522_ 0 32 3 55.387 64,076 5.653 65,853 4,7b4 0 16.4 56.6486 3 69,646 3s 2 _ 70- a612 8.7 5 8 5 57,350 72.026 1,653 72.280 2,201 0 4.6 57 705._74,048 1 279 749 5 2. 0,090 00 _2 7 58,079 75.662 0,032 75,685 0,000 0 2 __.58,446 _ 76,52_.,52 _76,420 0,000 0 2_ 9 58,805 76,397 0,097 76,466 0 000 0 2 i 0__ 591 76,5 4820.. 236.$ 512 0^3 _ - 2 VARIETY 3 GEN EFF __VG AVGS STD_ AVGS _N___.STS ].! NTR_ 1 75,81 75 81 S 0 000 75 81t1,000 32 2.. 75.568 75,324 3, 775 17.7 621 3,351 32_ 3 76. 217 78,815 2,766 80.173 2,469 0 16 4 7 7.7.32 _ 81.87.77 2. 503..2575 2.688 0 8 5 77,u34 83.686 1,589 84*557 1,248 0 4 6.__77206 _85 a2l2 0,494 8 5 8545;2 Q2.00! 0 2 7 77.378 85.476 0,035 85,501 0,000 0 2.. 77 543_ 85. 447 3._ 076 _85 501 _0..000______ _ 2 9 77.699 85,371 0.033 85.394 0,000 0 2.77 8$50ZL_85J371 033 25;394 __ Os 30_ _ _ 2 VARIETY 4.EN _ __EFF AVG STD AYGS. STOS NZ WNTR_ 1 80,956 80,956 0 823 80 977 0 000 0 32 2___ __.80,857___. 80 758 - 2 383 82. 16 2 2,147 0 32 3 81,471 83*928 1,602 84.732 1,539 8 16 4.81399 86.L.. _241 8 6.50P5 - 182_ 8 5 82 139 87,421 0,843 87,805 0,272 P 4 _6. 82.247__ 87,215 0,0a 67_ 87,262_ 0.,0_ ~0 P 2_ 7 82,351 87.216 0,000 87216,000e 0 2 8 82,450 887 193 _ 0,032 _ 87,?16_ 0,000 _ _ 2 9 82,545 87 239 0,032 87,262 0.003 0 2.10_ 82 6388.8,26a2 ___ 03 8.7 262_ 0000a 0_ 2 VARIETY 5 GEN EFF AVG_ STO AVGS STOS NIZ NTR I 86,326 86,326 0 023 86 346, 0 16 0 32. _2 86, 80 P 85 835 51,622 86,938_ 1 296 0. _32 3 86,370 87.529 1t325 88,202 0,626 e 16 4 886538 88 215 1. 448 88,894 1 2.94 _ 8 5 86,658 89,301 1 454 90,33, 048 4 6 86, 7 30 90 066 a___ 00 90,6 066 _ 0 0 ___ __ 0 _2 7 86,800 9,.066 0,000 90,066 0,000 0 2 8 _. 8i 86,8_. 90 _0686_ 00,00 _90,066 _ 0 00- ___0 2 Figure 30c Input data, initial and final parameter values, and generation statistics for six varieties in extended pedigree breeding for 8-parameter Plane using Gene Action 4 (Sheet 2 of 3) 114

_. 9 _ 86,9393 9,066 ____0,00i _ 90,366 0....., 009 _........... 2 10 86.992 90 066 0,065 90 112 0,P0' V 2 V_ ARIETY... 6 __ ____. _ GEN EFF AVG STO AVGS STUS NIZ NTR t_ L88! 8_8_6878 8R,687_ 3...a 0_ 88,687 0 0.1 ____.. _ 32 2 88,709 88,732 1,402 89,585 1,265 e 32 3 _ 89, 44 9, 384 0,_ 843 90,.761 0,__ 0 784 P___ _ - 16 4 89.269 91t.516,.72.6 91,808 0,924 0 8 _ 5 _ 89 396 _ 92,16 t_, 18a___92.391 1 1 7 _ 4 6 89,477 93,219 0,000 93,219 0, 000 P 2 7 89,555 93,219, 3,.00' 93,219: 1 _ 00 00.... __ 2 8 89,6;30 93,219 0.00;4 93.219 0,000 0 2 9 89,702 93 t2 1 9 0,003 _93, 21 9 _ 000_ _ __ _ 2 10 89 771 93.219 0,000 93,219 0r.000 2 Figure 30c Input data, initial and final parameter values, and generation statistics for six varieties in extended pedigree breeding for 8-parameter Plane using Gene Action 4 (Sheet 3 of 3) 115

O 13 03 41 -J 0 0 320 640 960 IE80 1600 INDIVIDUAL Figure 31a Phenotypic value of individuals during extended simple recurrent selection for 8-parameter Plane using Gene Action 4 16

1 1 ~ ~0'IE IB00 il 6to B l 12 1800 1t U~ ft Bal19 lInmm n jI,NOIVIIDUAL INDIVi ^IDlJL INDIVIDUAL INDIVIDUAL e..... I- II -..-. 4 —4-.. —-+ — -.4 — -- I L- W. _ <to < 0 0 320 640 960 I12O 1600 0 320 640 960 160 1600 0 30 640 960 1(380 1600 0 O 60 1 1600 INDIVIDUAL INDIVIDUAL _lB o c 0 320 640 960 1260 1600 0 320 640 960 1280 1600 I NDI TV I~DUAL I P~NDY I V ~IDUAL IN DVIDUAL I ND I UAL Figure 31b Parameter values of individuals during extended simple recurrent selection for 8-parameter Plane using Gene Action 4 117

80001 SRS2 7/12/73 NOVLP 4 _NVALU iPINV 0P,00 -. PTRA 0.000 PCROS 0,sa PCROL 0,5v00 PMUT 0,0e00 C_.V..-. 0 0 000. NPOP 32 NSEL 8 LCYC 10.. NPAR 8 NSEG 32 V.A R____ 5 IX I IPAP _ - IPBP 0 _IPAF__.__ IPCS 0 STO P. - - — _ t 50,000 32766 32766 32766. 32766 32766 32766 32766 32766........ 2 50, 00. 32766 32766 32766 32766 32766 32766 32766 32766 3 50,00X 32766 32766 32766 32766 2766 32766 32766 32766 _. 50.000 32766 32766 327656 32766 32766 32766 32766 33276 5 50,008 32766 32766 32756 32766 32766 32766 ____ _ 95 500. 032766 32766 3276 6 32766_. 327 7 o6226 7 50,000 32766 32766 32766 4 72 63182.8__ 50 i 000_ 32766 327C'2 V24 62776 3348 64048 9 5_0.^ 000. 6 *.... 59408 4720 63016 457_2 64016 o_ _/t0 18s6 60142 4960 63974 3586 63482._- __ __ 9320 563-6 59___. 64236. t _27944_ 63332_71 86 62956 __ 92,817 3186 60146 2050 63040 1520 55622 3108 55546 __ 09._ 92&69. 8 442 56320 1784 59124 5964 63544 6694 59388 3i1 95,467 4494 60130 5660 53362 1760 64648. 974 63224.... ~_11 95,200 4752 64242 5900s 62784 1520 59448 506 63180 3 12 93,480 7236 64212 2286 591t4 5810 63914 7172 63152 __ 313__ 92 73f _8569_5.91.6__ 56 30 _63980_ 5586 63704 ___6946 63 930 314 93.385 7012 60594 1794 62784 1840 59448 4586 59866 315.. 95.502 922 60C373 590._0 60352 2350 64454..1196 63750 316 93.363 652 59160 1794 60338 6110 64184 6948 59144 _.?7 __..95,512 8304 64224- 1.794 _60396 2240 63332 _ 492 63486 318 97,527 2722 64448 1836 63O10 1404 64408 746 64016.319. 9.4.381 681_ 601333 2.060 5914 8 51_40 64196 _ 2 _63244 320 94,909 8334 63006 5676 64222 1790 63332 3362 64050 YARIETYL__________________ __ ___ GEN EFF AVG STO AVGS STDS NIZ NTR 1__. __ 50 0e,....._ 00.__ 0.L,0 0.0___5 00_ 0 00.__.. _ __ 32 2 49,491 48,g93 6.034 56.483 2,401 0 32 3 51 858 _ 56,592 4,26; 62 22 7 2,088 0 32 4 54,e55 60,646 4,081 65,732 3,1d6 0 -32.__5.__S56 s55 _ 64,554 4. 3.77 69, 564 1.579 _ _ _ __ 32 6 58,348 69,314 4,137 73,841 1,969 0 32 7 60,383 _ 72.592_ 2.9661 75 671 1,634 __ 0 _ 32 8 62 314 75*835 2,989 79 618 2, 081 32 9 64 72.3 32 382 967 43 A ______32 10 65,783 8e,967 2,832 84,267,0937 e 32 VARIETY__ 2 GEN EFF AVG - STO AVGS STOS NZ NTR lf.8i.t_-S090 __5 0 y01_.. 0,0 V 0 5..00___, e0 Q.__.0_ 32 Figure 31c Input data, initial and final parameter values, and generation statistics for five varieties in extended simple recurrent selection for 8-parameter Plane using Gene Action 4 (Sheet 1 of 2) 118

__ 2._.. 9 1 8 _ 5 1 8 3 6 __. 7 1 0 1.. VI.. o__. 3 8 8.. _. _......3,2 3,54 d,44 61.375 4 592 67. 6-,6 1 748 P 32 4 _.5 57 521.... 6.R72 ___ 4. 35..72, t' 823__._ _ _.__ 32 5 6P,369 71,7ta 3,69 7 76.729 1,726 P 32 _6..62.94 7,6,L___ 3. 124__79,77.9 1.5.3 _ __P 3 7 65,376 79,729 3 163 83,667 1,341 32.8 _ 67 s525 82. 569 3, 98 98 87,945 __ 554 P_____ 3,2 9 69,568 85,909 2,58 88,979 1,503 P 32 _ 10.__ 71 30 0..._8 6, 8 86 _ 2 3_ 8__ 8 9_, 5 63 8 59 _ __ 3 2 VARIETY 3 _~N E F AV G a_ SD A GS ST D S N_ 1_ RNTR 1 87,237 872-37 2,641 90,276 1 141 0 32 2 8.7 1 4 ___ 7 4 __ __2 73 9 2 2._ __1 59 ___ ___ 32 3 87,869 89,325 2, 693 92 535 0 891. 32 4 _.88 674 ___.91. t?__?1..97.._ 93 566. 1 0.._ __ 32 5 89,220 9J,4'5 2,214 94 166 1 032 0 32 6 89,98 7 3___.3 4___32 1, _5._-638 P_ 8.9,2 0 32_ 7 9, 439 93,632 1,635 95,630 0, 5.2 0 32 8.90 77.3;93.14.._31.1_ 24 1 61.,..92, 67. 6 0 3._ 9 91,002 92,832 1,689 94,81 0 776 0 32 _ 9_A,21, 28.2,93.,798 1 269 9 54_8 0, 61 2 0 32 VARIETY 4 _ EN_ EEF AY 1T..D_ AVG CS_ STDS. NIZ _ NTR 91 1,936 P1,936 1,749 94,3'0 0,8;6 0 32 2 91. 6.40 93-4.3 8___40 6 93__4 _,__61 0 32 3 92 115 93,067 1,756 95.105 0,4680 P 32 4.92. 4.67 9.3_. 522 I t._970_ 96_,J 38_ 0., 6 1 8 0 32 5 92,782 94, 42 1,795 96,185 0,853 0 32 6 _3. 55-4 94, A656 t__35_.96.3.11_ 0_561.0 32 7 3,28 94,446 1.375 95,872 0,225 0 32 8 9 3,.4 67_ 9 4.21.7_2 1.-237__ 96.167,_29.2 _32 - 93,594 94,610 1,318 96 172 0.249 0 32 _ 1 _._93,696 94, 54. L,6 15 _3.8_ 96.29.5 0.577 0 _32. VARIETY 5 _E.~N...E _F AV.GS TO A_ V..?S STD_ NIZ N__ _ T R._ I 99, 390 94,390 1,331 95,944 0,413 0 32 2 9.__9 81L 3 r 23.3 t, 1.71_ S95.,378 ____,87 ___ 3,2 3 99,1893 94,055 1,825 96,267 0,721 P 32 4 9_3.972 9_4 7-2.4 ___6 1 9.. 7 4___ 0.676.32._ 5 94,070 94,463 1,777 96.339 0,609 0 32 6.. 9.4_,L33 9. 4,__48. ____ _..__~_6, 35 4 0-, 5_4_5 - 32 7 94,201 94 612 1 262 96,293 0,427 0 32 8 94,_ 3 02 95_.3 _.303._t3 6 ^45.3.0 _ 6.39 O 32 9 94,316 94,430 1627 96,598 0,692 ~ 32 I 0 94,3,9 9455_5 1. 47 8 _ 9_6J_.294 0 ___ 67 0_ __ 32 Figure 31c Input data, initial and final parameter values, and generation statistics for five varieties in extended simple recurrent selection for 8-parameter Plane using Gene Action 4 (Sheet 2 of 2) 119

'r. 0 3bO 640 #g0 10 Ism tNDIVI AL Figure 32a Phenotypic value of individuals during extended simple recurrent selection for 8-parameter Ridge using Gene Action 4 120

0 320 640 650 0 0 0 10 1 0 0 3 0 600 0 30 t 0 10 I INDIVIDUAL INDIVIDUJAL o 380 640 960 180 1600 0 320 640 960 1280 1600 INDIVIDUAL INDIVIDUAL I — ~cco 0 3E0 640 8 E1SO lO o0 o 350 640 96 1r 1600 INDIVIDUAL INDIVIDUAL Figure 32b Parameter values of individuals during extended simple recurrent ~ 31O 640 8 1800 1800 0 law l4o0 960 lw80 1600 INDIVIOUAL INDI VIODUAL selection for 8-parameter Ridge using Gene Action 4'121 % ~ ~ ~ ~ e~~~~e~

81002 SRS2 7/12/73. NOVLP 4 NAU............ 2._ PINV 0,0(400 PTRA___. 000._ PCROS 0.5000 _PCROL....0,b0__ PMUT a oo0 0 NPOP 32 NSEL. __ _ LCYC 10 _NPAR_ 6_ N-SEG 32 NVAR 5 IX. i _.PAP 1 IPBP 0 IPAF 0 IPCS 0 i__-80003__ -- - - - _ I - 50,l 9 32766 32766 32766 32766 32756 32766 32766 32766 ~2 50,109 32766 32766 32766 32766 32766 32766 32766 32766 3 50, 109 32766' 32766 32766 32766 32766 32766 32766 32766 50,109 32766 32766 32766 32766 32766 32766 32766 32766 5; 501o09 32766 32766 32765 32766 32766 32766 3276 - ___ 5_ _ 109 327666 32766 32766 32766 32766 - o3562 7-5oio9 32766 32766 32766, - 375 64430 599 62 --— 7 —5 0.I0 —326-6-P-376 6 —3766 3-7-63) 7~..I> ___6 8 _ 5,1(39 327.66 32766 out72 62030 61068 63800 9- 50.109 30 7- -__ _ 59678 62608 62298 575P2 59226 _ iB'~;w*uy j o^ 54616 5631 0 63902 586686 6578 63562 o, 4 720_ 6 4 43 6 62294 596901 63330 _62048 6298640 56362 _ 84.658 58730 64666 62054 51968 A 63572 62030 6593788 63818 39 93.124 64180 _6443 62042 _ 5616 63328 62044 62542 _ 55882 310 91,962 626086 64446 58230 52P26 63346 58670-5 63998 59736 311 88,774 58714 64432 62026 56076 63914 62016 60398 60442 312 87.992 64706.6_066 62536 60170 64656 62270 53436 59948 i 13 9.49 62778 644305_65458_59404 63902 62526 654238 59706 314 92,518 63048 56766 62266 59646 63316 61806 60142 59960 - 3 5____ 93,064 62328 __60530 57960 48140 63328 62270 63230 __60440__ 316 92.798 63018 56766 58692 55850 63086 62046 64942 63546 317 ~. 89,501 _67810_ 60830 54168_ 43720 64050 58416 60368 52040_ 318 87,592 59464 60590 54858 55610 63328 62286 60848 59706 _3419 9 __9a 245P8 1 56990 __ 7976 52?206 63808 62268 6299 2 59960 320 83,672 54872 64670 58216 55342 63794 62510 64464 56120 _VAR I E —Y_ GEN EFF AVG STO AVGS STDS NIZ NTR PI__ 0. 109 _50*1A_0 _5 1909____9 0000 5,29_.__ __ 32 2 47,923 45 736 10,522 59,952 4,859 e 32 3 550 636 56,063 8,461 65,465 3Pj44 32 4 52,766 59 1b4 7,257.68 502 3,362 0 32.5 __54,458 __.61 227.___ 6 644 6b8.814 _! 902 0___ 32 6 55,852 62,822' 6,931 71 224 3,243 0 32 7 _._.57, 03464 124, 1 26 6,38__ 70,511 __2,256. 32 8 58,059 65, 237 6,509 71 776 1,735 e' 32 9 58, 95....6 6,090 6,189 73,955. 1. 735 ____ 32 10 59,848 67,914 6,111 75,368 2,8b3 0 32 VARIETY 2 GEN EFF AVG STD AVGS $'STOS A N1Z NTR...__5L0.1. 09 ___5 Ol09 ____P 50,.! 09 ______,0.__0 __...___ 32 Figure 32c Input data, initial and final parameter values, and generation statistics for five varieties in extended simple recurrent selection for 8-parameter Ridge using Gene Action 4 (Sheet 1 of 2) 122

_ 2 _47,743 45 377 ____.12,26 60,446 6,373 ___. 0 32 3 49,911 54,246 9,*27 65.355 1,87 0 32 ____ 4 2 _ 499 9 6 O__6 2259 5.572 67 514 3431 0 32 5 53.551 571706 6.999 67 275 4,830 0 32 6 55,043 62,502 _ 7.365 70,976 2,015 e 32 7 56,464 65, 12 4.385 70,691 3,12t 0 32 8 57,825 __67 216 6,375 75, 24___1 955 Q____5____0 32 9 59,95 69,249 4,867 74.835 1.836 0 32 10 60,248 7, 632 4.843 76,565 2,467 0 32_ VARIETY 3 GEN FFF AVG STO AVGS STOS NIZ NTR 1 68,837 68,837 4,811 74,556 0,853 0 32 2 67.237 65,637 6.555 74,543 3,926 0 32 3 67.998 69,520 5,591 76,568 2,349 0 32 4 68.258 69, 41 4,905__ 74,692 2,546 0 32 5 68,405 68.993 6,467 76,980 2,542 0 32 6 68,349 68A0b8 7, t, 7 97.4 2,650 0 332 7 69,004 72,932 5,753 80.407 2,921 0 32 8 69,822 75,552 6,037 81.435 0,773 e 32 9 70.524 76,133 5,282 81,986 t.984 0 32 10 70,959 74.877 5,336 82.213 2,00B 0 32 VARIETY 4 GEN EFF AVG STD AVGS STDS NIZ NTR 1 71.205 71,205 6,947 8 0770 2,967 0 32 2 72. 941 74,677 4.247 80. 162 1,405 0 32 3 73,612 74,94 8 4,611 80,553 1 710 0 32 4 73,866 74,634 6,651 81,517 1,467 0 32 5 74,144 75.258 5.,185 81 354 1 723 0 32 6 74512 76f,348 4,799 82,275 1 937 e 32 7 75,o06 78,493 4.372 83,8^0 1 3?9 P 32 8 75,548 78,824 3,892 83,605 1,945 0 32 9 76,047 80r034 3;9Tg6 64, 755 1. 667 0 32 10 76, 350 79.078 4,588 84,462 1,336 - 32 VARIETY 5 GEN EFF AVG STO AVGS STS NIZ NTR 1 78,922 7R.9222 4.701 68480 1,366 0e 32 2 8s9,_g59_ 82,995 4,.424 d,30t 4 1 295 e 32 3 82 1992 84,660 3.173 88,695 0.999 0 32 4 82,573 83,715 3.761 88,164 1,339 0 32 53 83,069 85,053 3.659 89,229 1,118 0 32 6 83,688 __ 86j785 3,512 90,965 1,736 0 32 7 84,069 86.491 4,636 91,22 1,21 0 32 84,645 88.539 2,968 91 785 0,731 3 32 _ i......._.. 9 85, 146 89, 15 2.872 92,917 0,911 0 32 10 85.599 89.683 3,027 92,966 0,860 0 32 Figure 32c Input data, initial and final parameter values, and generation statistics for five varieties in extended simple recurrent selection for 8-parameter Ridge using Gene Action 4 (Sheet 2 of 2) 123

.g~ - o:#0 be~ 960 lmw 0ino INOIVIOUAL Figure 33a Phenotypic value of individuals during extended simple recurrent selection for 8-parameter Peak NE using Gene Action 4 124

w x 7lll T * ^' T 0. I D&'o ~ "o:.!sr 0 320 6O 90 160 1600 0 32 80 196 I60 1600 INDIVIDUAL INDIVIDUAL selection for 8-parameter Peak NE using Gene Action 4 XOI XI~lllrllll~~tlll~ll1411~ t~rlr~il,,~,liB r a I ~ g 0 30 640 960 810 1600 0 Eli o 96 le86 16 IND IVIDUAL INDIVIDAL 0A l 6 MO SW sea ILe lei" 0 380 640 cS I lIow llo rV ioUAL." N I V IND;DAL Figure 33b Parameter values of individuals during extended simple recurrent selection for 8-parameter Peak NE using Gene Action 4 r, I1~~~1L. I12

8VI003..SRS2 7/12/73 NOVLP 4 NVALU._._ 3 PINV 0,0~08 _PTRA. 0 0000 PCROS 0 5000... PCROL 0 5000 PMUT 0. 000 _C.V 0_0200NPOP 32.. NSEL 8 LCYC t0 _NPAR_ 8 NSEG 32 _-. AR_ _ 51 P A P ____ IP6P 0 _IPAF__ _ 0_ IPCS 0 48a.16 3704__ __. _ I 4,061 32766 32766 32766 32766 32766 32766 376 32766 3276 g _-4.061 32766 32766 327 3276 6 3 27 2766 32766 32766 32766 A4,.061 32766 32765 32766 32766 32766 32766 32766 32766 _.. _4._._.. 04.,61 32766 3276~ 32766 32766 32766 32766 32766 327A6 5 4,061 3266 32766 327 2766 32766 32766 32766 3'^ -.7956 s d4,36-14.1_332766_32766_32756 32766_ 3276f - e 49298 52068 7 4,061 327h6 327O6 32766. o p858 32786 48610 44164 _.._ t_ _ 4.061 32766. 32766 -,, 63396 1340 26706 48342 01768. 4,061 397C~.0o342.59452 -488.0~ 2062 28934 45472 48726 -— S0- 1.., 6530 13982 52014 52372 2078 28210 42130 51576 ^__,., 9.422 9___ 6__A 41640_55120 59360 _5678 21012_ 52450 43426 308 23.191 201. 45452 51772 48110 2270 32788 52974 48168 _.309.._..36,93.. 6766 26234 51522 596.0 1764 24852 48862 48228 310 34,516 2236 29852 59470 59600 1568 33042 45534 51824...1... 1 22,021 2524 37742 55854 59360 5394 28964 56770 47448 312 37.903 7246 29838 63038 5600 2512 28916 45026 44376 31U____26..79 6616 2.9625 _ 5536 0_524:00 2286 28706 45744 51602 314 15,375 634d 29562 55360 63200 1550 40692 49090 40984.. 315 16.650 21696 25982 59438 55476 1508 32022 49118 55366 316 28.973 6798 29102 5536o 44240 4912 36144 45504 47958 _ 317__ 22,892 10160 14250 _55614 51652 2482 36654 48866 52022 318 41.620 l700 25996 63502 63306 2046 25362 48848 48454.319.56.383 9396 22362 5149.2_5216? 1358 37614 52450 52052 320 25.679 6034 22184 55782 59330 2992 29684 45010 47944 VARIETY __ GEN EFF AVG STO AVGS STOS NIZ NTR.. 4 06 A ____ C 61 1_6.,000 __4, 06fi _ _ 0 00 0__ 32 2 3,513 2.964 4,501 9,069 5,571 32 3..___:33.2.35538 4,200._ 10,071____ 2781 0 32 4 4,118 5.910 5,o74 12,967 4,897 0 32 5 4,716 __. 7, i_9__ 5,687 t15,278 3_ 11 _32 6 5,216 7,715 5,733 15 797 2,333 0 32 _7 6, 372 __ 13.37 8_ _.8214 _?5 42P0 5 102 _.__ 32 8 7,337 14,093 8,527 25.510 3,280 32 B9 _?5__15.,5Y4S' 6,901 _. 24 191_ 2 364 6 32 10 9.228 17.968 9,647 30 519 7 139 0 32 VARIEY 2 I _____... _. GEN EFF AVG STO AVGS STOS NIZ NTR __ _.4,0l___,.. 4, 6 ___1..,0 00 4,061,,000 ___. 32 Figure 33c Input data, initial and final parameter values, and generation statistics for five varieties in extended simple recurrent selection for 8-parameter Peak NE using Gene Action 4 (Sheet 1 of 2) 126

2_ 4, P3. P36__..4 01 P _ _5 2.85_._.-1, 728.72. 6,80_0 _ e___ _ 32 3 4,338 4,942 5. b1 13.158 2,197. 32 -..A.4,427._4,693_.._4, 631 1.__. lj94.5 2,530 ____ 32 5 4,881 6,701 6,740 17, 007 3,544 0 32 _6.5-.4- 3 3 8 iL,_ 6 35 1 6.539 4, 125 __ 32 _ 7 5,735 7,546 7,81Q IR,954 5,145 0 32 8_ 6,543 __2,199 9*912 25.343_- 8,213_____ 32 9 7.218 12.616 7,581 22,281 1,966 e 32 10 2 QS..?.546 l5_5_.. 8 2_ _ 22,395 8, 52_2 P 32 VARIETY 3 GEN EFF.TAVG....STD _ AVGD$ ST[ $ N _Z N TR I 9,395 9,395 4,603 14,971 1,837 0 32 -_2. 10_,3622. 1 _,_3_29 7L9027 21,481 7718 P 32 3 11,158 12,7b0 8,503 23,933 8,640 0 32 4 L 4L.23 11.a 4___72 6.,g30a 90,6 6 25 P62 0 32_ 5 11,174 10.923 6,257 18,980 6,383 0 32 f 1 92,43 _-7,35__2 49,L2 8 32 7 13,667 22 452 11,754 36,756 2,252 0 32 8 1.A i.44,28 1 1 573 1,L79 33715_.4 851 _ 32_ 9 14,600 17, 158 12251 35.356 7,624 0 32 t __4__ 4, 95. I9 173 9.40 31,789 2,2__3 2_ VARIETY 4 _GEN EF ASlV.G. S.S__VG$ _DS_ T.R I 10,445 1(,445 4,619 15,625 1,602 0 32 2 9.603 8_ 761 6,849 17.2_3 _ 6,59_ 32 3 1, 787 13,154 10,319 28 171 4,093 P 32 4 A10, 9 6 L 1.5_44_ 7,7__2_ 2_39.5 524 _ 32 5 11,665 14,421 10,709 28,920 10,129 0 32 -. i,.33___15._t, 6 7 i 1_ 4 7___28 4...65_ 47 32, 7 13I.052 17.368 11,38Q 33,447 6.944 0 32 _ l3, 73, A_,22j 11.. 79 29. 1,6 9,629 P 32 9 13,565 17,504 13,470 36,846 100.02 0 32 I__ i 0 1 4. 422 22.3_4 14.71 3 4, 2 8 938 P _32 VARIETY 5 _~EN EFEE A V S STQ AVGS ST DS NIZ___ NT R 1 23,850 23,850 12,a41 39,938 9,949 P 32 2_ 2. 204.976._18.1__2 1 i _79 3 3__ 5,1 91_ e 32 3 20 959 2. 924 11,627 37.526 4,654 0 32 4. 2a118 25.9 A 42 33938______15 I9 6 32 _ 5 21.027 2. 667 12, 10 37 177 10,375 P 32 6 2_2 3 2^6,9.9 1h63 39._27 5 7.419 0 32_ 7 20,915 20,267 10 723 34,699 8,892 0 32 8 2_1,114___22z510 1_0_ L.94.4 38. __7380_______ 32_ 9 21,748 26,818 10,046 39.096 8,759 0 32 _0 2.2288 _ 27. 146 11.7 1 32_..072.'32_ Figure 33c Input data, initial and final parameter values, and generation statistics for five varieties in extended simple recurrent selection for 8-parameter Peak NE using Gene Action 4 (Sheet 2 of 2) 127

1.4 O 30 - 640 960 18M0 1600 I NO IVI OUAL Figure 34a Phenotypic value of individuals during extended simple recurrent selection for 8-parameter Peak W using Gene Action 4 128

0 320 640 90 1 0 1600 X 30 64 96 X 0 1! 600 INOIV IDUAL I NDI V I DUAL'IHt LL | wn LI to Lfln X X 0 380 640 960 1280 1600 0 30 640 960 1280 1600 INDIVIDUAL INDIVIDUAL ~-~.l III,, I MT a o g 320 640 960 1290 1600 0N 30 640 6 0 160 1600 INllvfW1WL f~lbSJIN AL 0 I ~ 2 III4 Iff 0 a r S 16 INDIVIOJAL INDIVIOUAL Figure 34b Parameter values of individuals during extended simple recurrent selection for 8-parameter Peak W using Gene Action 4 129

8000 4SRS2 7/12/73 NOVLP 4 NVeALU 4 PINV V. p PTRA ___ 4, ^ PCROS 80.5000 PCROL 0j500__ PMUT.,' V NPOP 32 NSEL_ 8 LCYC 10 NPAR 8 NSEG 32 NVAR 5 IX 1 IPAP I IPBP 0 IPAf 0 IPCS I 2.440 32766 322766 32766 3 2766 32766 32766 3276= 6276 2 2,440 32766 32756 32756 32766 32756 32766 32766 32766 3 2.448 32766 32766 32766 32766 32756 32766 32766 32766 _4 2.,440 3275' 32766 32766 32766 32766 32766 32766 3276* 5 2,448 327.66 32706 32766 32766 32766 32766 6 2, gt4.4.0 32766 32765 32766 32766 327f - _. 1768.4 -7 2,4471 32766 327o5 32766 -32 42118n l135 S 2.440 32756 3276t 1- -'* 798 28982 42142 17112 9 2,'-448 v -.. 6 29658 9496 32552 41650 17634 e........_ o720.._ 16t12 37322 5892 29192 38062 17636 -,,- o 2032 34640 2726 293P4 2056 29192 42128 25284 w_~t_ 60.92.6_ 14 31324 7252_33946 1_ 814_ 32794 41630 _2095__ 308 57,968 1330 30816 2692 29162 5598 36616 41645 16884 _. 389..68,o95. 1090.346d6 2436 _ 29416 2054 32522 37536 20740 310 47,815 1360 31326 6340 33226 9748 32776 42112 21190 _ 11. -.. 55.591 lb0 _ -35166 - 91 0.37564 6332 36394 38030 17364 312 67,343 2048 35420 908 33962 1544 28950 37836 17366.313_ 34773822___ 53._4. 96 27J8_37323 36092_36646_ 34192 2950 314 65,180 1314 354^6 1134 37592 2506 32762 37598 17380 315_ _69,385 1614 30816 878 _2916 _ 2084 32312 _33740 17830 316 61,839 2288 34655 1638 33704 5908 36134 3P382 21220 __ 31 7__56,062 _._.252d. 3000 5482.36824 _ 2254.37112 38272 17874 31P 63,433 1570 35138 1130 37322 2012 29446 33742 21702..9319 41,862 5664 3A __2952 32296863__3348 2.8952 3806. _20964 320 54,598 6412 39230 650 33464 1826 28950 378P6 25032 -_V.ARIETY. ____ _..____... __._ —.... GEN EFF AVG STO AVGS STUS NIZ NTR _1____ 2,440 __ 44_ 0. 440___,00. -__2 240 _,0 8 32_ 2 2.640 2.840 3 851 8,427 3,988 0 32 _3 i3 l81 3.962 5 1S 556___ 4 801 0 32 4 4.639 9,315 7,749 20.41 4,51 0 32 5__5_ 6__ 019_ 11,539 _ 7,64 _22 312 2..191 0 32 6 7,265 13,492 8 357 24,893 2,261 0 32._. 7 _.. 8,341 _1J,798. 8,727 _ 27, 152 __ 3 822. __ 0.. _____ _32 8 9,76 19.9d1 10,414 32,649 9,738 0 32 - __9_ _ 11.167 22. 133 1., 264_ 35,638 5,553 _ 32 10 12,477 24,274 1, 168 37,990 4,653 0 32 VARIE.LY. __... GEN EFF AVG ST) AVGS STDS Nfi2 NTR _... l....24 4 40..._......0_00__ 2.40......__ 0,00................_....... _..32 Figure 34c Input data, initial and final parameter values, and generation statistics for five varieties in extended simple recurrent selection for 8-parameter Peak W using Gene Action 4 (Sheet 1 of 2) 1350

2 _ 3,63 3.66d5 4 273 9,380 4,826..._ _ 41. 2._.... 0 32 3 4,344 6,9v7 7 99A 18,976 6.2O6 0 32 _4 _ 5.16 7,616 7,3 18.'05 _ 4,647 _. 0_ 32 5 6,'25 1 P9~S 9 771 26,695 5,154 0 32.. 7,937___13,96 7,354.__ 23,778 2,209 0 32 7 8,883 14,5'2 81 15 24.813 4,108 0 32 8 9, 83 16.457 7,35. 25,694 _ 3,879 0 32 9 10,670 17, 35 9,757 29.743 4,669 P 32 _10I._... 11.32 1__. 7176 _1J, 296___ 31,31 ___ 4,88 _ ___ _ _32_ VARIETY 3 N _ FF AVG STD AVGS __TST_ NIZ_ NTR 1 16,803 16.843 8,843 28,264 6,*33 O 32 _ 2 ___ 515.553 _ 14,304__ 11.384 30,792 5,755 _ _32 3 17,677 21,925 9,253 33, 01 4,920 P 32 4 18,874 _ 22,463..10.,476 37,279 _ 6,449 0 _..._ 32 5 21,326 31,135 11,370 45,304 3,680 P 32 6 23.44 396 14A18I 37___5_89____ 5,375 P 32 7 25,338 36,707 12,829 52,617 2,496 0 32 8 __27,34 ___41,357 12,636 56,734 7,.202 0 32 _ 9 29,023 42,483 10,630 55,720 4,279 0 32 1. 3,419 4 2,_98 9 14,558 63, 186 4_, 982 P, 32_ VARIETY 4 _E6N.EFF AVG STO AVGS STDS NI ___ NTR 1 30,621 30,621 1-.168 43,822 2,434 0 32 2 28,276 _25.31 11,235 39,162 4,429 ___ ____ 32 3 28.912 30,184 9 451 41,797 5,130 0 32 4 30,215 34,126 11,226 46,971 5,863 0 32 5. 31,3866.369,07 10 482 48,924 3,582 0 32 6 32,.10.9 35.723 9,761.47.847 3,429 0 32 7 32.532 35.,076 10 001 47,339 4,15 0'32.8..33,666 41 599 _ 12 779 57,027 2,623. _ 32 9 35.204 47a 508 9,689 59,741 3,669 -0 32 10 36,315 46,31 5 212,30 60,.997 4,702 2 32 VARIETY 5 EN EFF AVG __ STO AVGS____ STDS NIZ___ NTP 1 44,861 44.861 11.392 59,39 5',733 3-0 32 2 44 127 43,394 1,.754 56.175 6,282 P 32 3 4 44,716 45.894 11,375 61,221 5,919 P 32 4 46.355 5 51,2b9 _ 9,730 63,772 3,298 _ 32 5 46,648 47.820 9,695 60,632 3.945 0 32 6 46,948 48m448 9.580 59,619 3,0(45 _ _______ 32 7 47,169 48,495 11,614 62,527 4,645 0 32.8.. 47,63(0 5o,857 __ 9569 61,911 ___. 4418 __._ ___ 32 9 48,299 53,650 8,342 63,508 3,021 P 32 10 49 118 -__. 56,4 91 __9, 214.. 67,1 1 2.2..236 ___ __ 0 32 Figure 34c Input data, initial and final parameter values, and generation statistics for five varieties in extended simple recurrent selection for 8-parameter Peak W using Gene Action 4 (Sheet 2 of 2) 131

o__ em. z 0 1"._. II e8. o0, - ----.... I. -- - -......I ~ 0 20 3 640 90 1280 1600 INDIVIDUAL Figure 35a Phenotypic value of individuals during extended simple recurrent selection for 8-parameter Hypersphere using Gene Action 4 132

0 320 640 960 12UO 1GCO 0 310 40 960 1 0 1600 INDIVIOUAL INDIVIDUAL 0 320 640 ^S0 1280 1600 0 2*0 860 850 1280 1S0 IND V IDUAL INDI VIOUAL,S m 0 320 640 960 1280 1600 0 320 640 960 1280 1600 INDIVIDUAL INDIVIDUAL x? x 0_ 0 320 640 960 1 1600 0 30 640 960 1280 1600 INOIVIDUAL INDIVIDUAL Figure 35b Parameter values of individuals during extended simple recurrent selection for 8-parameter Hypersphere using Gene Action 4 155 l, ff i:::) 3;WC 640 logo I a 640 Sao lew low INDIVIDUAL IN1IVIVUAL x x 0 O 6' 960 120 1600 0 WO 640 960 1280 600 I'NOI V IDUAL N i V NIVIDAL Figure 355 P aramete r value s of individuals during extended simple recurrent

SRS2 7/12/73 NDVLP 4 NVALU 6_ PINV 0."A __ PTRA.._ _ PCROS 0,~500" PMUT 0. 000 NPOP 32 NSEL ____ —.LCYc 1t _ NPAR 8 NSEG 32 NVAR R 5. IX I __.__I PAP L IPBP 0 IPAF 0 IPCS 0 VARIETY I GEN _ EFF _ _AVG __-STD._ _ AVG$ __ STDS NIZ NTR 1 1a,000 1opt 000 0 007 100,0p0 0a 00 0 32 94 91 _ 88.182..__ 3, 83 92,913._.....2,05 __ 32 3 93,111 91,152 4.245 95,961 1,51 0 32 4 92,935 92,406 3,513 95,541, 510 e 32_ 5 92,792 92.222 2.894 95.537 0,684 0 32 6 _ 92.657 9.. 91,979 3,06 95.416 0 0722......32 7' 92 815 93,764 3,118 97.202 0,939 ~ 32 3_ 92 929 93,725 _ 3,128 97.267 0,820 0 32 9 93,105 94,513 2,353 97,5(0 0 815 0 32 _.0.. I 93.5 242. 9a4 475 2,.32 _97 076 32 VARIETY 2 -_.-G. EN_. EFF AVG _ STO. T AVGS ___ STDS NI_. ZTR i 100,000 100000 0, L0 0 1000'0 0,0 0 32 2_ -. 0. 4 06, 6 __ 88,132 _ 4,897 93 325 0,874 _ 32 3 93,140 91,266 4,841 96,275 1.183 0 32 -3 2______ 93.2._. -92A,697 3. 41..__ 96, 234 0 92 4 32 5 92,962 92 696 4 136 97,407 1,036 0 32 6 _ 93,107 93 832 3, 421 97,369 0.738 0 _2 __ 7 93,163 93,500 3.496 97,458 0 718 0 32 __ 8 93,27 94 94,046 2,938... 97, 17 __. 0,775 _ 32 9 93,353 93,983 2,791 97,288 0,302 0 32 10 93,513 94929 2,763 97,557 0,311 0 32 VARIETY 3 GEN EFF AVG STO AVGS STDS NIZ NTR I 95,760 95,760 1.766 97,991 0,741 0 32 2 94,516 ___ 93 272 _ 3,434 96,625 1.127 _ 32 3 94,653 94,927 2.903 97 528 0.245 5 32 4 94 R34 995,_379 2..344 98,097 0,734 0 32 5 94,8b2 94,973 2.376 97,587 -3,'?75 0 32 6 __ 94,73 __ 95,524 _ 2.2151 97.857 0,592 0 32 7 95,128 96,058 2,357 98,528 58 0,512 ~ 32 a....95,325 96 704 1.263 98. 167 0,536 p 32 9 95.452 96,473 1.599 98 310 0,417 0 32.10 _..95,612 ___ 97,53 1.639 98. 716 0. 54 e 32 VARIETY 4 GEN EFF AVGSTO AVGS STOS N _ NTR'1 96.841 96,841 1,797 98.692 -0,405 0.. 2 2__ 95.964 95,086 2,392 97,360 0,387 0 32 Figure 35c Input data, initial and final parameter values, and generation statistics for five varieties in extended simple recurrent selection for 8-parameter Hypersphere using Gene Action 4 (Sheet 1 of 2) 154

3 95,923_ 95,841 2.,{08;.9 97.301 0,563 0 32 4 96,048 96,423 1.829 98,304 0,501 0 32 5 _ 96,084 96,231 __ 189',98, 35 __0,433 E ____ _. 32 6 96,067 95.982 1.465 97.809 0580 P 32 7__9.7.96, 128 __9, 49$ ___ t, 623..98,376, 46_6.1 P 32 8 96,272 97.282 1,518 98,871 0.317 0 32 9 96..39._3 9.7_364 ___ 273 8___894_8 0,.3 3.1 P 32 10 96,478 97.,'36 1,272 98.552, 392 P 32 _VARIET.Y_ S ___ GEN EFF AVG STO AVGS STD$ NIZ NTR 1 97..Q2_, _. 97_,109 t.3103_ a.98 685, 527 0;532 2 96.882 96.654 2,123 98,618 0,3b8 e 32 __3.9 _ 908. 96. 959. I64 __ * 6 1 4 8 a 6Oi4 -.0, 54 8____ __32 4 97,127 97,785 0,841 98,876 0,277 0 32._5. 97 245.__.97,716 71. a286.__99,65 0 346 30 32 6 97 323 97,713 t1471 99. 63 0,339 0 32 7 97_,. 4. 1.6. 9 _7_,.97 3 1 _.8 5___ 9. _ 25 4. _32 8 97,529 98,324 0,770 99.252 0,341 0 32 9S.9 7, 659_ 98,692..,70_0 99 460 _,..0 5__ _ 32 10 97,787 98.940 0.683 99,515 0 173 P 32 Figure 35c Input data, initial and final parameter values, and generation statistics for five varieties in extended simple recurrent selection for 8-parameter Hypersphere using Gene Action 4 (Sheet 2 of 2) 135

a! a 8 a 320 40o 3G0 I280 1600 TNDOIVT UAL Figure 36a Phenotypic value of individuals during extended simple recurrent selection for 8-parameter Plane using Gene Action 4 with random inversion and translocation of chromosome segments and random mutation of gene conformation 136

w -t o 3zu 60u 96 )?,n isnn c 3C ot.L) SG),2oj:), INJI1 V I DUAL,. Nn i V 1n' IAI'.) o T I I i. -o INOIVIDUAL TNnTvTfnuAl IZ ~ ~ nTV~~~~niJ~~~~l I 1 O -"' - o —-- --- 8 o,, i Wlu 0 3320.340 960 150 1030 0 3Y0.40 9610 1280 1600 - NrtVtniAI INDIVIDUAL NT IVI T UA Figure 36b Parameter values of individuals during extended simple recurrent selection for 8-parameter Plane using Gene Action 4 with random inversion and translocation of chromosome segments and random o. X mutation of gene conformation 157 15C

8P031 SRS2 7/2o/73 NOVLP 4 NVALU _ I PINV PTRA. 01. o PCROS. 50 o0 PCROL ___ 0 5,-0pi PMUT 0. 1ao Cv 0_____0C Q NPOP 32 NSEL 8 LCYC 10 NPAR 8 -NSEG 32 NVAR S Sx I IPAP 1 -I- P-BP 0 IPAF 0 I P CS 0 80032 I 5, - 30 I 0:;0 3766 327 66- 3 766 327f-6 —27-6- 27-6-6 —3 —76-6 —-3 2766 2 5.,0. 2 32766 32766 32766 32766 32766 32766 32766 32766 3 50 00-0 32766..32?66 32756.327 e 66'32766 32766....3276 -— 32766... A4 5r,,.W 32766 32766 32766 32766 32766 32766 32766 37TM 5 5 09,"01- 32766 3276'5 —- 32766;32766 327'66 — 32766' "'" 6 5C 0P,0 ~0 32765 32766 32786 32766 3p7?0 ___. 63964 50,.300 3276 32'7d6 3~?76r'"-,-,44e 1448 59156 8 50 Poo 32766 327 - 1114 64446 1672 64186 ~ —-?"~~~5n9 5^(^B"'1"' - 64562 4952 64460 1420 62996 ~il~ <* " ovM~.,?76 1I.52 60692 1352 6421 8 2180 63072 -. —.,i 3720'...639..4 826 65126.1624 64444 1690 64414,o/__ P97 Q42. 15' 8368$8 14730 64fi34 1112 64458 2438 63250 S.- f97, ".29 4~2.4332 32423 61932 1096 64458 2422 F3996,309 97.478 162 63Y94 3.4 64PP2 1096 64444 2168 60096 310 96I' 636 4170 4144. 64 61 14 1096 64428 1164 63q.40 311 05.895 388 63p88 3012 64564 2994 64444 2180 56296 312 -97 3 7 38 6"3914 I 54 64324 4936 64218'2' 6- 63312 313 9'.711 66J 63888 81? 6480.4 1112 64204 1926 56508 314 96.12P6 15i 63904 4398 647S6 4938 64458 1926 60094 315 _96.Pi 393y _ 64144 1O52 64996 1354 64458 1956 60678 316 96,734 393kg 6391)2 4186 64532 1354 64444 1674 63284 317 98.082 416 64156 1052 64774 1096 63724 2182 64206 318 97.941 640 6391 4 828 648~4 1368 63964 248 63918 319 96.623 41d 64144 576 64998 1110 64428 2648 55616 320 97. 535 162 66a68 816 64776 1112 63966 5290 63964 VARIETY 1I ______ — GEN EFF AVG STO -AS STOS I NTR _ _ 5o.c'ie 5 A010_____00 b10 5 pi 5.0p. OO O 0 32 2 5 0224 5',. 48 6 275 58,835'3,6a8'32 3 5PU5 7 508914 5.067 65 859 1 683 3 32 4 ----- 5 \7i —---,5 66 43R 4.571 72 264 1,,424 0 32 _ 5 5 9, 4,2 71.611 3,90 2 76.2303 2.563 32 6 62,215 7, 276. 3 87A 8,. 964 2 644. 32 7 64,F84 79,50 0. 3 188 83 731 1.240 0 32 8 66.971 8.-". 2. 397 86.i'.1.". 84P6 84 3". 32 9 _68RQt __85.' 5 6 2,244 87 863 0 9t1 32 10 7' o 2;, 87 ou 2 3P 69'.978 2l 904 9 97 32 VARIETY 2 GEN EFF AVG STO AVGS S'TDS' NIZ NTR' o 5cP'iio 5 _ P.oo 0.0'A 5_.0 01p 00,0 1 32 Figure 36c Input data, initial and final parameter values, and generation statistics for five varieties in extended simple recurrent selection for 8-parameter Plane using Gene Action 4 with random inversion and translocation of chromosome segments and random mutation of gene conformation (Sheet 1 of 2) 158

2 49, Ptt 4,.772 5.,93 56,313 4,607 P 32 3 1 51, 5 5 54.c9f 9 4.194 5.2~5 2.593 P 32 4 53,4 6 56S.2 3 3,548 63.9h5 1,768 P 6 _ 32 5'.i,F94 6. 4,5~ 7.CA38 6 2,V78 P 32 6.__ FI 7.,fb7 7 ____ 2,9b 3 74.634 1___ 918 0 32 7 b6Q.',3' —74-o56 3 5 o 79.297 1,359 P 322 _ 8 52.~o, 70,127 3,40 83.2P5 1,b34 0 32 9 6i4.PJ? "".,7Q~ 3.426'85,149 2.355 p 32 10 656.894 84,910 2.337 88.195 _ 1,P098 P 32 VARIETY 3 GEN FF___ AVG STO_ AVGS ST0S N 7 NTR 9I.4t- 9 841.155 -'93. 27...,96 ~ 32 2 92,9 81 9,.922. 32 2.34 93.632 0,5tb8 P 32 3.91.,112 " 91.S25 1. 773 93.624 - 0,983 - 32 4 9 S1.14)I? 91. 209 1 87A 93,455 1,002 0 32 5.'..91.373. 9.3..329. 2,9 7...95. 5.,8638.........32 6 19,675 ___?9. 152P 1.764 95.32P. 0.589 32 7 91,76' 9.3 736 1 374 96.,4.. -I —.7..538'. ~' 32 8 92. 209___ 93 43 i.279 95.442 0 _,794 _4 0 32'~~99 92.43 — 3 94,~39 1628 96.4 3 7 0.454 5 3 -- 10 92.628 94,28 t,.798 96,5561 0.683 0 32 VARIETY 4 G~EN EFF AVG STO AVGS STOS NIZ NTR i 91.R 7 3 9.73 1,895 94.7T: 7 —— 87 82 —----- --— 3 2 91.722 9_1. 57 2.. i2 94.332 01,583 P 32 3........2,1206 ~. 9-, 8/Y7 1,914'd 95,240..'0,6 4.0 -3 4 92.423 93,376 1. 567 95.273 0.727 0 32 5 92.7 i 94.1 07 1,371 —— I — 77 5 -2 0,361 - 2 6 93 3 n 17 94.3 1 1.473 95, 075 P.7 0 p 32 - 31 76- - 9. ---- -— 52 —-- 8 ----— 3 8 93,283 94.035 1.705 96,013 0,279 0 32 9 9 3.5 "94,38 7 1. i6 95761-i 0 —-- 072 5 --- - -32 pi 93,561 __ 95,.164 1.194 96,516 0.,326 p 32 -'- VAR I ET Y. _-5-._... GEN EFF____ AVG ___ STO ______AVS STUS Z NTR 95.443- 9g. 443 3"974 96,542 6.7324 P 32.' 2 o5,45 95,47 __142 96,762 _.561 P 32 3 95'.311...5.444 1.212.96,943...... 0 4 1 9 -32 —4 95.223 94.96C) 1,417 96,798,.698 __32 5 -- 5,321 95.713 1,...96;-952 0,4o9" P 32 6 95.436 96.t11.1243 97.5P9 0.324 _ 32 7 957-592 96.527 944 97'.612 2'i 2 " — 328 95,7 50 966,A9 0,735 97. 762 0.a249 P 32 9 9578d5 96.6~61 0,794 97.9-7 8 0,243 0 32 10 96,V16 97a,2- 1 Os,729 98.972 P.133 32 Figure 36c Input data, initial and final parameter values, and generation statistics for five varieties in extended simple recurrent selection for 8-parameter Plane using Gene Action 4 with random inverstion and translocation of chromosome segments and random mutation of gene conformation (Sheet 2 of 2) 139

8 "8-,LDlle___._ 5 3 3E0 ~40 96 1580 I6U00 TNDIVZOUAL Figure 37a Phenotypic value of individuals during extended simple recurrent selection for 8-parameter Ridge using Gene Action 4 with random inversion and translocation of chromosome segments and random mutation of gene conformation 140

0~T -t —-S 0 40 a law I 0 320 640 960 0 O 1600 0o 320 640 960 10 1600 TND VIOUAL INDIVIDUAL a Cd 0 30 40 960 1290 16 O 320 640 990 16o 1600 Be if i 0o 3 6ine rsi0 1ona 1600 a 3so t0 1o Sc s 1n n600 INDIVIDUAL INUIVIOUAL or 0 o 00 3B0 6WO ^ VI6.B0 1600 0(-a -0 v40 SWn l*aw0 Jim INOV ItUAL INU'VIOUAL Figure 37b Parameter values of individuals during extended simple recurrent selection for 8-parameter Ridge using Gene Action 4 with random inversion and translocation of chromosome segments and random mutation of gene conformation 141

85032 SRS2 7/21/73 NOVLP 4 NV.ALU? PINV 0 001 PTRAS I.ti PCROS 3 5'. PCROL_ 0, 500 P-MUT'.0,A l CV Q1. ~. 3, C.v..0, 0.... NPOP 32 NSEL 8 LCYC 10 NPAR 8 NSEG 32 NVAR 5 Ix I IPAP 1 -Ipep 0 IP.AF 0. IPCS — --- 80033 1-, t-o 0 327-6 3 2T6 —— 2 —-'32766 32766-32766 —32766 _2 _ I59,19 32766 32766 3 3766 32766 32766 32766 32766 32766 3 — 50,-1 9-;3276 6-'3a765 — 3'2756 32766'-.32766..32766 —32766 32766 4 50, lg9 32766 32766 32766 32766 32766 32766 32766 32766 5~ 5 1i 50~9 32766 327o6 32766 32766 32756 32766 3o37' 6 5, 1e09 32766 32755 32766 32766 32766 6 370 bP 3 32o3 3 75 - — 276 7o 70 63512 "627988 5P, 109 32766 32766' -.,,u 3984 55356 55844 59136 9- -- 5..5' l 8^ 0 1.36 57334 3 58 5 434....63976 64974 A___ 1 ___' oY304 6272P 61428 59916 55104 63224 62766 ~ ~.. 52402 42440 02526 61650 5990:2 55328 60 134 60640 / 92,874 57230 5108A 64270 616928 60144 54846 59926 54846 306 88,139 52U696 4697 64044 ~61~6'38 599,2 47394 — 63494..62750 ___09 91,68 56976 47226 638'A4 57816 60130 55100 63542 63230. 310 85,439 5 2b6 349d5 64704 61652 63 4 5634 5130 63736 60370 _ 11 87,346 52910 39530 631774 65214 56064 55330 63254 63020 312 85.206 52882 3929- 64-3- 57550 56320 5-1490 59640. 59602 313 9g 597 5'i736 43625 62750 61656 59906 55314 63702 64014 314 88,099 52642 47225 63 34 65242 64030 55114 63060 66296 p' _315 84,347 48560 46506 59136 61414 59918 59170 63480 64014 316 285,68.. 563948 431 o. 63190 53720.'59922 47408 -— 632544. 6743 317 87,082 48788 429e46 64310 65346 55820 55304 63720 62722 318 86.521 49086 3933-6 62726 6.1 76 63996 51756.63978 65198 319 87 174 56750 43336 63804 61882 59888 47392 63484 64480 320 86.741 5292U 39'3 63170 64974 6P4 156 "55356 5..6 9 1 606 — 3 2 1 6 VARIETY I GEN EFF AVG STO AVGS' STDS N ^IZ' — NTP 1 5 a 1i09 5n, 109,000 50 1P,9 0 000 P 32 2 47'94Q 45,79- ita,73. 58 334 3,685 ~ 32 3 49,9.67 549.092 6,485 61 362 4,325 _0 32 4 51*,53 556 t1 6-,8-59 64,127 T,176~ - 32 5 53,. 03 59,d04 5.570 65.226 2 196 0 32 6 54, t64 50,371 7,18. t8, 398 3,614 -..0.- 32 7 54,954 6n.4 99 620 6,03 66,797 1 933 32 8 55, P09 63. 242 6. 2 9 71, 0 04 2, 5 7 6.- 3 2 9 56,658 62 003 4 84 1 68 182 1,953 0 32 10 57, 406 64,141 5.547 70.931 1.676 0 32 VARIETY 2 GN - EFF AVG TOAVGS. - STDS NZ NTRI 50.109 5,.109, 000 50,109 0,_00 _ 0 32 Figure 37c Input data, initial and final parameter values, and generation statistics for five varieties in extended simple recurrent selection for 8-parameter Ridge using Gene Action 4 with random inversion and translocation of chromosome segments and random mutation of gene conformation (Sheet 1 of 2) 142

2 49,P:^i 48,292?.135 58,449 1,842 0 32 3 5l...)2 57t 57,1'.b 7,12 66. 74 - 3,174 7 -- - - 4 53,4h9 5H,2el b,925 67,3 b 1.696 _ 32 5'54, 6. 2'6s.5/2' 6.197 68.654 2.780 0 2 6 56.430 64,1h 7,685 72,Q55 3,243 32 7 7,.42q' 63.'.4 7,114 71,47 1,867 0 328 _ 57,9u 616.b3 ___ 7,004 70,253 1,380 0 32 9 P.74j1 64,829 5.955 72 112 i.561 0 32 10 59.359 64,918 5,422 71.097 2,264 0 32 VARIETY 3 GEN EFF AVG STO AVGS STDS NIU NTR 1 66.305 66,3'5 5 763 73.238 1 784 0 322 65.261 63.817 6.28 ___ 71.251 3,711 0_ 32 -3 65.887.67.540 5.193 -73,741 2,697 ~ 32 4 66,937 77. 67 5,93 76,575 1,431 0 32 5 67,534 6-.9'23 4,675 75.654 1 921 P 32 6 67, b7 60.533 6 592 76.28 2.449 0 32 7 6.751 74.,'5;3 5.669, 8.35 1 if.'697 0 32 8 69.417 74.~77 3.913 78.988 1.518 0 32 - 9 - ~69,P73 -747427- 4* 80-1 79,656 1 833 -— 32 10 70,503 75.271 4,033 80,267 1.679 0 32 -_.................... VARIETY 4 GEN EFF AVG STO AVGS STDS N11 NTR I 70,P1 7I. 19 4,803 76.258 2.2302 Q 32 2 70,897 77,975 5.139 76.833 1.633 0 32 3 71,453 72;563 6,037 79.240~ 0987 e 32 4 71.704 72.459 4,59 7 78,44 2, 17 0 32 5 72-74 7,551 --- 5 - 3. 8 b —-80.273~~~ 2 630 2 7 ------- ----- 32 6 72.049 75.327 5.287 1.48__ 2,147 0 32 7 73*401 76.533 4.275 $81.224 t.26'P 32 8 73,9 2_ 76.9 35 4,259,1.8P95 2.237 - 32 9 74 539.79,634 3.915 64,14 1, 37 31 37"' 32 10 75 2;9 81.'245 2. 828 84.829 1_ 499 0 32 VARIETY 5 GEN EFF AVG STO _ AVS STOS NIZ __ NTR i 79.8 9 7A 79.-39 3 213 83,734 1i49 0 32" 2 800 P,8 4 8o.233 4_4251 P4,84;5 1 934 0 32 3 80,453 81,268 3.455 dS. t510 0 763 -0 3 4 a8P385__ 8..180 4.127 85.433 1 303 0 32 -5 8,0.65 82,787 3,847 87.866 1,685.' "32 6 81.412 84,144 3.37 3 88,o23 1,719 3 2 7 t81.89 84,755 2 906 88.456 1,715 e 32 8 82 3680 85 655 2, 87 88. 951 1,243 _ 32 9 82 745 85 826 3 434 9.0 t 0'9 9 44 0 32 t1 83.21 t 87, 407 2 327 90. 54 1,442 e 032 Figure 37c Input data, initial and final parameter values, and generation statistics for five varieties in extended simple recurrent selection for 8-parameter Ridge using Gene Action 4 with random inversion and translocation of chromosome segments and random mutation of gene conformation (Sheet 2 of 2) 143

L.JV C 0 3e0 640 960 280 I 6UJD IND I VIDUAL Figure 38a Phenotypic value of individuals during extended simple recurrent selection for 8-parameter Peak NE using Gene Action 4 with random inversion and translocation of chromosome segments and random mutation of gene conformation 144

INDIV IDUAL INOIVIDUAL 0 3:O 60 9B 1290 1800 1O 6o 960o 12a90 1900 INDIVIDUAL INDIVTIDUAL XI x INDIVIDUAL INDIVIOUAL it IL 250 0 320 640 960 1290 1600 ~ 3I U sano 960 1f80 2l60 IOICVIDUAL INDIVIDUAL 145 I- O 52[1 Or1O 960 l0'' 16ow0 600 6 INDIVIDUAL 1600 IN(:V IDUAL selection for 8-parameter Peak NE using Gene Action' with random mutation of~~~~~ gnecnomtn

8(1033 SRS2 7/2C /7 __ NOVLP 4 NVALU 3 PTRA __. 10 PCRUS A 5k00 PCROL 0. 5000 PMUT 0 0010 CV___ _ 0000 NPOP 32 NSEL 8 LCYC 10 NPAR 8 NSEG 32 NVAR 5 IX 1 IPAP I IPBP 0 IPAF 0 IPCS 0 STOP 406132766 3276 766 32766 32766 32766 32766 6 3 3766 32766 2 4,4.61 32766 3;2766 32766 32766 32766 32766 32766 32766 3 4,061 32766 32766 32766 32766 32766 32766 32766 32766 4 40d,61 32766 327766 32766 32766 32766 2766 32766 3276^ 5 4,061 327663276 32766 32766 32766.32766 —' fi 4_t 61 32766 32765 32766 32766 327r -' 4t066 7 4.061 32766 32766 32766 o-' to,0 51754 521A6 8 4.061 32766 327t'A 01 470 51726 55100 56228 9 -4,-61 -~i "',12 1311 4 477d4 4 4 7367 4 0 50538 63682 10 B 2i29. 26618 8554 47 196 47150 5 260 55760., o6 466'26 bO52?o66 265b' 4956 - 51260 -' 51473 7 47660 -44720 __o 5;,156 4fib7O 4866o 34478 5420 55730 56048 486 4 48R80 386 27,39 46656 S55i 25;874 16't6 5 -948 51 936- 51498..56016 309 13.212 38976 52545 22776 634 51020 47164 47898 52160 310- 47., 75...50480 5249 2.6588 1..596 51260 51726 43818 48320 311 41.794 54338 48878 26588 9018 51978 51950 51006 48050 312 6-4,672 51 551 529-6 3.i218 4936.s51456'51726..51596 52160 313 35.121 5C736 48o54 18442 4920 55536 56062 46686 51920 314 49,2?50 46656 4862; 26122 934 47688.47 50I- 5484 6 59360315 41,466 5b226 52714 22794 16710 47916 51696 47164 48336 316 37,~25 430456 489.'06 26362 856 47180 47484 51708 48320 317 31,611 46446 52986 _31216 1593 51470 51726 43596 48080 318 4,99 5,99- 7 6 565f8 34540 4938 47196 — 47164- 5 1036 51920' 319 18,790 3s752 52746 35922 5192 47196 43324 51276 48080 320 11.915 5052.d 37 08 3438 -157 4-55746 — 52448 55566-'5 165 0 VARIETY 1 GEN - EFPF AVG ST —- AVGS - TOS NI NTR-. I 4,01 4.061 0 VI00 t 4 61 __ 0,00 _ 0 _ 32 2 3- 939 3.816 4,682 9, 364 ~ 6, 427 0- 3 2 3 4.335 5.J 137 6,7,3 14.67 ___ 6.819 _ 32 4 \-4.867if. 3,2 6 795i 15.776 6 413 3 2 5 5o,333 7,316 7,187 18. 25 5,107 0 32 6 5,7 78 -6d76.6 - --- 3S7 8.326, 23 32 ___ 5,7 42 6.4b8 7.21 17,2(i 5,807 F 32 8 — 6, — 2q n^ i' 36. 8-,-84'6 ~?',"789'. — 5,969 -- -329 6,635 1.6682 9,281 23.279 4,593 0 32 10 6,78q 8. 86 9,520 21.760 8,'3 05 o 32~ VARIETY 2 __ GEN... E'F AVG S —-- AVGS ST -ISTDS 2 -- TR 1 44,061 4.061 0 800 4.061,0.00. 0 32 Figure 38c Input data, initial and final parameter values, and generation statistics for five varieties in extended simple recurrent selection for 8-parameter Peak NE using Gene Action 4 with random inversion and translocation of chromosome segments and random mutation of gene conformation (Sheet 1 of 2) 146

2 4,62 ___..5.179.. 6*,587 13Q, 2 7 7.815 Q 32 3 4,968.o4 -t5.62 9,;6 8 123" ~ 32 A 4.,97__.9d5 5.26_ 12.864 3,726 _ 32 5 5,075 8.1, 6 7.61' 19 363 4 22 - 0 32 6 5J324 5,971 6.912_ 15,.'8 7,21t P 32 7 5,9 2 1A,5b94 9.4 b 24. 42 7.497 -0 32 8 _ 6,855 1___j. 2 9,614 26.241 5.004 0 32 9 -7.6'r7 13,622 12.832 32. C1 9 4K4 4 32 1_ 8.6_ 2 17.55757 14.2 6 36.625 7,9 18 a 32 VARIETY 3 GEN EFF AVG STO AVGS STDS NIZ NTR i 10,270a 1.,270 11 78 26.278 7.778 0 32 2 9.352 8,434 9, 14 22.4d9 5,321 ___32 3 9.785 1.649 11 716 27. 2o 69 0'32 4 1__.,583 1P,978 13.5)9 32.476 5,45t __ 32 5 11.491 15.122 14.337 33.5-14 1o.511 0 -32 6 12.249 16.'41 12. 92 31.786 5.417 0 32 7 1 3. 39 17 7.72 13, 3.63 34,746 5.i 37 0 32 8 13._5;3 t16,746 13.1-4, 32.780 7,716 0_ 32 13.4 17. 13915-,4 179-399 36,924 9.844 e-0 32 -10 14.595 26. 012 11.519_ 3$2,722 4,079 0 32 VARIETY 4 GEN EFF AVG STO AVGS STLS NIZ NTR I 19.664 964 664 10533 3. 592 7,.17 0 32 2 20,764 _ 21,863 _1,3887 35. 165 3,488 _ 32 3 19,678 1.i7.55 14,804 37 633 12,069 0 32 4 20,084 _ 21.32 11.81i 35'852 6.177 0 32 5 19.668 18. 07 1 I,619 32 115 3,369 0 32 6 19974 21.5 5 1 0. 539 35 P.A5 5 9,684 e 32,7 20,.25 21.Yo 11, 149 36 640 5,-07- - 32 8a__ 2, 464 22.43 5 11.77 4 3,7,334 7.036 0 32 9 G..,29,R 18,6 81 1 2,69s9 35.659 8.838 0 -.32 1 21.?57 27,893_ 14.822 2 47,55 5,084 0 __ 32 VARIETY 5 GEN F_ FF __ A V STO AVGS STDS NIZ NTR i 21,7'i 21.7' i 11.356 37.236 4.713 32 - 2 ~2,3i22 22.9,93 11.952 38.34. 5.313.32 3 22,572 23.113 11 762 38.933 7,943 e 32 _4 23, B2_ 25,412 14.2b4 45,472 6.374 7 32 5 24.117 27.4 59 13.155 44.86 8,933 0 32 6 2 5 715 33,7)3 t11_ 2 5 _5 47.51 5_ 3.928 0 32 7 26,897 33,939 14 445 51 982 7,818 0 32 27 i56.5 32.,287 16.4474 54.249 6,592 0 __ 32 9 28,6i73 37.537 15.746 58,0,2 8,817 0 32 10 3h0,03 41,9pQ 14,739 59,747 5,851 0 32 Figure 38c Input data, initial and tinal parameter values, and generation statistics for five varieties in extended simple recurrent selection for 8-parameter Peak NE using Gene Action 4 with random inversion and translocation of chromosome segments and random mutation of gene conformation (Sheet 2 of 2) 147

0 320 640 96U 1280 1600 INDIVIDUAL Figure 39a Phenotypic value of individuals during extended simple recurrent selection for 8-parameter Peak W using Gene Action 4 with random inversion and translocation of chromosome segments and random mutation of gene conformation 148 0 3L0~4 gm1 190 1600 I NE) IVlIOUJAL Figure 39a Phenotypic value of individuals during extended simple recurrent selection for 8-parameter Peak W using Gene Action 4 with random inversion and translocation of chromosome segments and random mutation of gene conformation

or, 0 320 640 960 1280 1600 U 320 640 960 1280 1600 INtI VI DUAL INDI V DUAL't _- ~....~..... ~'1 - -- X4 2 0 O 40 6n960 1O 60 o 3ao0 INOIVIOUAL IN01 VIOUAL -------------- - g. —^-1 a-~o_- 4 13 320 640 9 I0 lf)O cM 1280 1600 I V IITUAL INDI VIDUAL Figure 39b Parameter values of individuals during extended simple recurrent selection for 8-parameter Peak W using Gene Action 4 with random inverstion and translocation of chromosome segments and random mutation of gene conformation 149!NDIVIDUAL xI X' 320 GqO 9GO l -0 ] GOC muatinoeecnomto

8 r('034 _ SRS2 7/2O0/73 NUVLP 4 _NVALU______ 4 _ PTkA __ _ PCROS (A,5?O "' __PCROL____ tA^ci_ PMUT JPOP'?32 NSEL B LCYC 10 NPAR _______ NSEG 32 NVAR _____ h IX I IPAP I _IPAF_________0__ IPCS 9 ______ 8('35 ______ ____ __ __ __ 1 2,440 327c 327o6 3266 3227 3626 o327 66 32766 32766 32766"32766 2 2 s2440 32766 32766 32766 32766 32766 32766 32766 32766 3 2,44CA 3I266 i 7 32766 3P7^ 6 32766 32766 32766'32766 4 91?440 327 66 327o5 327S6 32766 327 66 32766 32766 327^ 5 2.440 3 276 "327t6 32766 32766 32766 32766 ~ ___6 ___2P.440 3276r 327655 3?766 32766 397^ 6s2164 7 2,44 3P76u 32766 32756 v ro / 5974 ~32178 8 _ 4 4 0 327fb 327^0 1594 32572 170('8 28338 9 2.440 -- to 33954 1 868 32570 " 2090 72178 _____(? _ ___?<S^^8__1392 33556 1626 36680 59268 32178 *.^<f 3036 3V27'c46- 1394"31QV 1624 32t( 98528 36P.02 __ 6f____ 0^88a 8 3030_ 327 4 4 27168 301&2 14'0 26492 5416 32162 3' _8 83.676 3036 32" 94 11 T637 4 4 2 ~~' b5 4 3 63 3 23 3 1114 "321 92 ____3h9 77 72_ 6676 327 18 1348 33362 1372 35920 5658 32164.310 78 144 3 36 33164 1332 34 96 844 35438 88 O 8 36002 311 94.i55 10604 329 44 2944 336'0 1866 32826 20P6 32192 %3 78,947 3i34 3r$ ^da 66 ~ 33570 2486 35692 5944 32162 313 73 641i 8c(A 4 3684 4 P464 30(0CO_ 2246 31866 9048 36002 314 68,740 034 36784 1156 41294 71990 393 71144 32176 315 82P234 30334 37054 4 1632 3766ti 1610 32078 1354 36016 316 70,198 5676 3'299>i 11B4 "33570 6056 320(80 -. 57404 36ei02 317 682.530 I 2794 3320- 2478 37664 2202 26238 2202 32192 31 85,7sci 279b 291j~ 2704'3354O ~1592 32574 1894 28354 319.73,202 2794 36768 1332 3717 0 5196 35694 5194 32176 3WW2 5,)39 jW5 974 2464 37y-22323980 49843219 — VARIETY I ______ ___ GEN EFF AVG - -- ST -VG -- S TINZ N NTR 1 ____ A2 443 2. 44 0 ______ 2.44l 0001 3 2 2 27938 3'435 3343 8.8 ~ 2 940 -32 3,622 P 4 991 i 6 144 13 q,Q9 _ 765 a 32 4 4.'A0^ 5. 333 4,6" fy 4 1 96-4E t54 -25_ 5 ____4.5i39 5, 744 6.s 028_ 15 53__ 6,243 0 32 6 5.^9 " 7, 596 8 25541~16 -- 7 98 3 --- P3 7 5 * 4 66- 7.t>7 6 o,370 17.94 6,246 P 32 8 6.188', I 31 0 9,254 225 232 5 5 123 3 2 9 7.1144 t4 51B 6 9 79 27 384 7 423 P 32 10 8,26^ 1 8'0 I-3 >5 9,646 %3 3i 2909 b,036~~' ~ — P32 VARIETY 2 _____ _ _G I EFF AV3G - NS1-.-A. — 2,443 2,P44 4.0fe 2,440 0,0^A 9 32 Figure 39c Input data, initial and final parameter values, and generation statistics for five varieties in extended simple recurrent selection for 8-parameter Peak W using Gene Action 4 with random inversion and translocation of chromosome segments and random mutation of gene conformation (Sheet 1 of 2) 150

__2 4,62 ___.179.,i 57___ o;2....7.815. 3.___. 32 3 4,.6-A 2o,o4 e,62s 9.06 8.123 * 32 a A4, 97 __.9d5 ___ 5.2bIi 12.44 3.726 32 5 575.8..186..7.61 19.363 4.,221.~ - 32 6 5?24 i5.971 6.912 15.'8 7,251 __ 32 7 5,~92 1.b94 9.4 - 24, 42 7.497 0'32 8 6,855 12.q02 9,614 26.241 5,404 0 32 76 7...' 13.622 12.'832 32~''1 9'.4a4 0 32_1 81.6'~2 77,557 14,26A 36.625 7,918 0 _ 32 VARIETY 3 GEN EFF AVG STO AVGS STDS NIZ_ NTR 1 l,027Ii 17.27I 112 78 26.278 7.,778. 32 2 9,352 8,434 __ 9,14 22.149 5,321 ____ 32 3 9.785 1.649 \ 716 27,*2 - 6 ^ 6 P9 ~ 3 32 4 10,.53 12.978 13,5 9 32,476 5.451 32 5 1 1.a491 15. 122 14,337 33.514...10.511 0' 32 6 12.2 49 1. 6 41 12. 92 31.786 5.417 0 32 7 13.039 17.7d2 13,363 34,746 5.i137 32 8 13,53 3 16.746 LJ,143 32.78. 7,716__ 0 32 9 13,Q94 17.926 15 399 36,924 9.844 0 32 10 14,596 20,n12 112.519 __ 32.722 4,079 0 32 VARIETY 4 GEN EFF AVG- STO AVGS STOS NIZ___ NTR I 19,6064 19,664 1. 533 33.592 7',70 — 0 32 2 __ 20.764 218d63 1.887 35.165 3,488 __ 32 3 19,678 17,55 14 804 37,633 12,.69 0 32 4 2o. 84 _21342,1 81Si 35,852 6.,177 0 32 5 19,66S 18. i7 1, 61 32,115 3,369 - 32 j6 1,974 ___21 5i5f 1' 5_3___ 9 35,55 _9.684 68______4_ 32 7 2o,2a5 21o 9' Y 11.149 36,640 5,'740 0 32 8 2 2,464 22 435 11.77. 37,334 7,436 0 32.9 ~.,29g 1808,2l 12,699 35,659 8,838. 32 10 2-1,57 27,893 14.622 47,515 5,084 __ 32 VARIETY 5 GEN _____FF AG ______ ST AV___S STDS NZ NTR I 21,7 21.7 11,356 37.236 43.71 713 32 2 2,302 229 229..3 11 952 38.3zW4 5.-313. 32 ^3 22.572 23.113 11,762.38.933 7,943 32 _4 2_ 23, B2__ 25,41 2.14. 2 b 4 45,472 ___ 6.37 4 _ 32 5 24.117 27.459 13.155.44.86 8.9333 0 32 6 25.715 3,3. 7 a3 11,255 47.515 3, 928 0 32 7 26,897 33,939 14.445 51.982 7.818 0 32 8 _____27565 _ 32.287 16474__ 54.249 __ 6.592 0 __ _ ____32 9 28,673 37.537 15,746 58.002 8,817 0 32 10 30.043 41,9?J1 14,739 59.747 5.851 ____ __ __ 32 Figure 38c Input data, initial and final parameter values, and generation statistics for five varieties in extended simple recurrent selection for 8-parameter Peak NE using Gene Action 4 with random inversion and translocation of chromosome segments and random mutation of gene conformation (Sheet 2 of 2) 151

o -+ -j 0 U mutation of gene conformation 152 Q 320 140 S;O 1 280 1GOO T NOT I V T DUAL 7igure 40a Phenotypic value of individuals during extended simple recurrent selection for 8-parameter Peak S using Gene Action 4 with random inversion and translocation of chromosome segments and random mutation of gene conformation 152

.! _ * l..'..V JN lI ViaL 9'c t ihiiai~iiL t||'l|3 0 380 640 960 1g80 1600 l0 39 6C 0 9 10 1600 INOIVIDUAL INDIVIDUAL:too I, m xI xIDVUA gI, 2 1 I8 ] 31.0:0 96 J86 O So90 130 60 6 S0 lW0 iNDIVIDUAL INDIVIOUAL i o 0 3R0 640 OG 1S60 1600 0 380 640 960 8L00 160 IN iVIOUAL INDIVIDUIAL Figure 40b Parameter values of individuals during extended simple recurrent selection for 8-parameter Peak S using Gene Action 4 with random inversion and translocation of chromosome segments and random mutation of gene conformation 155

80035 SRS2 7/20/73 NOVLP 4 NVALU_ 5 PINV 0 00ic PTRA 0.0 0010 PCROS -- 5i00 PCROL 0.5000 PMUT 0.0010 CV 0.000a NPOP 32 NSEL 8 LCYC 1I NPAR 8 NSEG 32 NVAR 5 IX 1 IPAP 1 -IPBP IPAF___ -IPC3 -. —--— 60 STOP 1 1.642 327'6' 327 6-S6 $2 —-- 776632 6762___ 1,642 32766 32766 32766 32766 32766 32766 32766 32766 3 -— ~,642 — 3766 32766 32766 32766 32766 32766 32766 32766 _4 _1.6i$42 32766 32766 32756 32766 32766 32766 32766 3270 5 1,642 2 32766 32766 32766 32766 36 3 2766 3766' - 6 1,642 32766 32766 32766 32766 32?7 __ 5002 1. 642 3?76 327 3'276 366 ^- w8 2568 9 126 8 1,642 32766 327i _ e__ 474 _ 2976 29654 8588 9 1-,642'"'"./ 200 24138 5486 25560 9110 _B0 __ t10 27678 2016 20778 6770 29102 5272 - cJ 27486 9694 23598 1568 24632 5360.33210 8870 -_o 86,.373 3r84d6 1996 28142 5918 28714 6514 24888 5242 3089 6q.40e 27480 9692 27915 1598 32388 1646 21048 9354 30Q9 80.989 2749d 9676 24076 5410 24424 99r6 21496 1672 310 85.'76 26782 5824 27454 9954 2081 0 2914 25324 5286 311 85.956 27740 9678 27916 5680 28220 1984 2912 8590 312- 60,309 27016 19 4- 20.236 58 8 26236 14480 33496 -— 4732 -31 64,338 308603 13504 27922 2062 24424 10850 32718 4748 314 86,267 2390.' 9678 24076 226 24168 6034 28864 4988 315 74.Q95 27260 1985 31366 1822 20598 5682 25520 5062 ~316 f 84 583 23646 5598' 24076 51 68 20824 6...318 29372 9068 317 8___179 27246 5600 31546 2500 24394 1856 25340 8842 318 62,750 274-86 5616 -31 i4 20321-6458 — 605 0-25052 12950 31 83. 39 27742 9438 27692 2M48 28234 6034 21724 9128.9 - 2 7742 9438 27 92 320 82.930 27980 5599 27692 1810 28218 2208 29388 8604 VARIETY GEN- EFF AVG STO AVGS STOS N IZ. NTR 1 1 642 1 642,0 00 _ 1.,642 0, 000 __ 032 2 3, 52 4,463 4 617 01.50 4,276.0 32 3 4,Q72 8.611 9.871 22,847 9.195 _ 32 4 6,911 12.727 11.282 28,622 6,9,2 0 32 5 9. 207 18,395 12,863 34,463 10,047 ___32 -6, 12 V 2 06$5. —-'853- -3 794 8,224 -- 32 7__ 13,*b3 27,448 13,1b3_ 465. _O 7.48 ___ 32 8 15.6k0 30k 633 13.63> 48 33.79 7,813 0 32 9 17.634 33.91 12.53A 49.017 7 1844 32 t1 1iP451 Y 35-~62 14899 54 661 601 0 32 VARIETY 2 -GEN -EF —-F AV G —--- ST GS — SS ---- R - NI 1 1.642 1.642 a,.003 S1642 0.000 0 32 Figure 40c Input data, initial and final parameter values, and generation statistics for five varieties in extended simple recurrent selection for 8-parameter Peak S using Gene Action 4 with random inversion and translocation of chromosome segments and random mutation of gene conformation (Sheet 1 of 2) 154

2 2.8RI 39O7 4,66 8 t 193 5, 148 a 32 3 3.11...4(.1 I 2 3, 0,' 5 9. ^67 2. ^4i ~. a32 4 3,418 4,.42 4,562. 10,.522 4,61 0 _ 32 5 3.83,;t7.....5,519 -75,7 —3 13.978 4,634 - 0 - 3 6 4 3t2? 7 116 5,344 18 Q59 8s,5I 0 32 7 5'.5';7 129,b 40 9"4 b.-,'~ O--6-2 —- 8 5 6 7 --- 3 238 7,485 21,122 1,.36 34,425 8,645 _ 32 9.9.7 17 27 571. -. 12 682 3"-.759.-.- 7,982- ~ - 32 10 122 17 34,721 11 271 48,830 6,v91 0 32 VARIETY 3 GEN EFF AVG STD AVGS STDS NIZ NTR -1 -31 81 ST0- 3 i. 8 I T 16 e9.-5 4 5~9'22 —— 5 348 ~- -322 351356 3;93103 15,192 49,48 113,726 0 32 3 -— 33..- 3 -1 -— 9 T-1 5 3i t5 53 730 3,397 0- 32 4 _ 36,709 45,133 12,351 61,315 5,184 32 5 39 385 5M, 91 14 4~1 69,897' —89 7,784 --.0. 32 6 41, 28 5P.841 13.981 68 916 3,361 0 32 7 44,35Sg 9 6.,748 12,43-5 75' —— 3 3,598 0 32 8 46,561 61 970 12 894 76,875 4,116 0 32 9 49,?244 8 9'?~,742 - 9 777. 83, 25 2 -",3 3618 0 —--- 32 10 51,436 71,129 11,073 85,562 5,533 0 32 VARIETY 4 GEN EFF AVG STO AVGS STDS NIZ NTR 1-S, 77 5 1 6 77-6 9,528 -6 —4-, 92 2-647 2 —----- 2 48.159 44,542 15,422 65 118 5,868 32 3 5 —— 5i Pq59 5 55 --- 1-4 —925 — 76,338 3 5 0093 32 4 __ 52,94 63,099 11,475 77.123 5,411 Ae 32 -- - 55.47 -~d 6g4-f 17- -T -12 i68 -- 76 450 4,167 --- ~ 32 5 57.35.2 66,720 11,201 80,978 4,42 __. 32 7 58a128 6275- [3.141 78.69 - 3- 979 -- 328 58.836 63,789_ 1, 547 77,061 7, 26 P 32 -y9 — 59,A444 64,3~7.4 — 5 4s2 78,514 - 3,3b62 - -?. —--- 10 59., 9 78 648,3'5 7.4 8 35 5,847 I;32 — VAR-IETY - 5 ------ GE^ EFF _ _AVG STO_ AVGS STDS NIZ _ NTR I 72.519 72.519 8 322 83- 248 1,731 0 32 2 67,571 6 26 23 ji?491 75, 063 4 398 e; 32 53 68'-, 62 7. t,0a 1. 262 -82,977;3 525 0 324 68, 324 6 i8, 0d 9 1, 16.6 81,583 4,374 0 32 5 68,55 7 694, 468 12 965 83, 8 1 1 4 863 0 — -. --.32 6 69,624 7,L964 10,13 85, 159 2,81 __ _32 7 70,265 74,1 0 8,642 82930 3,151 32 8 7,0553 72,569 8,4990 82512 5,e019 _ 32 9 70,476 69 857 8- 5 6 8.-0 8 5 -3. 75 -- 32 110 7S l,37 76,083 8,055 85,359 1,592 e 32 Figure 40c Input data, initial and final parameter values, and generation statistics for five varieties in extended simple recurrent selection for 8-parameter Peak S using Gene Action 4 with random inversion and translocation of chromosome segments and random mutation of gene conformation (Sheet 2 of 2) 155

4 CONCLUSIONS One objective of this study was to determine the relative effectiveness of additive vs. epistatic gene action algorithms for numerical parameter synthesis. Four additive and twelve epistatic algorithms were investigated in conjunction with five ARTIFICIAL BREEDING procedures. Six mathematical functions were used to test the direct-search performance of the method. Additive Gene Action 4 exhibited superior performance in a majority of the experiments. In this algorithm, four, 16-gene complexes control the synthesis of each numerical parameter. Four levels of effect are used to obtain a parameter range of [0,65535], but, within each complex, the genes contribute additively and with equal effect. Redundancy of encoding extreme parameter values is provided by a transformation of the primary, cummulative effect of the individual loci. Of the epistatic models, Gene Action 6 was judged most effective. This algorithm avoids a basic problem of the binary number system as a basis for artificial genetic encoding —the requirement that the conformation of genes at many loci change in order to produce a small change in the encoded parameter value. It too provides redundancy of encoding extreme parameter values by a transformation of the value determined by the primary algorithm. Another objective was to model and investigate the effects of intra-allelic dominance at the genotypic level. Eight of the sixteen gene action algorithms developed in the study incorporate dominance modifier loci that act in conjunction with the functional loci. There appears to be no advantage to dominance modification in parameter optimization where storage of latent information is not essential. The most noticeable effect is an increase in parameter variance during the early generations of a breeding program. Dominance would be more important in adaptive system applications of ARTIFICIAL BREEDING. 157

A third objective of the project was to develop specific ARTIFICIAL BREEDING systems for direct-search optimization in up to 32 dimensional parameter spaces. Seven such systems were developed and investigated in many different experiments. Five are single-breeding-program systems that begin with completely heterozygous source populations of artificial organisms. Two are extended-breeding-program systems that generate a sequence of varieties, starting with two derived from completely heterozygous source populations; improved varieties are bred from crosses of the most valuable of previously developed lines. The breeding methods used in these systems simulate the following techniques of agricultural plant breeding: 1) pedigree method, 2) bulk population breeding, 3) mass selection, 4) simple recurrent selection and 5) reciprocal recurrent selection. The most effective results were obtained by an extendedbreeding-program system using additive, polygenic control of parameter synthesis and simple recurrent selection for the objective character. The most versatile artificial organisms appear to be those capable —as many plant species are —of both self- and cross-fertilization. They can be crossed to create and systain genetic variation required for exploration of the genetic parameter space; and they can be selfed to rapidly fix desireable combinations of alleles. Linkage seems to inhibit the dismantling of desireable gene combinations, but it also accelerates fixation of undesireable alleles. The net effect is to impede the progress of short-term breeding programs. Random inversion and translocation of chromosome segments during simulated interphase and the random mutation of alleles in zygote genotypes appears to significantly improve the performance of extended-breeding by simple recurrent selection. This is based on a sequence of ten experiments in breeding for five different objective characters, with, and without random aberrations of chromosome structure and gene conformation. These experiments were conducted at the end of the study. They are not considered conclusive, but they do indicate the potential of the ARTIFICIAL BREEDING method and will be investigated in further studies. 158

REFERENCES R. W. Allard, Principles of Plant Breeding, Wiley, 1960 R. B. Hollstien, "Artificial Genetic Adaptation in Computer Control Systems," University of Michigan Technical Report 032960-14-T, April, 1971 G. J. McMurtry, "Adaptive Optimization Procedures," Adaptive, Learning and Pattern Recognition Systems, J. M. Mendel and K. S. Fu, eds., Academic Press, 1970 L. E. Mettler and T. G. Gregg, Population Genetics and Evolution, Prentice-Hall, 1969 F. W. Stahl, The Mechanics of Inheritance, Prentice-Hall, 1969 W. H. Swann, "Direct Search Methods," Numerical Methods for Unconstrained Optimization, W. Murray, ed., Academic Press, 1972 J. D. Watson, Molecular Biology of the Gene, W. A. Benjamin, Inc., 1970 159

APPENDIX COMPUTER PROGRAMS USED IN EXPERIMENTAL INVESTIGATIONS OF ARTIFICIAL GENETIC BREEDING PROCEDURES Artificial breeding experiments were run on a Digital Equipment Corporation PDP-9 computer at the University of Michigan's Simulation Center. The PDP-9 CHAIN/EXECUTE system structure, format of input data, and listings of all programs used in these experiments are included in this Appendix. The input variables are defined as follows: NDVLP integer from 1 to 12 specifying the gene action NVALU integer from 1 to 6 specifying the objective character PINV probability of chromosome rupture between adjacent gene complexes and refusion with a chromosome segment in an inverted position PTRA probability of chromosome rupture between adjacent gene complexes and refusion with segments of two chromosomes translocated PCROS probability of crossing over between adjacent gene complexes PCROL probability of crossing over between adjacent loci within gene complexes PMUT probability of independent mutation of zygote alleles POUCR probability of outcrossing in Bulk Population Breeding CV lower bound of objective character values for parameters within the admissible domain NPOP population size (sequence of values for Pedigree Breeding) NSEL number selected (sequence of values for Pedigree Breeding) LGEN last generation NVAR number of varieties LCYC last cycle of recurrent selection NSAMP size of half-sib families in Reciprocal Recurrent Selection NPAR number of parameters NSEG number of gene complexes A-i

NREP number of replications IX initial (odd integer) value of the pseudorandom number generator IPAP parameter print control (1 specifies all trial points are to be printed) IPBP parameter print control (1 specifies only trial points having objective value greater than previous trials are to be printed) IPAF allele frequency print control (1 specifies frequencies are to be printed for each generation) IPCS chromosome structure print control (1 specifies locations of gene complexes in each chromosome are to be printed in the last generation) Graphical results of the experiments were generated by the computer on a storage-type CRT and hard-copy unit. A-2

Input Data PMl 6/7/73/ NDVLP 1 NVALU 6 PINV. pi0i0 P"RA 17 c0~00 PCROS 95000 PC.OL 58<00 PMUT (1AO p0. CV O, )"00 NPOP 64 64 32 16 8 4 4 4 4 NSEL 32 16 8 4 2 i t 1 NPAR 2 NSEG 8 NREP 5 x.i IPAP 0 IP8P i IPAF 0 IPCS STOP Main Program (MPM1) i001 C MPi 1 Vi 3002 C PEuJIGREE McTHO' 1 00d C MAIN PROGRAM OF GENETIC PROGRAMMING SYSTEM PMI P00i4 INTEG~RE CP(256,23),S(256,2,3),R(100),X(256) 005 LOGICAL EVENTVIAA 006 DIMF.SINn 4 A(12),CDATA(2),FI (2),F2(2) F3(2) PFILE(2 007 1 v r V ), VS (10),NP ( 1),NS (10) 008 COMMON /CPS/CPS e09 DATA F1i1),F2(l),F3(C)/SHF1,5HF2,5HF3 / e010 r1,FC(P),F2(2),F3(?),PFILE(2),CDATA(2)/5*4H SRC/ 011,STOP/5rSTOP /,PFILE(1)/5HPM1 / 012 C REAO PFILE, NUVLP NVALUPINVPTRA PCROS,PCROL PMUT 013 C CV NP NS, NPAN, NSEGNHEP I XIPAP, IPBP IPAF, IPCSw 014 C COATA FROM DISK FILE 015 IF'(IT('G(2).EQ.O) GO TO 6 016 WRITE (6, ) 017 1 FORMAT ( 1X DATA FILE') 018 REAr (55) PFILE(l) 019 5 FORMAT(A. ) 020 6 CALL ScEK(1,PFILE) A-4

021 1 REArn(1, 15)PFILE( 1),NULPNVALUPINV,PTRA 022 1,PCRS, PCROLPMUT, CV 023 15 FORMAT(9XA5/12Abp2(/9XI6) 5(/g9XF64)/8X,F7.4) 024 REAn ( 0) NP(I),Im2, 10) (NS(J),J2,10) 025 20 FOATR^A X, g91l6/XQIl) 026 REAfi It 2,) NP'Ar NSEG, NREPa IX 027 2.5 FORMAT (9QX Ib,(/9X, I)) 028 REA'OkI1,30)IPAP,IPAP,IPAFIPCSCDATA(1 029 3( FORMAT (X. TsI,3 (/SX, I6/XA5) 030 CALL. CLOSt (C) 031 C DELETE ANi, rECCH~ATE PRINT FILE 032 CALL OLFTE(7,PFILEI) 033 CALL ENTTE'(7,PFILE) 034 C WRITE PFILE.,NDVLP,NVALU, PTNVPTRA,PCROS,PCROLPMUT, 035 C CV, NP, NS, PAk, NS, NEP, IX, IPAP IPBP, IPAF, IPCSw 036 C CDATA INTO PhINT FILE PFILE 037 RIT (/, 35) PF ILE(), A, NOVLPNVALUPINVPTRA 038 I,PCkOs,PCHOL,PMUT,CV 039 35 FOR4AT(l0XA.b/l/X,125/ NfVLP',Il0/' NVALU',I10 040 1/1 PINVlF11.4/' PTRA',Fll,4 041 1/' PCRO',FI3.4// PCROL',Fl04// PMUT',F11.4 042 1/' CV',F13.4) 043 WRITE (7,40?) (NP(I), I2 10), (NS(J),J"2,10) 044 40 FORFMAT( NPOP P,I11,8I6/1 NSEL'1181 6) 045 wRITE t7,45) NPAR, NSEG, NREP, IX, IPAP, IPBP IPAF, IPCSCDATA t ) 046 45 FORMAI( I NPAR,Ill/l NSEG6'Ill/' NREP'lli 047 1/' IX',I13/' IPAP, IT11/ IPBPt,113/ IPPAF,I11 048 I/' IPCSI',IX/Il0XA5) 049 C ASbTGN LAST tENERATION 050 LGE'N. Iti 051 C UELETE ANr; WODEFINt.UIECT ACCESS FILE Fl USED TO STORE 052 C UP TO 1.00 CHNOtOSOME ARRAYS 053 CALL OLETE(1,F1,lI 054 CALl. IDFIrNEC(14*NSEG, 1 01, F!,IV1 1t0,0) 055 C DELETE AND REDEFINE OIkECT ACCESS FILE F2 USED TO STORE 056 C EFF, AVG, 6Tu, AVGS, STOS, NIZ, NTR FOR EACH GENERATION 057 CALL OLETEC2,F2,I) 058 CALL' )EFINE(2,i, (N EP+3)*LGEN,F2,IV2, 1 00) 059 C UELETE ANn REDEFINEt UIIECT ACCESS FILF F3 USED TO COUNT 060 C THE NUMJEP OF'"" ALLELES IN THE POPULATION AT EACH LOCUS 061 C AND GENERATION 062 CALL OLFTE(3,F3,I) 063 CALL DEFINK(3, 16,NSEGF3,IV3,0t0,0) 064 C START IAN.OOM NUMI6Ek GENERATOR AT IX 065IX=.Ix 066 CALL UN NCI XU) 067 C INITIALIZE RUN COUNTER ANO BEGIN RUN IRUN 068 IRlUN 1 069 50 I ND I IV a 070 NTHRTr. 071 VSUM(l. 072 E=e. 073 IGE.M? A-5

074 IVs~1. 075 ISTORnM 076 IDRAW85 077 C FeGIN GENENIATION IGEN 078 6r ITNO1 079 NIZ.,v 080 NTR=., 081 NPQP NP(IGEN) 082 NSEL. NSCIGEN) 083 C FAMILY SIZE 084 NFS ZNPOP/NSEL 085 C SELECT PARENTAL GFNOTYPES AND LOAD INTO CORE 086 C ARRAYS CP ANu $ 087 7c IF IC6E.i,GT,2)GU TO 72 088 C F'ORM RANDOh HETEROCZYGOUS PARENT GENOTYPE 089 C FROM VIRTUlAL F1 POPULATION 090 DO 71 lI,NSEG 091 CALL ltRN (IXU) 392 00 7 1 K.1,2 093 lDO 71 Jul,2 094 N(CT-1)/t1+ 095 MI=m(N=l)*8 096 CP(CfJK) IPAC (N,M) g97 IF (J,.. 1]) 8s(,J,K) aTX a98 IF (J.EU2) $CIJ, -) -IX-1 99 7 1 CONTINUF 100 GO TO 76 01 C FETCH PARENT 102 72 IFAMm( INU- 1)/NFSZe I 103 IFC(IrJlnEW.1)O TO 75 104 73 IFM=IFM+l 105 IF.CIF.AM.NE.FAMQ)GO TO 75 106 I.F TOG(1).EU l)wRITE(,74) IFAM IFM, I 107 74 FnRMAT (2x,316) 108 GO TU 76 109 75 Im R(IFAl.)+IORAw 11 0 I 2 I1 111 READ(l'1) ((CP(IJ, 1),S(I,J, tl) Is lNSEG),Jl, 2) 112 REAIt)I'12) ((CPCI,J,2),S(I.J,2),Il,NSEG),Jml,2) 113 IFAMO IFAM 114 IFM.0 115 GO TO 73 116 C FORM ZYGOTE LGEirOTYPE BY UNION OF GAMETES DERIVED FROM 117 C PARENT GENOTYPES BY INDEPENDENT SEGREGATION AND CROSSOVER 118 C WITH PROBABILITIES PCRUS AND PCROL OF CHIASMA BETWEEN 119 C ADJACENT SEGMENTS ANU AOJACENT LOCI RESPECTIVELY 120 76 CAL I V R CCP, NSE;GPI NV) 121 CALL TANSCCP, NSEG PTRA) 122 CALL FZYrO (CP, S NSEG, PCRO$,PCROL) 123 CALL MU TAT rS,NSEG,PMUT) 124 C PRINT CHROMOSOf4 STRUCTURE DURING LAST GENERATION IF IPCS u 1 125 TF IGEi L.LEN.9AND. IPCS.EQ. 1)CALL DCS(IND,CP.NSEG) 128 C ABURT INn)TVIDUAL AND ReTURN TO SELECT NEW PARENT IF A-6

127 C ZYGOTE IS INVIABLL; l28 IFP(VIAo(SNSe5G))GO TO 77 129 NIZmNIZ.+ 130 GO TO 7?131 C INCREMENT COUNT OF "I" ALLELES AT EACH INDIVIDUAL AND 132 C PRINT NUMP'R OF "1" ALLELES AT EACH LOCUS AT END OF EACH 133 C GENERATIOrIN If IPAF 1I 134 77 IF fPAF.EQe,)GO TnO S 135 CALL CACIGENLGENINO, NPOP,NSEG) 136 C DEVELOP ParAMETER VALUES USING GENE ACTION SPECIFIED 137 C BY NOVLP 138 do GO TU(tl,NF2,V3,84,85,86.87BB,,89,810,811,812) NDVLP 139 81 CALL SA1l(NSeG,5,NPARX) 140 GO TO 90 141 d8 CALL StAi (NSEG, S NPAR X) 142 Gn TO it 143 8) CALL S(iA5(NSEI S,NPAR, X) 144 GO TO W 145 6a CALL SLA 4 (NG, S,NPARX) 146 GO Tu 9. 147 85 CALL S$A3(N5$GS.,NPARX) 148 GO TU 90 149 df CALL SGA6(NSEGSNPAR X) 515 GO TO 90 151 87 CALL SA7 (NSEGS IPAR, X) 152 GO TO 9m 153 88 CALL. SAd(NSEGSNPARX) 154 GO TO 90 155 69 CALL SA;9 (NSGS. $ NPAR, X) 156 GO TU 9 157 81 CALL.. SGA1il(NEG, S,NPAR,X) 158 GO TU 9S 159 81 1 CALL SGAl (NSEG,S, NPAR,X) 160 GO TU d9 161 812 CALL IA 1(NE2 G, SNPAR, X 162 C EVALUATE INDIVIDUAL PHENOTYPIC VALUE USING TEST 163 C FUNCTION SPECIFIED BY NVALU 164 90 GO TO(91,9S2,93,94,95,96),NVALU 165 1I CALL vl1NPARXV(INO)) 166 GO TO 97 167 92 CALL V (NPARX,V(INO)) 166 GO T(O 7 169 93 CALL V3(N4PAkXV (IND)) 170 GO TO w7 171 94 CALL V4(NPARX,YVCINO)) 172 GO TO 97 173 95 CALL V:(NPAk, XV(IN)) 174 GO TO 97 175 96 CALL VoCNPAKX,,V(INO)) 176 C INCREMENr INuIVIDUAL COUNTER 177 97 INDU.tv=lNIV+1 178 C UPOATE TRIAL CUUNTc',S ANO EFFICIENCY IF PARAMETERS 179 C ARe wIrrHTN THEi AOMISSIBLE OOMAIN A-7

180 IF(V(INn).LT.CV)GO TO 100 181 NTRuNTH* 182 NTRTwNT4WTl 183 VSUMaVSLIm+VC IND) 184 IF ( ND. EU. POP) EIVS.M/FLOAT (NTRT) 185 C wRITE INDIV,VALUEAND PARAMETERS INTO PFILE IF IPAP r 1 186 C OR IP3P 1I ANi) VALUE OF INDIVIDUAL EXCEEDS VALUE 187 C OF ALL PRECELDING INOIVIOUALS 188 1.0 IFCTPRBP.E. 1)SO TO tot 189 IF(TPAP'.EQ. l)) TO 102 190 GO rT 11i 191 1 1 IF(v(IIND).L..HIV)GO TO 110 192 HIV (VC INU) 193.. 102 10 IF (NPARH.,e. *J I TE (710n5) NDIV.V (IND), C(X ( ) t I t lNPAR) 194 1?5 FORMAT(1X, I5,F10.3,8I7) 195 IF (MPA.RiT, T wI E (7, 106) INOIV V (IND), (X (), II1, NPAR) 196 1m6 FORMAT ( X, I,F 1,3,I 7/( 6X,8I7)) 197 110 IKal 198 C 6RANCH ON iGENERATION AND FAMILY MEMBER 199 IF(CEN,.EQ?)GO TO 121 200 KnIFAM+ISTOR 201 IF (IFM.GT.) O TO 120 202 C STORE FIRST IN)IVIUUAL OF EACH FAMILY 203 VSC ( fA) V (1NO) 204 WRITEfl' ) C(CPCIJ,3,S(IJ,3)5,I1,NSEG),Jt,2) 205 IF(ITOCl,).EQ.1)GO tO 125 206 GO TO 130 207 C REPLACE F4MILY REPRESENTATIVE WITH THIS INDIVIDUAL 208 C IF THIS INDIOTVTUL HAS HIGHER PHENOTYPIC VALUE 209 120 IF(V(INn) LTVS(IFAM))GO TO 130 210 VS (FAM) a (CINO) 211 WRITE ( I'K) CP(I J 3), S S( J 3) I I i 1NSEG) J I 2) 212 IF(ITO(rf). (il.)GO TO 125 213 GO TOi 1i3 214 C STORE FIRST NSFL GtNOTYPES DURING F2 GENERATION 215 12 IF(INI),GTNSEL)GU TO 122 216 KIfNU+1STOR 217 WRITEf'IK) ((CP(IPJ,3),S(IJ,3),IolpNSEG),Jmlt2) 218 VS( Np D V (INU) 219 IF(XTOG(1) EQ 1)GO TO 125 220 GO TO 130l 221 C REPLACE LnNEST-VALUEO GENOTYPE STOREO SO FAR DURING 222 C F2 RENERATION IF VALUE OF THIS INDIVIDUAL EXCEEDS 223 C THE LOWEST VALUE 224 122 LOWal 225 00 123 I 1,NSEL 226 IF(VS (I) LT V (LO ))LOWmI 227 123 CONTINUE 228 IF(vIND).LTVS(LOW) )GO TO 130 229 K~LOW+ISTOr 230 WRITE(1 K) C(CP(I,J,3),S(ICJ,3),I1,NSEG),Jl,2) 231 VS (LOW) V( IU) 232 C PRINT GENFRATIUN, INDIVIDUAL, VALUE, AND LOCATION IF 233 C GENOTYPE IS STORED IN F1 AND PEDIGREE IS REQUESTED A-8

234 1?5 IF(IT0G(l)oi.ej*WRITE(6,1265IGENINO~V(INO),K 235 126 FORMAT(2I6,F11,3I 6) 236 IKai 237 C PRINT GENFRATTUN, INDIVIDUALp AND VALUE IF PEDIGREE 238 C IS REQIJESTZD 239 10 IF(ITF G(l) EQ..1.AND.IK.EQO.p)WRITE6,l 26)IGEN,INDVIND) 24' IF(ITNrEW,NPOP)GO TO 140 241 INODINU+l 242 GO TU 70 243 C E iD GENERA l IN I GE 244 C LIST FAMILIES ACCORDING TO SUPERIOR FAMILY MEMBER 245 140 CALL LIST(VS NSELR) 246 C AVERAGE VALUE AND STANDARD DEVIATION OF SELECTED INDIVIDUALS 247 CALL ASrn(VSNSEL, VGSSTDS) 248 C AVERAGE VALlIt AND STANDARD DEVIATION OF POPULATION 249 CALL ASi(VNPOP,AV(G,STO) 250 C STORE IGEN,E,AVG,STO,AVGSSTOSNIZNTR IN F2 251 Km (TRUN1) *LGEN+IGEN 252 bRITE(2'Kc, 10) IGEN,E,AVGSSTDSAVGST NIZNTR 253 15i FORMAT( X, I3,5F 03, 2 0) 254 C TEST FOR END OF RUN 255 IF(IGFNEQ.LGEN)GO TO 160 256 C BEGIN NEw GENERATIUN 257 IGEN I.N+ 1 258 IOAw.IAOR 4Ai+561 259 IF CURAw. TiS0) IDRAW 260 ISTOuI.-STOR+50 261 IF( STOR.GT 50) ISTORm 262 GO TO SP 263 C TEST FOR END OF REPLICATE RUNS 264 16? IF IRUNEQNREP)GO TO 170 265 IRU I RIlN+ l 266 GO TO 5M 267 C MEAN AND EXTREMES OF REPLICATE RUNS 268 170 CALL ME C(LGN, NREP) 269 C CLOSE FILES 270 CALL CLOSE(1) 271 CALL CLOSE(Cj 272 CALL CLUSE(3) 273 CALL CLOSE(7) 274 C TEST FOR STOP 275 IF(CATA 1).EQSTOP) STOP 276 C PRINT NAME OF NEXT OATA FILE IN SEQUENCE AND PAUSE 277 C IF ITOG(2)? 278 IF (ITOG(2),E- 2)RITEC(6,180)COATA(l) 279 180 FORMATC(X, R6START AT 1,A5) 280 IF(ITOa(2) ~Q.E2)PAUSE 281 C CONTINUE USING INPUT OATA IN FILE CDATA 282 CALL StEK (CCOATA) 283 GO TUO 1 284 END A-9

Pedigree Method 2 (PM2) PDP-9 CHAIN/EXECUTE System DOS-15 VIA [.DOS,-15 u lA s.J 0 A OKA -31,-4 SC HA I N CHA I N V7 A NA.E X.CT FILE > PM'2 LIST OPTIONS & PA F;tA F TErS > Nil DEF IN E RESIDENT CO' )E > PM2. I S V1 E R TRAN S, F',7 TY G., CWG 4 S, M, UTA T A, tl 1, I t A, L I S T, ASD U!RN IRAN r) EV Ef:T F I.PA, NP A C, DCS C- SA DESCRIBE I. LIN"IKS. STUfI.CTURlt >G 1= SGA1, PGAl >G 2 = SG A2 3 P A2 >G 3=SGA3, PGA3 >G 4= SGA, PGA4 >G5=S'GA 5,PGA5 >G6='SGA6, PGA6 >G7 =SGA7 P PG. A7 >G8=SGA8 PGA8 >G'9= SGA9, PRA9 >G 1 0=SGA 0 PGA10 >G I =SGA1 sPGA1 1 >6 12=S(GA12, PG A12 >G1 G2:G2 3:3 GG:GS:G6:G7:GS:G9:G(10: G1 1:G1.2: P)DFSV >V1:V! 3:V4:V 5: V6 CORE REQ' D I 6646-57636 DOS-15 VIA $$EXIT A-10

Input Data 60001 PM2 7/9/73 NDVLP 6 NVALU i PINV,0 000 PTRA p l0 0000 PCROS 0 5000 PCROL 0 0500 PMUT 0 0000 CV 0 1000 NPOP 32 32 16 8 4 2 2 2 2 2 NSEL 16 16 8 4 2 1 1 1 1 LGEN 10 NPAR 2 NSEG 2 NVAR 6 IX 1 IPAP l PBP 0 IPAF 0 IPCS 0 STOP Main Program (MPM2) i01 C MPM2 VI 012 C PEOIGREE METHOD 2 a03 C MAIN PROGRAM OF GENETIC PROGRAMMING SYSTEM PM2 104 INTEGER CP C250 2. 3), 8 (25. 2,3 ), R ( 10). X (256) 805 LOGICAL EVENTVIAB 0d ODIMENSION A t2),COATA(a),F 2)).C(2) F3(2) PFILEC2) 00e l, V 00, VS( l00),NP (c0B), NS ( l VV (2) 0ll COMMON /CP$/CPS 069 DATA Fl(1 )F2(l),P3(1)/SHFt,5HF2,SMH3 / 010 F t, (2).F2 C2.) F3 C2) PF. ILE ( 2) CDATA(2) /8*4H SRC/ 611 l,STOP/SHSTOP /,PFILE(1)/SMPM2 / 012 C READ PFILE NOVLP NVALU PINV PTRA, PCROS,PCRL PPMUT, 013 C CVNP NS,LGENNPAR, NSEG, NVAR, IX I PAP IPBP, PAF P XPC8, B14 C CDATA FROM DISK FILE 1t IF(FITOG(2).EO.0)GO TO 6 o01 WRITEC6.s 1^) 017 1 FORMAT(lX.DATA FILEI) 018 READ(C5,5)PtLE(1) O19 5 FORMATCA5) 020 6 CALL SEEK(1,PFZLE) A-ll

t1 10 READ(li5)PFILE(l),ANDVLPNVALU,PINV.PTRA 2n I,PCRO, PCROL. PMUT, CV 0 235 FORMAT(9XwA/12A5,2C/9XI6),t(/9X,F6,4)/8X,tF7.4) 214 READ(l,20) CNP(X), Il,10), NS(J),J",0) 085 20 FORMATC10X, 10S/10X,10I5) 626 REAOD1,25)LGENNPARNSEGNVARIX 027 25 FORMAT(9X, I6,4( /9X, I6 028 READ (C,30IPAP IPP, IPAF, PCS,COATA(lI 029 30 FORMAT(9X, I6,3(/9X, I)/9X,AS) 038 CALL CLOSECI) 031 C OELETE AND RECREATE PRINT FILE 032 CALL DLETE7,PFILEI) 633 CALL ENTERC7,PFILE) S34 C WRITE PFILENDVLP N.VALU.PINVPTRAPCROS,PCROL, PMUT, 035 C CVNPpNS,LGEN,NPARNSEG,NVAR IXXPAP, IPBP, PAF, IPCS 636 C CDATA INTO PRINT FILE PFILE 037 WRITE(7,35)PFILE1), A, NDVLP,NVALUPINVPTRA 0386 1PCROS,PCROLPMUTCV 039 35 FORMAT(10X,A5/lX,12A5/t NDVLP'lI10/' NVALUI160 4l i/' PINV',Fll.4/ PTRA',PF.4 041 1/P PCROS, 4/ PCROL'.Fl0,4/ PMUTPF,4 042 1/' CV',PF13.4) 043 WRITE (7,40) CNP C),I 110)), (NS (J),J1,10) 044 40 FORMATC( NPO.PDI,19IS5/1 NSELl,111i915) 045 WRITE(7,45) LENNPAR,N3EG.NVAR IX, PAP IPBP 04l I.P AF, IPCS, C.DATA C(1 047 45 FORMATCt LGENII1//' NPARIXll/' NSE5Gt,11/' NVAR',Ill 048 1/, IX',I13/1 IPAPXll/' IPBP',I11/ XIPAFP,I 1 049 1/1 IPC8i,Xl1/1OXAS) 081 C DELETE AND REDEFINE DIRECT ACCESS FILE Ft USED TO STORE 051 C UP TO 102 CHROMOSOME ARRAYS 052 CALL DLETE(l rF,I 053 CALL DEFINE(1,4*NSEG, 102,FIV 0,,,0) 654 C DELETE AND REDEFINE DIRECT ACCESS FILE F2 USED TO STORE 055 C EFF, AVG, STO, AVGS, STDS, N N NTR FOR EACH GENERATION l56 CALL DLETE(2,F2,I) 057 CALL DEFINE(2, 8,NVAR*LGENF2,IV2,1,,O0) B05 C DELETE AND REDEFINE DIRECT ACCESS FILE F3 USED TO COUNT 059 C THE NUMBER OF "1" ALLELES IN THE POPULATION AT EACH LOCUS 066 C AND GENERATION 061 CALL DLETE(3,F3,I) 062 CALL DEFINE 3,16,NSEGF3, V3,0,0,0) 063 C START RANDOM NUMBER GENERATOR AT IX 064 IX".IX 065 CALL URNCIX.U) 0b6 C INITIALIZE VARIETY COUNTER AND BEGIN VARIETY IVAR 067 IVARNI 068 50 INDIV.O 069 NTRTaO 070 VSUMm0o 071 Ew0M 672 IGENu1 073 HIXV0. A-12

074 ISTORmO................... i OR A W 086 C 8EGIN GENERATION IGEN 877 61 INDOw 078 NIZuS 079 NTR.O 080 NPOPNNP(IGEN) 08..1.. NSEL"NS C (GEN) 082 NFSZuNPOP/NSEL 083 C SELECT PARENTAL GENOTYPES AND LOAD ARRAYS CP AND S 084 St IF(IGENGT,1)GO TO 72 085 IF(1VAR.GT.2)GO TO 63 86s C FORM RANDOM HOMOZYGOUS PARENT GENOTYPE FOR INITIAL CROSS.7..0 D 2 KD l6, 2 086 DO 62 IslNSEG 089 CALL URN(IX U) 0908 ISIX 0@_9.. IF (EVENT (.5) ) 1SmvX I 092 00 62 Jdl,2.A.s(.... N,"I1)/8+l 094 M,1C(N1t),*8 895 CP(I,JK) IPAC(NM) 896 S(XI,JK)mIS F97 62 CONTINUE 098 GO TO 76.19A_. C.ETCM.H PARENTS OF VARIETAL CROSS 1el 63 READO(t 11) ((CP(I,J,,) S(I,J 1),I 1NSEG),Ji,2) 1it REAODlC' Ia 02)C.(.CP (I!. J t 2 (I, J 2), X11.,NS',9) JIt.21) 102 GO TO 76 180) C FETCH PARENT 104 72 IFAM(IXND 1)/ NFSZ* L.QE...XF (..NDO..EQ t1)GO TO 75 ee6 73 "IFM.FM+. 1e7 IF(IFAM.NEXFAMO)GO TO 75 8 IrF(ITOG (1).EQ1)WRITE(6,74) IFAM,IFM X 1l9 74 FORMAT(29X,3I6) 10 GO TO 76.111 75 IlwRC(XFAM)4.IORA 112 12I11.S REAO(lC*Il) c(CP(I,J, ),S(tSJ, l) IltNSEG) Jl~2) 1-14 REAOClI2) C(CPCIJ,2),S(tSJd,2),Il,N.HEG),Jl.i2) 115 IXFAMOIFAM 16 IFMO0 117 T 7_ __.___ _ 116 C FORM ZYGOTE GENOTYPE BY UNION OF GAMETES DERIVED FROM 119 C PARENT GENOTYPES BY I ENEPNDENT SEGREGATION AND CROSSOVER 120 C WITH PROBABILITIES PCROS AND PCROL OF CHIASMA BETWEEN 121 C ADJACENT SEGMENTS AND ADJACENT LOCI RESPECTIVELY 122 7. CALL INVR (CP, NSEG, PNV) l23 CALL TRANS(CPNSEG,PTRA) 124 CALL FZYGO CPS, NSEG,PCROS PCROL) 125 CALL MUTAT(S,NSEG,PMUT) 126- C PRINT CHROMO80ME STRUCTURE DURING LAST GENERATION IF TPC8 IS 127 IFCIGEN.EO.LGEN.ANO.IPCS.EO. 1)CALL OCS(INDCP,NSEG) A-13

It2 C ABORT INDIVIDUAL ANO RETURN TO SELECT NEW PARENT IF 119 C ZYGOTE IS INVIABLE 1398 IF(VIA(SNSEG))GO TO 77 131 NIZINXZ*i 132 GO TO 61 133 C INCREMENT COUNT OF "1" ALLELES AT EACH INDIVIDUAL AND 1a4 C PRINT NUMBER OF "I1 ALLELES AT EACH LOCUS AT END OF EACH 135 C GENERATION IF IPAF * i 136 77 IF(IPAF.EQ.0)GO TO 80 137 CALL CA(XIEN,LGENINO,NPOPNSEG) 138 C DEVELOP PARAMETER VALUES USING GENE ACTION SPECIFIED 139 C BY NDVLP 14a e8 GO TO(8t,82,8,3#4,85,86,87,t8,89,8,811,812,),NDVLP 141 81 CALL SGA1CNSEG SNPARX) 142 60 TO 90 143 82 CALL SGA2(NSEG,S,NPARX) 144 GO TO 90 145 83 CALL SGA3 NSEGS NPARX) 146 GO TO 90 147 84 CALL SGA4C(NSEGtSNPARX) 148 GO TO 90 149 65 CALL SGAS(NSEG,S NPAR,X) 159 GO TO 90 151 86 CALL SGA6(NS.E, NPAR X) 152 GO TO 90 153 87 CALL SGA7(NSEGSNPARX) 154 GO TO 90 155 88 CALL SGA8(NSEG,SNPAR, X) 156 GO TO 90 1.7 89 CALL SGA9(NSEGS NPAR X) I9S GO TO 90 1:9 810 CALL SGA0(NSEG, S,NPAR,X) 160 GO TO 90 161 811 CALL SGA11(NSEGSvNPAR,X) 162 GO TO 90 163 812 CALL SGA12(NSEGSNPARX) 164 C EVALUATE INDIVIDUAL PHENOTYPIC VALUE USXNG TEST 165 C FUNCTION SPECIFIED BY NVALU 166 90 GO O( 91,92r,93,94,9, 96) 8 NVALU 167 91 CALL V1(NPARX,VC(NO) 168 GO TO 97 169 92 CALL V2(NPAR,X,V(INO)) 1..7 GO TO 97 171 93 CALL V3(NPARVX,V(NOD)) 172 GO TO 97 173 94 CALL V4(NPARX,V(INO)) 174 GO TO 97 175 95 CALL V5(NPARXV(IND)) 17.. GO TO 97 177 96 CALL V6(NPARX, V(ND)) 178 C INCREMENT INDIVIDUAL COUNTER 179 97 INDOIVINDIV+1 168 C UPDATE TRIAL COUNTERS AND EFFICIENCY IF PARAMETERS 181 C ARE WNTHIN THE ADMISSIBLE DOMAXN A-14

1.2 IFCV(IND).L TCV)GO TO 100 163 NTR.NTR+X 164 NTRT$NTRT.l 185 VSUMmVSUMV (INO) 186 IF(IND.EQNPOP) EVSUM/FLOAT(NTRT) 187 C WRITE INDIVVALUEANO PARAMETERS INTO PFILE XF IPAP s I 188 C OR IPBP 1 AND VALUE OF INDIVIDUAL EXCEEDS VALUE 189 C OF ALL PRECEDING INDIVIDUALS 190 leo IF(IPBPEQ,1)GO TO 10 191 IF(IPAP.EO, 1)GO TO 102 192 GO TO 110 193 101 IFV(IND).LE.HIV)GO TO 110 194 HIVV(I ND) 195 102 IF(NPAR.LE.8)WRITE(7,1t05INDIVYVCIND)C(X(CI),IlNPAR) 196 105 FORMAT(tX'IS,FIO,3,817) 197 IF(NPAR.GT*,)WRITE(7,106S)INIVV(IND)5(X(I),Il1.NPAR) 196 106 FORMAT(IX, I5,F0.3, 817/C 18X, 817)) 199 e IK".0 200 C BRANCH ON GENERATION AND FAMILY MEMBER 201 IF(XGEN.EQO1)GO TO 121 202 KmIFAM+ISTOR 203 IFCIFM.GT.1)GO TO 120 204 C STORE FIRST INDIVIOUAL OF EACH FAMILY 23. VS (I FAM).V( ND) 206 WRITEClK) (CP(ICXJ,w3)S(I.J,3)wtl NEG),Jlt,2) 207 IF(ITOG(C) EQ,1)GO TO 125 208 GO TO 130 209 C REPLACE FAMILY REPRESENTATIVE WITH THIS INDIVIDUAL 210 C IF THIS INDIVIDUAL HAS HIGHER PHENOTYPIC VALUE 211 120 IF(V.(IND). LTVS(IFAM))GO TO 130 212 V8(IFAM) V CINO) 213 WRITEC(IK) ((CP(CIJw3),SCI,J,3) I 1 NSEG),J,2) 214 IF(ITOG(1).EQ,1)GO TO 125 215 GO TO 130 216 C STORE FIRST NSEL GENOTYPES DURING Fl GENERATION 21.7 121 IF(CND.GT.N$EL)GO TO 122 218 KIXND+ISTOR 219 WRITE(ltK) ((CP(IJ,3)3,S(I.J3) ItINSE$G),J,2) 220 VS(IND) V(INO) 221 IFCITOG(1.tEQ.1)GO TO 125 222 GO TO 130 2293 C REPLACE L OWEST-VALUED GENOTYPE STORED SO FAR DURING 224 C F2 GENERATION IF VALUE OF THIS INDIVIDUAL EXCEEDS 225 THE LOWEST VALUE 226 122 LOWul 227 DO 123 I l,NSEL 228 IF (VSC(I) LT.VS(LOW) LOW I 229. 123 CONTINUE' 230 IF(VCIND),LT.VS(LOW))GO TO 130 213 K!LOWI$STOR 232 WRITE(t K) (CCP(I,J,3),S(IJ,3), alNSEG),JL2) 233 VS(LOW)V(XINO) 234 C PRINT GENERATION, INDIVIDUAL, VALUE, AND LOCATION IF 2aj ~C GENOTYPE IS STORED XIN F1 AND PEOIGREE IS REQUESTED A-15

136 125 IF( (ITOGC (l)Q.E ) WRITE(6, a126 IGEN IND~ V (ND]) K 237 126 FORMAT(2I6,F 1 30I61 aaXK IKtl 239 C PRINT GENERATION, INDIVIDUAL, AND VALUE IF PEDIGREE 24 C IS REQUESTED 241 130 IF (TOGC(l),EG.AND.IK.EGQ ) WRITEC6o, 26) IGENINDOV(I ND) 242 IF(CND.EQNPOP)GO TO O 40 243 INDnIND1l 244 GO TO 6.1 245 C END GENERATION ISEN 2Af4 C LIST. FAMILIE8 ACCORDING TO SUPERIOR FAMILY MkMBER 247 140 CALL LIST(VSNSEL,R) 246 C AVERAGE VALUE AND STANDARD DEVIATION OF SELECTED INDIVIDUALS 249 CALL ASD(VSNSELAV$SSTD83 251 C AVERAGE VALUE AND STANDARO DEVIATION OF POPULATION 251 CALL ASO(V,NPOP,AVGSTO) i2..C.STOR IGEN.,EAVYGSTOD.AV_.G, TOS.Nl,,NTR XN P2 253 K(!VARI) *LGEN*IGEN 254 WRITE(2', K15 t0) GEN, E,AVG STD AVGS STOS NIZ NTR 255 150 FORMAT(CX,X 3w5F10.3,210) 256 C TEST FOR END OF VARIETY 2597 F(IGEN.EQ.LGEN)GO TO 160 2A C..B N.NE..W GENERATXION 259 XGENuIGEN+l 260 IDRAWx D RAW*50 261 IF (IDRAW.GT. 0) IDRAWf 262 ISTORw ITOR_+50 263 IF(ISTORGT.590)ZSTORw0 24 GO. TO.60. 265 C TEST FOR END OF RUN 268 160 KIRCI) 267 WRITE (6, l6 ) S (K), VV 268 161 FORMAT(lX, VS.I'FiO,3/' VV.2F10.3) 269 LOWwIVAR 27a1 IF C(VAR.Le.2) T 163 271 LOW"l 272 DO 162 I1l,2 273 I (VLVV() I.LT.VV LOI) LOW.I 274 162 CONTINUE 275 163 IF (V(K) LT.VVC(LW))GO TO 164 27 VV CLOW) VS (K) 277 KwK+ISTOR 278 REAO DCK) CCCPCI, J, ),S(,Jl),I Xl, NSEG), Jl,2) 279 Kt1'0+LOW 2.0 WRI.TE(lK). (CP(CIJ, l) S(IJ.l) Itl~#NSEG) J.l~J) 28t 164 IF(IVAR.,EQNVAR)GO TO 170 2U2IL V ARw IAR.+1 283 GO TO 50 284 C PRINT DATA FROM SUCCESSIVE VARIETIES 285 170 CALL PDFSV(LGENNVAR) 2e6 C CLOSE FILES 267 CALL CLOSE(l) 261 CALL CLOSE (.) 289 CALL CLO'SEC3) A-16

290 CALL CLOSE(7) 291 C TEST FOR STOP 292 IF(COATA(1) EQ.STOP)STOP 293 C PRINT NAME OF NEXT DATA FILE IN SEQUENCE AND PAUSE 29A4. I. TO.QG (2) 2 299 F (lTOG(2),EG,2) RITE.(6 80)COATA () 296 180 FORMAT(IX,'RESTART AT tAS) 297 IFP(TOGC2 2 EQ.2PAUSE 291 C CONTINUE USING INPUT OATA IN FILE CDATA 299.CALL SEEK(, COATA) 300 GO TO 1ip 301 END A-17

Bulk Population Breeding 1 (BPB1) PDP-9 CHAIN/EXECUTE System 8 PR DOS- 15 VIA $$SJOB A DKA -1,-4 SCHA IN CHAIN V7A NAME XCT FILE >BPB1 LIST OPT IONS. PARAAM FETERP S >NM DEFINE RES ID[ENT CODE >M B P B 1, I NV. ER, T RAN Sr- F ZYG O, CY! S, MUJ TAT, MUT ~ T VIA H, L I ST, - ASD3 URlJN I RAND J EVENT I PAC N PAC DCS. CA, SA DESCRIBE LINK<S & STRUCTURE' >G 1=SGA 1 PGA1 >G2=S.GA 2, PGA2 >G3= SGA3, PGA3 >G- 4=SGA4! PGAA4 > G 6 = SG A', P G7A4 >G5=SGAS5 PGA5'>G.6=.SGA6.. PGA6 >G'7 = SGA7, PGA7 > G.8= SG A8 P GA8 >G 9= SG A9^ PGA9 >G 1 @0 SGA1;. rPGA.10 >G"1 2 =SGA 12 PG A1 2 >G"1:G(2:'G'3: G4 G 5:G'6: G7: Gg': G9: G10:G 1 1: G 1 2: MERR >V-'V2': V 3 \:: V: 5: V6 CORE REO QI 1 5532-57 636 DOS''-1S VIA $ $EXIIT A-18

Input Data 8PB1 6/7/73 NDVLP 1, NVALU 6 PINV, 01 PTRA P (a0, PCROS S00 PCROL 500 PMUT P. t* 0PI POUCR 01 000 Cv i, 0~ NPOP 32 NSEL 32 IGEN 1t NPAR 2 NSEG 8 NREP IX 1 IPAP 0 lP8P P IPAF 0 IPCS cr STOP Main Program (MBPB1) 0~1 C MRPB1 Vi 002 C iBULK POPULATION IRiEDtING 1 003 C MAIN PROGRAM OF GENETIC PROGRAMMING SYSTEM BPBl 004 INTEGER CP(25S,2,3),S(256.2,3),R(100),X(256) 005 LOGICAL EVENTVIAB 006 DIMENSION A(12),CATA(2),FI(2),F2(2) F3(2)PFILE(2) 007 1,VV (15,V S(1 9a),F(100) PIa8 COMMUN /CPS/CP,S 009 OATA Fl (),pF2(1), F3(1/5HFl,SHF2 SHF3 / 010 l,Fl(2),F2 (2),F3C2).PFILEC() CDATA(2)/5*4H SRC/ 01'1 lSTUOP/SHSTOP /,PFILE(1)/5H8PBl / 012 C REAn PFILE, NO)VLP NVALIU,PINV, PTRAPCROS,PCROL PMUT, 013 C POUCRCV,NJPOP, NSEL f LENNPARNSeG, NREP IX, IPAP, IPBP. PAF, 014 C XPCS,COATA FROM DISK FILE 015 IF(!i'O0(2).E.W*.)GO TO 6 016 WRIT E(6, 1) 017 1 FORHAT(1X,'OATA FILE') 018 REAO (55) PFIL. (1) 019 S FOR1lAT(AS) 020 6 CALL SEEKC1,.PFILE) 021 A RAn( 1 ) PFILE (, A,NDVLP, NVALUPINV, PTRA A-19

622 1,PCOSPCROL, PMUTPOUCR CV 023 15 FORMAT(9XAAS//12A5,2(/9XpI,6C/9XF.64)/8XF7.4) 024 REA (1, 24) NPOP,NSELLGEN 025 20 FORMAT( X, I6,2(/9XI6)) 026 READ i tS) 25)NPARt NSEG, NREP, IX 027 25 FORMAT(9X, I6,3C/9X,I 6) 028 REAO(1,3a)IPAP, IPPIPAF,TPCSCDATA(1) 029 3c FORMAT (9X, I6,(/9X, 6)/9X,A5) 030 CALL CLOSE(I) 031 C DELETE ANO R'CREATE PRINT FILE 032 CALL rLETE(7, PFILE, 033 CALL ENTERC7,PFILE) 0.3.4 C WRITE PFII,t,NOVLPNVALUPINV PTRAPCROSPCROLPMUT 035 C POUCR, CV, NPOP, SELLGEN, NPAR, NSEG, NREP, IX, IPAP, IPBP, IPAF, 036 C IPCS,C.DATA INTO PRINT FILE PFILE 037 WRIT:(7,4P1)PFILE(1) A, NOVLPNVALUPINVwPTRA 038,PROS, PCROLPMUTPOUCRCV NPOPNSELLGENNPAR 039, NSEG, NHEP, X IPAP, IPBP PAF, IPCSCDATA l) 040 40 FORMAT(C 1XA5/X,12A5/' NDVLP',IB0/l NVALUI.'I10 341 1/' PINVFI1.44/' PTRAlFt1,4 042 1/' PCROS',F1.94/' PCROL',F10.4/' PMUT',F11,4 043 1/ POUC?,F1X. 4/1 CV',F13.4/' NPOP:tI/' NSELI,11I 044 i/t LGENIp11/1 NPARiIll/' NSEG,1llt/l NREPI0,ll 045 1/' IX'I,13/' IPAPI,It1/' IPBPI1:tl/ IPAFPll 046 / TCS', Il /l0X, AS) 047 C OELETE ANn UDPFINEN OIRECT ACCESS FILE Fl USED TO STORE 048 C UP TO 2*NSEL CHROMOSOME ARRAYS 049 CALL OLETE(1 F1,I) 050 CALL OFINE C 1,4*NSEG,2*NSELFl, IVi i,0 0) 601 C DELETE ANO REDEFINE DOIRCT ACCESS FILE F2 USED TO STORE M02 C EFF, AVG( STO, AVGS, STOS, NIZ, NTR FOR EACH GENERATION 053 CALL DLETE(2,F2,I) 054 CALL DEFINE (2,80,( CNREP*3)*LGENF2,IV2.l,0,0) 055 C OFLETE ANn kEDEFINtE IRrECT ACCESS FILE F3 USED TO COUNT 356 C THe NiJMBER OF "1" ALLELES IN THE POPULATION AT EACH LOCUS 057 C ANU GENERATION 058 CALL DLETE(3,F3, I) 059 CALL i)ItINE(3, l,NSEG,-F3;V3,0"00) 060 C START RANO!OM NUMUBE GENERATOR AT IX 061 IX-ijX 062 CALL UiNCITXJ) 063 C INITIALIZF RUN COLUNTER AND BEGIN RUN IRUN 064 IRUNNI 065 5 IN I va 366 NTRTxcP 067 VSUMmoo 0668 E. 069 IGEN 1 070 HIVStI., 071 ISTORa: 072 IDRA.*s=SEL 073 C BEGIN GENERATION IGEN 074 ( INOmi 075 NIZ=< A-20

0176 NTRm0 077 C SELECT PARENfAL GENOTYPES AND LOAD INTO CORE 078 C ARRAYS CP ANl S 079 7r IF(ItGEN.GTt1)GJ TO 72 080 C FORM RANDOM HFTEROZYGOUS PARENTS.8.1 DO 71 Ka1w,2 082 00 71 IX1,NSEG 083 CALL UitN(IXU) 084 DO 71 J1#,2 085 Nt(I-l)/8l1 08a MsI-(N-1)*8 087 CP (IJ J ) IPAC N, M) 088 IF(J. 1) S( I:, JK) mIX 089 IF (J,.E.2) 8(1, JI ) "IX-1 090 71 CONTINUE 091 GO Tr 70 092 C FEFCH PARENT 093 72 IFCINO.)T.1)GO TO 75 094 NR f ) 093 FC1)VC(N) 096 DO 73 1=2,NSEL 097 NaR(I) 098 73 F ( T)NF ( I ) +V (N) 099 DO 74 ImlNSEL 100 74 F (I I F(I)/F(NSEL) 101 75 CALL iJRN(L,U) 102 00 76 I 1,NSEL 103 IF(u,L.F (I))GO TO 77 104 76 CONTINUE 10. 77 I 1L I)IJ +X1RA 106 I2"I1 107 C OUTCROSS SiLECTED iNJOIVTDUAL WITH PROBABILITY POUCR 108 IF(EVENT(POUCR) )-IBIRAND1,NSEL)*IDRAW 109 REArI)i'.I) C(CP(IJ, ),CS(IJ, l),rI'lNSEG),Jl,2) 110 RFAD( I2) ((CP(I,J,2),S(IJ,2),Ili,N8EG),JI,2)..111 IF( ITOG (1).EQ. WRITE (6,78 I1,12 112 7? FORMAT (2X, 216) 11a C FORM ZYGOTE GENOTYPE 3Y UNION OF GAMETES DERIVED FROM 114 C PARENT GENOTYPES BY INDEPENDENT SEGREGATION AND CROSSOVER 115 C MITH PROBABILITIES PCROS AND PCROL OF CHIASMA BETWEEN 116 C ADJACENT SEGMENTS ANQ ADJACENT LOCI RESPECTIVELY 117 79 CALL INVR(CpP, NSG,PINV) 118 CALL TRANS(CP, NSEGfPTRA) 119 CALl FZYGO(CRP,SNSEG,PCROSPCROL) 120 CALL MUTAT(SNSEG PMUT) 121 C PRINT CHROMOSOME STRUCTURE DURING LAST GENERATION IF IPCS u I 122 IF ( XEN, gQ LEN AND IPCS,EQ. 1)CALL DCSCINDCP,NSEG) 123 C ARORT INDIVIUUAL AND RETURN TO SELECT NEW PARENT IF 124 C ZYGOTE IS INVIABLE 125 IF(vlA6i(,NSEG)G O TO 790 126 NJIZaNIZ+1 127 GO TO 79 128 C INCREMENT COUNT OF "1" A-LLLES AT EACH INDIVIDUAL AND 129 C PRiNT NUMBER OF "1" ALLELES AT EACH LOCUS AT END OF EACH A-21

130 C GENERATION IF IPAF 1I 131 79( IF(IPAF..EQ0)GO TO 80 132 CALL CA(J IEN LEN INONPOPNSEG) 133 C OEVELOP PARAMETER VALUES USING GENE ACTION SPECIFIED 134 C BY NOV LP 135 d8 GO TU(81,82,83,84,85,86,87,88,89,81i,81t,8l2),NDVLP 136 81 CALL SGAl(NSEGS,NPAR.X) 137 GO TO 90 138 8a CALL SGA2(NSEG, S NPAR,X) 139 GO TLO 9 140 83 CALIl SGA3(NSEG SNPARX) 141 GO 7TO 142 84 CALL SGA4CNSEG, SNPFARX) 143 GO TO 90i 144 85 CALL $SAS (NSG, S, NPAR, X) 145 GO TO 90 146 86 CALL S6Atb(N$SEG SNPARX) 147 GO TO 90 148 87 CALL SGA7 (NSGS NPAR, X) 149 GO TO 90 150 88 CALL SGd(NSEGS, SNPARX) 151 GO TO) 9Pi 152 B CALL SGA9(NS~G,SNPARX) 153 GO TO c90 154 810 CALL SGA l0(NSElSNPARX) 155 GO TO 90 156 811 CALL SGA11CNSEPS,NPARX) 157 GO TO 9P 15s8 812 CALL SGA12(NISEi,SNPAR,X) 159 C EVALUATE INDIVIOUAL PHENOTYPIC VALUE USING TEST 160 C FUNCTION SPECIFIED 8Y NVALU 161 90 GO TUt91,92,93,94,9596, NVALU 1i2 91 CALL V I (NPAR, X,V(ND)) 163 GO TO V7 164 92 CALL V2(NPAR,X,V(IND)) 165 GO TO 97 166 93 CALL V(CNPAX, V(INO)) 167 GO TU 97 16 94 CALL V4(NPAR,XV(IND)) 169 GO Tb 97 170 95 CALL V5(NPAR,X, V(INO)) 171 GO TO 97 172 96 CALL V6(NPAXV (INO)) 173 C INCREMENT INDIVIUUAL COUNTER 174 97 INOTVTINUIV*1 175 C UPDATE TRIAL COUNTiRS AND EFFICIENCY IF PARAMETERS 176. C ARE WITHIN THt: ADMISSIBLE DOMAIN 177 IF(V(TIN0) LT.CV)GO TO 100 178 NTRmNTW+ 179 NTRT=NT'RT+ l 180 VSUM=VSUM+VCiNU) 181 IF( IND, E. ENPOP) EV$SJUM/FLOAT CNTRT) 182 C wR1TE INOQV,VALUE,ANO) PARAMETERS INTO PFILE IF IPAP. I 183 C OR IPBP a 1 aN) VALUE OF INDIVIDUAL EXCEED8 VALUE A-22

184 C OF ALL PRECEUING INXDVIDUALS 185. 100 IF(XPBP.EQ,1)G0 TO 101 186 IF(TPAP.EQ.1)GO TO 102 L7. GO TO 110 188 11 IF(V(IND).LE.HIV)GO TO 110 189 HIV (IjN0) 190 lI? IFCNPAR.LE.8)WRITE(7,l15)INDIVV(IND)O.(X(I)tIlNPAR) 191 l. FORMAT(1X, I5,F1.3,8I7) 192 IFC(PAK.GT.8)WRITEC7,106)INDIVV(IND), (X(I), I1,NPAR) 193 106 FORMAT (1, I5,Fl3 1 8I7/( 6Xi,8I7)) 194 11 IK(T 195 C STORE FIRST NSEL GENOTYPES 196 TF(IND.GT.NStL)GU TO 115 197 K<INO+iSTOr 198 WRITf(l'K) C(CP(I,J,3),S(IJJ,3) Il#NSEG),Jl,2) 1.99 v.s CIND) V C(INO) 200 IF (irTOG () EQ )GO TO 125 201 GO TO 130 202 C REPLACE LONEST-VALUEO GENOTYPE STORED SO FAR DURING 203 C F? GENERATION IF VALUE OF THIS INDIVIDUAL EXCEEDS 204 C THE LOWEST VALUE 20.5 15 LOW l 206 00O t2r^ I 1,NSEL 207 IF VS (I),LT S (LOW) LOW~I 208 120 CONTINUE 209 IFfV(INOD)LT.VS(LOW))GO TO 130 210 KaLOw+ISTOR 211 WRITTEC(K) (CP(IJ, 3),S(I,J,3),I liNEG) vJl,2) 212 vS LOW) V(INU) 213 C PRINT GENFRATION, INOIVIDUAL, VALUE, AND LOCATION IF 214 C GENOTYPE IS STUREO IN Fi 215 125 IF(I rOG(1 ).EQ.l) RITE (6,126)IGENt IND V(IND),K 216 126 FORMAT(2I6,F11.3,I61 217 I K = I 218 C PRINT GENERATION, INDIVIDUAL, AND VALUE 219 130 IF(ITOG (l) 5EQ. AND.IK.EQ.0 WRITE(6,126) IGEN I NDV (IN 220 IF(TNO.EU.NPOP)GO TO 140 221 INO=aINU+ 222 GO TO 70 223 C E.ND L) NERArION I'GEN 224 C LIST INDIVIDUALS ACCORDING TO PHENOTYPIC VALUE 225 14 CALL LXST(VSNSELR) 226 C AVERAGE VALUE AND STANDARD DEVIATION OF SELECTED INDIVIDUALS 227 CALL ASD(VS,'SEL,AVGS STDS) 228 C AVERAGE VALUE AND STANDARO DEVIATION OF POPULATION 229 CALL ASD(VNPOPAVGSTD) 230 C STURE IGEN,E,AVG,STOAVGSSTDS,NTZ,NTR IN F2 231 KC INUNw1)*LGENIGEN 232 WRITE(2'K, 150) GEN,E,AVG,STDAVGSSTDSNIZNTR 233 150 FORMAT (IX,I3,5F10.3,2 11) 234 C TEST FOR Eni) OF RUN 235 IF(CIEN.EQL'iEN)G) TO 160 236 C.E.TlN NE^ GENERATIUN 237 IENI GEN+ 1 A-23

238 IDRAWSIDRAW+NSEL 239 IF(IORAW,GT,NSEL) IORAWM 240 TSTOm ISTOR+NSEL 241 IF (ISTOR.GT.NSIL)ISTOR"0 242 GO TU 60 243 C TEST FOR END OIF REPLICATE RUNS 244 6l IF (IRUN.EQ,NREP)GO TO 170 245 IRUNM I hJN+ 2406 GO TU 50 247 C MFAN AND EXTREMES UF RtPLICATE RUNS 248 170 CALL MtK (LGEN, NEP) 249 C CLOSE FILES 250 CALL CLOSE(l) 251 CALL CLOSE(2) 252 CALL CLOSE(3) 253 CALL CLOSE(7) 254 C TEST FOR STOP 255 IF(COA -A ( 1 Q. STOP) STOP 256 C PRINT NAME OF NEXT DATA FILE IN SEQUENCE AND PAUSE 257 C IF TTOG(2) = 2 258 IF(ITOG (2).E,W2)W RITE(6, tCOA)CDATA () 259 180 FORHATC(X1, RESTART AT',AS) 260 IF(ITOG(2) EiJ2)PAUSE 261 C CONTINUE ISING INPUT DATA IN FILE CDATA 262 CALL SeEK (,COATA) 263 GO r0 1I 264 EFNO A-24

Mass Selection 1 (MSl) PDP-9 CHAIN/EXECUTE System B PR DOS-15 VIA $SJOB A DKA - 1 -4 $C HAI N CHAIN V7A NAME XC:T FILE >MS 1 LIST OPTIONS & PARAMETERS >NM DEFINE RESIDENT CODE >MMS1 INVER, TRANS, FZYG O, CL WS, MU TAT, MUT V I ARB L I S T = ASD, UR.N, IRAND, EVJENT, IPAC, NPAC DCS CA SA D[ESCRIBE L INKS & STRIJCTURE >G 1= SGAl 1 PG:AI >G2=SGA2. PGA2 >G3= SGA3. PGA3 >G4 SGA4 =. PGA.4 >IG- 5= SG A.5 PGA5 > G6= ='SG A6., PGA6 >G7 =SGA7, PGA7 G 8= SG A8' PG'A8 >G9=SGA9., PGA9 >G 1 0= SGA 10 VPGAi 0 >0G:1..1=SGA 1-1, PGA i 1 >G 12= SGA1: 2, PGA- 2 >G-'1:G2: G3: G4:G'5:G6:G7 G8: G-9:G 10: tG12:MERR >V1:V2:V3: V4:V5:V6 CO:RE REQ D 1 72 14-57636 DOS- 15 VIA $ EXI T A-25

Input Data 300t 1 MSI 6/7/73 NDVLP 1 NVALU 6 PINVY 00010 PTRA (,t010 PCROS 0. 509 PCROL 0 500P0 PMUT 0.0010 CVY O 0,010 NPOP 32 NSEL 16 LGEN 1E NPAR 2 NSEG 8 NREP 5 Ix I IPAP 0 IPdP1 IPAF IPCS t STOP Main Program (MMS11) 001 C MMSt VI 002 C MASS SELFCTION I 003 C MAIN PROGRAM OF UGEtTIC PROGRAMMING SYSTEM MSl 004 INTEGEk CP(25623)S2562356,23)wR(100),X(256) 005 LOGICAL. EVENT,VTIA 006 )IMENSION A(12),COATA(2),FC(2),tF22)F3E(2)pPFILE(2) 007 l,Vclt,) wvs(li:5 008 COMMON /CPS/CPS 009 OATA FJ () F2(l),F3(l)/5HFP1 5HF2 w5HP3 0109,F!(2),F2(?):F3()5PFILEC28)COATAC2)/5*4H SRC/ 011 1,i STP/SHSTOP /,PFIL'E(1)/5MS1 / 012 C REAO PFILENOVLPNVALUPINVPTRAPCROSvPCROLPMUTCV, 013 C NPAR,NSEG,NREPwIX, x PAPIPBP, IPAFIPCSCDATA 014 C FROM OISK FILE 015 IF(TOG(2).EQ.o)G0O TO 6 016 WRITE6, 1) 017 1 FORMAT(X, OATA FILE') 018 REAO(5,5)PFILEC1) 019 5FORMAT AS) 020 6 CALL SEKC(1,PFILEI 021 1 REAr5 (ll5) PFILe(l), ANDVLP NVALUPINVPTRA A-26

022 PCROSPCROLPMUTCV 423 15 FORMAT(9X,A5/12AS,2 (/X I6) 5(/9XF6.4)/8XF7.4) 024 READ (120) NPOP, NSEL LGEN 025 20 FORMAT( 9X,6w2(/9X I6)) 026 REAF),25) NPAR, NSEGNREP, IX 027 25 FORMAT (9XI 3(/9X I6) ) 028 REAI(1 30) IPAPw IPBPw IPAF, IPCSCOATA(1 029 39 FORMAT(9X, I 3C/9XI6)/9XA5) 030 CALL CLOSE(l) 031 C DELETE AND RiECEATE PRINT FILE 032 CALL OLETE(7,PFILETI) 033 CALL ENTERC7,PFILE) 034 C 4RTlfT PFIL, NOVLPNVALUP INVPT.RA PCROS PCROL, PMUTPCV 035 C NPP, P.SELLGtN,NPA, NSEG,NREP,IX, IPAPIPBPIPAFIPCSw 0i36 CDATA INTO PRINT FILE PFILE 037 WRITE 7,40)PFILE(i) a,NOVLP NVALUPINV PTRA 038 1 P,PCPCROLPMUT,CVNPOP, NSEL,LGEN NPAR 039 1INSEG',NREPIX, IPAPIPBP IPAF IPCSCDATA(t) 040 4r FORMAT(l10XA5/X,12A5/ NDVLP',I10/l NVALU',I10 041 1I/ PINV,Fll.4/' PTRA',Ft,4 042 1/''PCkOS',F10.4/' PCROL',F10.4/' PMUT',F11.4 343 1l/ CV',F13.4/I NPOP',Ill/' NSEL',Ill 044 1/' LGtN',11/' NPARIll/ NSEGC,IIl1/ NREP',Il1 045 1/' IX',I13/' IPAP',11/' IPBP,Ill/! IPAFt,I11 346 I/' IPCS',Ill/lIX,A5) 047 C DELETE ANO REDEFINE DIRECT ACCESS FILE Fl USED TO STORE 048 C UP TO 2*N$tL CHROMOSOME ARRAYS 349 CALL DLETE(1,F1,I) 050 CALL.OtFlNE(l,4*NSEG,2*NSELtF lr IV1,0 0) 051 C OFLETE AND REDEFINE DIRECT ACCESS FILE F2 USED TO STORE 052 C EFF, AVG, STU, AVGS, STDS, NIZ~ NTR FOR EACH GENERATION 053 CALL fLETE(2,F2,Ir 054 CALL OEFINE(2,83, CNREP+3)*LGENF2,IV21,0O,0) 055 C DELETE AND REDEFINE OIRECT ACCESS FILE F3 USED TO COUNT 056 C rTHE NUMB~ER OFi "1" ALLELES IN THE POPULATION AT EACH LOCUS 1057 C AND GENERATION 058 CALL OLETE(3,F3,I) 059 CALL DEFINE(C3 1l6 NSEG,F3,V3,00,O0) 060 C START RAN,)OM NUMliEW GENERATOR AT IX 061 IX'-IX 062 CALL URN(IX.,U) 063 C INITIALIZE RUN COUNTER ANO BEGIN RUN IRUN 064 IRUNJI 065 INOI V 066 NTRTaS 067 VS Li:.M. 068 EP. 0i6.9 IGENI a 070 HIV=VJ, 071 ISTDONs 072 IDR4w=NSEL 073 C BEGIN GENERATION IGEN 074 6p INOI.l 075 NI Z a A-27

076 NTR"0 077 C SELECT PARENTAL GENOTYPES AND LOAD INTO CORE 078 C ARRAYS CP ANO) 079 70 IF (IGENGT. )GO TO 72 080 C FORM RANDOM HFTEROZYGOUS PARENT GENOTYPES 081 00 71 Km1,2 082 00 71 l1,NiSEG 083 CALL LItNCIXJU) 084 00 71 J1,2 085 N (I-1)/8+1 088 MmI (N-1)*8 087 CP (I, J, K.) IPAC (N, M) 088 IF(J.EQ. 1) (3 JK) IX 089 IF(JE,2)S(I, J #K) -IX090 71 CONTINUE 091 GO TO 74 092 72 I TRAND 1, NSEL) IDRAW 09. I2"TRAN(lNSEL) +IORAW:094 REAnr C1i! 1 ) C(CP( I J, ) S ( I,J, ) a l I, NSEG),J,2) 095 REAnd(II)(CCP(IJ,2),St(IJ,2),IPlwNSE6),J*l,2) 096 IF CITL( ).EU.l) WRITE(6,73 I1,I2 097 73 FORMAT(29x,2I5) 098 C FORM ZYGOTE GENOTYPE BY UNION OF GAMETES DERIVED FROM 099 C PA.ENT GENOTYPES BY INDEPENDENT SEGREGATION AND CROSSOVER 100 C WITH PROBABILITIES PCROS AND PCROL OF CH.IASMA BETWEEN 101 C ADJACENT SEGMENTS ANO ADJACENT LOCI RESPECTIVELY 102 74 CALL INVER(CP,NSEGPINV) 103 CALL TRANS(CP,NSEGPTRA) 104 CALL FZYGO(CP,S, NEG,PCROSPCROL) U1S5 CALL MUTAT (S NSEG,PMUT) 106 C PRINT CHROMOSOME STRUCTURE DURING LAST GENERATION IF IPCS * I 107 IF ( GEN, O.tLGEN.AND. IPCS,EO, 3 CALL DCS(INDtCPNSEG) 108 C A80RT INODVIULJAL ANDi RETURN TO SELECT NEW PARENT IF 109 C ZYGOTE IS INVIA8LE 110 TF(viAo(SNSEG))GO TO 75 t111 N Z NIE Z+ 1 112 GO TU 70 113 C INCREMENT COUNT OF "1" ALLELES AT EACH INDIVIDUAL AND 114 C PRINT NUMRER OF "1" ALLELES AT EACH LOCUS AT END OF EACH 115 C GENERATION IF IPAF u I 116 75 IF(IPAF.EQ.0)GO TO 90 117 CALL CA IGEN, GEN, IND, NPOP NSEG) 118 C DEVELOP PARAMETER VALUES USING GENE ACTION SPECIFIED 119 C eB NOVLP 120 8o GO TUC61,82,d384,e85,$6,87,R8889,810,811,812) NDVLP 121 81 CALL SIAI (NSEG G,S.NPARX) 122 GO TO se 123 82 CALL S6A2(NSEG,S.NPARX) 124 GO TO 90 125 83 CALL SGA3(NSEG,SNPARX) 126 GO TO 9&i 127 84 CALL S$lA4(NSEGS, NPARs,X 128 GO TO 9P A-28

129 85 CALL SGAS(NSEG,S,NPAR X) 130 GO TO 90 131 8f CALL S(A6(NS~GSNPARX) 132 GO TO 90 133 87 CALL SGA7(NSEG,S,NPARX) 134 GO TO s' 135 88 CALL SGA (NSEG, S NPAR, X) 136 GO TO 90 137 89 CALL SLA9(NSEG,S.NPARX) 138 GO TO 90 139 810 CALLI S A 1 $, NSEG,, NPAR X ) 140 GO TO 90 141 811 CALL SGA1(CNSEG,S,NPAR,X) 142 GO TO 9 143 2 12 CALL SGA12CNSG,S,NPAR, X) 144 C EVALUATE INOIVIDUAL PHENOTYPIC VALUE USING TEST 145 C FUNCTION SPECIFIED BY NVALU 146 90 GO TO(91.!92,9394a,95,96),NVALU 147 91 CALL V1(NPARX,VVIND)) 148 GO TU 97 149 92 CALL, V2NPAR,XVCINO)) 150 GO TO d7 151 93 CALL V6(NPAR X, V(INO)) 152 GO TO I7 153 94 CALL V4(NPAR,XV(INO)) 154 GO TO 97 155. CALL V5(NPA, X,VC(INO)) 156 GO TO 97 157 96 CALL V6(NPANX,V(INO)) 158 C INCREMEN'r INOIVIDUAL COUNTER 159 97 INOTV=IN)IV+1 160 C UPUATE TRIAL COUNTERS AND EFFICIENCY IF PARAMETERS 161 C ARL wITHIN THE ADMISSIBLE DOMAIN 162 IF(V(INO).LT.CV)G TO 100 163 NTRsNT+ 1 164 NTRT NTR T+ 165 VSUMVSUM+V (INO) 166 IF (IND,.E.NPP)E:VSUM/FLOAT(NTRT) 167 C WRITE INODV,VALUEANO PARAMETERS INTO PFILE IF IPAP w 1 168 C OR IPBP a I AND VALUE OF INDIVIDUAL EXCEEDS VALUE 169 C OF ALL PRECEDING INOIVIOUALS 170 1.00 IF(IP~PEO,1)Gu TO 101 171 IF(IPAPEQ,1)GO TO 102 172 GO TO 1 1 173 1I1 IF(V(IND).LE.HIV)Gt TO 110 174 HIVCV(INU) 175 102 IF(NPAR.LE. )WRITEC7,105)INDIV,V(IND),(X(I), I1,NPAR) 176 105 FORMAT(1X, I5FL0.3,8I7) 177 IF(NPAR,.iT.8).RITEC7,106)INDIVV(IND),(X'CI),IlNPAR) 178 106 FORMAT(l X I5,Fl.3, 817/( lX, 8I7)) 179 110 IK 180 C STORE FIRST NSEL GENOTYPES 181 IF(INOGT.NSEL) GO TO 115 182 I KlND+ISTOR A-29

_8s 3 RITE(IK) ( (CP (IoJ,3J3),I vlNSlreG)Jl2) 184 VS(ND).V (INO) 185 JIFITOlb(l).E. l)GO TO 125 186 GO TO 130 187 C REPLACE LOPEST-VALUED GENOTYPE STORED SO FAR DURING 188 C Fq GENERATION IF VALUE OF THIS INDIVIDUAL EXCEEDS 18O C THe LOWEST VALUE 190 115 LOWal 191 DO 12O IIu,NSEL 192 IF (V (I).LT. VS (LOW) )LOW I 193 120 CONTINUE 194 IF(V(IND).LT.VS(LOW))GO TO 130 195 KLOW+ 1'ISTOW 196 WRITE (iK)((CP(IJ,3)SI 3)(I,J3),IlNEG),Jtl,2) 197 VS(LOw)V (INO) 198 C PRINT GENERATION, INDIVIDUAL, VALUE, AND LOCATION IF 199 C GENOTYPE IS STORED IN F 200 125 IF CITOG(c ),EQ.1)WRITE(6,16) IGENINDV(INO),K 201 126 FORMAT(26, Fl1.3, 6) 202 IKal 203 C PRINT GENEkATION, INDIVIUJAL, AND VALUE 204 1 3 IF(lO ((TO l).Eu I AND IK.EQ.0)WRITE(6,126)IGENIND,V(IND) 20. IF(IND.EQ.NPOP)GO TO 140 206 IND~INO*1 207 GO TO 70 208 C END GENERATION IGEN 209 C LIST IN.IVIDUALS ACCOROING TO PHENOTYPIC VALUE 210 140 CALL LIST(VSNSELR) 211 C AVERAGE VALU.l AND STANDARD DEVIATION OF SELECTED INDIVIDUALS 212 CALL ASD(VS, NSELAVGSSTDS) 213 C AVERAGE VALUE AND STANDARD DEVIATION OF POPULATION 214 CALL. ASD(VNPOP,AVG,STD) 215 C STORE IGENE,AVG,STUAVGS,$TOSNIZNTR IN F2 216 K( TRUN 1 ) LGEN+IGEN 217 WRITE ('K l15i) IGENEAVG,STTDAVGSSTDSNIZNTP 218 150 FORMAT(1X,l3,5F1.3,2110) 219 C TEST FOR END O' RUN 220 IF(TGEN.EO.LGEN)GO TO 160 221 C BEGIN NEW lENERATION 222 TGENILGEN+1 223 IDRAW=l.HAW+NSEL 224 IF ( IRAWGTNS~EL) IORAW0 225 ISTO ISTO.R+NSEL 226 IF( ISTOR.GT. NSL)ISTORm 227 GO TO o? 228 C TEST FOR END OF REPLlCATE RUNS 229 160 IF(IRfLN.EiqNREP)GO TO 170 230 IRUNJ I UN+ 1 231 GO TO "0 232 C MEAN AND EXTREMES OF REPLICATE RUNS 233 170 CALL MERR(LGEN,NEP) 234 C CLOSE FILES 235 CALL CLOSEC() A-30

236 CALL CLOSE(2) 237 CALL CLOSEC). 238 CALL CLOSEC( ) 239 C TEST FOR STOP 240 IF(C.A TA( 1).CQ. STST OP 241 C PRINT NAME OF NEXT OATA FILE IN SEQUENCE AND PAUSE 242 C IF ITOG(2) *?. 243 IF(ITOG').EQ,2)w IrITE(6, 180)CDATA 1) 244 180 FORMAT(CX,'ftSTAkT AT 0tAS) 245 IF (ITOG(2).PA2) PUSE 246 C CONTINUE tSIrNG INPUT DATA IN FILE COATA 247 CALL SEEK (1,COATA 248 GO TU 10 249 END A-31

Simple Recurrent Selection 1 (SRS1) PDP-9 CHAIN/EXECUTE System B P R DOS-.15 VIA $ $JOB' A DKA -1,-4 SCHA IN CHAIN V7A NAME XCT FILE > S KS 1 LIST OPTIONS & PAPRAMETERS >NM DEFINE RESIDENT CODE >MSRS 1, I'NVERp TRANS FZYGO, CfA'SMUlTATPMIJTV IABLI ST, - ASD URN, I RAND, EVENT, IPAC., NPAC'DC'S'CASA DESCRIRE LINKS & STRUCTURE >G 1 =SGA. vPGA1 >G 2 =SGA2:PGA2. >.G 3=.SGA3,.PGA3 >G4=SGA.4,PGA4 >G 6=5SGA6v PGA6 >G7=SGA76.PG3A7'>G7 ='SGA7 PGA7 >G. 8= SGAS'. PGAS >G9=SGA9, PGA9 >G. 10=SGA.10., PGA1 0 >G'l 1 =SGA1 I.PGAi 1 >GG 12= SGA1 2, PGA 12 >G 1:G2:G3:G4:G5:G6:G7:'8G-:G9:gG1:G11:G I12: MERR >V1:V'2:V3:V V4:V5:V6 CORE REO'D 14 607- 57636 DOS'-15 V.IA $$.EX IT A-32

Input Data SRSI 6/7/73 NOVLP 1 NVALU 1 P INV V. 0ra PTRA * tla00I PCROS i net PCROL. ^, 5n PMUT i NPOP 28 NSEL LCVC NPAR $ NSEG 3~ NREP 1 J,2~~X 1' IPAP l IP4P 01 IPAF 0 IPCS H Main Program (MSRS1) 301 C MSRS~ Vt 302 C SIMPLE RECUliREiT SELECTION I 003 C MAIN PROGRAM OF GENETIC PROGRAMMING SYSTEM SRSI 004 INTEGER CP(256,2,3), S(256,2,3), R(100) X (256) 005 1, TCP (256,2),TS (256,2) 006 LOGICAL EVENT,VIAl 007 DIMENSION. A(12),COATA(2),F (2) F2(2) F3(2), PFILE(2) 008 I,V f10),VS(310) 009 COMMON /CPS/CPtS a010 ATA F1(i),tF2( 1),F3(1)/5HF1,5HF2 5HF3 011 i,Fl (2),F2(2),F3C(2),PFILEC2)~CDATA(2)/S*4H SRC/ 012 1,STOP/SHSTOP /,PFILE(1)/5HSRS1 / 013 C READ PFILE, NUVLP,NVALUPI:NV PTRAPCROSPCROLFPMUTCV, 014 C NPOPNSFL,LCYCNPARtNSEGNREP, IXIPAPIPBP IPAF, PCS 015 C COATA(I) F^OM lISK FILE 016 IF(ITOG'(2),.Ct*)GO TO 6 017 WRITE(6,1) 018 1 FO RATClX, OQATA FILE ) 019 REAO S,5)PFIL.. (l) 020 5 FoRMAT AS) 021 6 CALL SEEK( 1,PPFL) A-33

022 1l REAO(l1lS)PFlLE(.lA wANVLPpNVALUPINVPTRA 023 1,PCROS,PCROLPMUTCV 024 15 FORMAT (X,AS/12A5 2 (/9X, Il),5 /9XF6,4)/8XF7.4 025 REA ( 20)NPOP, NSELLCYC 026 2a FORMAT(9X,I6,2(/9, I6)) 027 READ (l 2) NPAR, NSEG, NREP IX 028 25 FORMAT(9X, I6 3(/9X,6)) 029 REA(Dl,30)IPAPIPP, IPAFIPCSCDATA C) 03 30 FORMAT (9X, 16'3 (/9X, T6) /9X A5) 031 CALL CLOSE(l) 032 C DELETE AND RECREATE PRINT FILE 033 CALL DLETEC7wPFILEI) 034 CALL ENTER(7,PFILE) 035 C WRITE PFILENDVLP NVALU,PINVPTRAwPCROSwPCROL~PMUT.CV, 036 C NPOP NSEL LCYC NPA,NSEGNREPIXt IPAP IPBP IPAF IPCS 037 C COATACl) INTO PRINT FILE PFILE 038 WRITE(7,40)PFILE(I) ANDVLPNVALUPINV PTRA 039 1 PCROS,PCRL, PMUCV,NPOP,NSELLCYC NPAR 040 1, NSEG, NNEP, i X, IPAP, IP8P, IPAF IPCSCDATA (1) 041 40 FORMAT ( dX AS/X5 X25/ NDVLP' I 0/' NVALU, I 0 042 1/' PINVIF11.4/1 PTRAW F1l.4 043 1/1 PCROS0,F10,4/' PCROL'.Fl0.4/t PMUTFll*.4 044 1/' CV',F13.4/1 NPOPI,I11/' NSEL',Ill 045 1/' LCYC',I11/ NPAR, I11/l NSEG',Ill/' NREP'.I11 048 1/' IXI13/' IPAP!,I11/ IPBP',I11/! IPAFI,It1 047 1/' IPCS',Il1/10XA5) 048 C OELETE AND REDEFINE OIRECT ACCESS FILE Fl USED TO STORE 049 C UP TO 2*NSEL CHROMOSOME ARRAYS 050 CALL DLETE(C,FII) 051 CALL DOF NE, 4*NSEG,2*NSEL,FI, IV l- a,0) 052 C.ELETE AND PEDEFINE DIRECT ACCESS FILE F2 USED TO STORE 053 C EFF, AVG, STO, AVGS, STOS, NIZ, NTR FOR EACH CYCLE 054 CALL OLETE(2,F2,I) 055 CALL DEFINE(2,80,(NREP+3)*LCYCF2,IV21,#,0,0 056 C DELETE AND PtDEFINE DIRECT ACCESS FILE F3 USED TO COUNT 057 C THE NllMBER OF "1" ALLELES IN THE POPULATION AT EACH LOCUS 058 C AND CYCLE 059 CALL DLETEC3,F3,I) 060 CALL ODFINE(C,16,NSEGF3,IV3,0,0,0) 061 C START RANDOM NUMBEN GENERATOR AT IX 062 IX. IX 063 CALL URN(IXU) 064 C INITIALIZE RUN COUNTER ANO BEGIN RUN IRUN 065 IRUNxi 066 5. INDTV=a 067 NTRT0O 068 VSUMs;p 069 E0. 070 ICYC=1 071 HIViO. 072 ISTON3t' 073 IORAwBNSEL 074 C BEGIN CYCLE ICYC 075 63! INOD1 A-34

076NIZa 077 NTR"mm 078 NlI 079 N2 1 080 65 IF(ICYC.GT.1)GO TO 67 081 C FORM RANDOM HETEROZYGOTES OF SOURCE POPULATION 082 DO I6 I",NiSEG 083 CALL lIwN(I XU) 084 DO 66 Jw1,2 085 N(T1-w)/d+1 086 MI. (N-t) * 087 CP( I J 3) IPAC(N, M) 088 IF (J.EF 1) 8( I,J,3) mIX 089 IF (JvF.,2)S(1,J,3) w-IXw1 090 66 CONTINUE 091 GO TO 74 092 C DETERMINE PARENTS UF OIALLEL CROSS 093 67 N2=N2*. 094 IF(N2.LE.NS.EL)GO TO 68 095 N 1NI+I 096 IF (N.EQO.NSEL) NImr 097 N2"Nl+1 098 C PRODUCE FIRST PARENT OF DIALLEL CROSS BY SELFING AN 099 C INDIVIDUAL S$LECTE'u FROM THE SOURCE POPULATION OR 100 C PREVIOUS CYCLE 101 68 I 1 N+IDOAW 102 READr(1'I1) (CP(I,J,,S(I,J, 1),Iil,NSEG),Jlt,2) 103 READ(1 Ill) C(CP(I,J,2),S(IJ,2),inwNSEG),Jlt,2) 104 CALL INVER(CP,NSEGPINV) 105 CALL TRANS CCP,NSEG PTRA) 106 CALL FZYGO(CPS, NSEGPCROSPCROL) 107 CALL MUTAT(SNSEGPMUT) 108 C STORE FIRST PARENT IN TCP~TS 109 69 DO 70 Jul,2 1d 00O 70 Iml,NSEG 111 TCP(I,J)CCP(I,J,3) 112 7 TS( tJ)mS(I,J,3) 113 C PRUOUCE SECOND PARENT OF OlALLEL CROSS BY SELFING AN 114 C INUIIVIOUAL SELECTEO FROM THE SOURCE POPULATION OR 115 C PREVIOUS CYCLF 116 ImN2+IDRAW 117 REnAO( I2') ((CP(I,Jt),S5(IJ,),IlNSEG),Jml,2) 118 REAO(1'12) ((CP(IJ,2),,S(IJ,2),Irl,NSEG),J1l,2) 119 CALL INVER CCP, NSEGPNV) 120 CALL TRANS(CPNSEGPTRA) 121 CALL FZYVO (CP S, NSEG,PCPOPCROL) 122 CALL MUTAT(S,NSEG,PMUT) 123 C PRINT PEDIGREE IF REQUtSTED 124 IF(ITOG(1).EQ.1)RITE(6,71)NItN2,Iltl2 125 7 FORMAT(2QX, IS) 126 C DIALLEL CROSS OF SECOND-YEAR PROGENY OF PREVIOUS CYCLE 127 Dn 72 J"l,2 128 DO 72 Iui,NSEGQ A-35

129 CP(I,J, l)TCP(l,J) 130 S(CI,J, 1n TSCI,J) 131 CP(IJ,2) CPCI,J,3) 132 72 S(I,J,2)"S(I,J,3) 133 CALL INVEiCCPNSEGPINV) 134 CALL TRANS(CRP NSEGPTRA) 135 CALL FZVLO(CP, b,NSEGRPCROSPCROL) 136 CALL MUTAT(S,NSEGPMUT) 137 C PRINT CHrOMOSOME STRUCITURE DURING LAST CYCLE IF IPCS i 138 IF(TCYCE(,LCYC.ANO.IPCS.E. 1)CALL DCS(IND,CPNSEG) 139 C ABORT INDIVIDUAL AND RETURN TO SELECT NEW PARENT IF 1.40 C ZYGOTE IS 1NVIABLE 141 7a IF(VIAr(SNSEG))GO TO 75 142 NIZMNIZ+ 143 GO TO 65 144 C INCREMENCNTCON OF "I" ALLELES AT EACH INDIVIDUAL AND 145 C PRINT NUMBER OF "1" ALLELES AT EACH LOCUS AT END OF EACH 146 C YCLE IF I^AF * 1 147 75 IF'(IPAFEQ,0)GO TO 9? 148 CALL CA( ICYCLCYC,INONPOP,NSEG) 149 C DEVELOP PARAMFTER VALUES USING GENE ACTION SPECIFIED 150 C BY NOVLP 151 e8 GO TU(b1,82,63,84,85,86,87,88,89,I80e811,82) NDVLP 152 a81 CALL SGA1(NSEG S, NPARX) 153 GO TO 9c 154 82 CALL SA2 (NSEGS S, NPAR, X) i55 GO TO 9I 156 83 CALL S6A3(NSEG,S, NPARX) 157 GO TO sY 158 84 CALL S A4 ( NSE G, SNPAR X) 159 GO TO cO" 160 id CALL $GA5(NSGS,SNPARX) 161 GO TO 9V 162 86 CALL SiA6(NSEGc,,NPAR,X) 163 GO TO P 164 87 CALL SGA7(NSEGS,NPARX) 165 GO TO SO 166 88 CALL $GA8(NSEG,S,NPAR,X) 167 GO TO 90 168 89 CALL 5GA (NSEG, S, NPARX) 169 GO TO 9i 170 810 CALL SGA (NSEG, SNPAR, X 171 GO TO 90 172 811 CALL SG1iA(NSEGS,NPARX) 173 GO TO 9P 174 812 CALL SGA12(NSEGS, NPAR,X) 175 C EVALUATE INDIVIOUAL PHENOTYPIC VALUE USING TEST 176 C FUNCTION SPECIFIED BY NVALU 177 9( GO Tf(91,92,i3,94,9S,96),NVALU 178 91 CALL Vl(NPAR,X,V(INO)) 179 GO TO 97 180 92 CALL V2 fNPAR, X,V(IND )) 181 GO TO 97 182 93 CALL V(NPA, X, V(INO) A-36

183 GO TO 97 184 94 CALL V4(NPAR,,V(INO)) 185 GO TO 97 186 95 CALL V (NPA, X, V(lN)) 1.87 GO TO 97 188 96 CALL V6(NPAR,X,V(INO)) 189 C INCREMENT INDIVILUAL COUNTER 190 97 INDOIVmLNIVV+ 191 C UPUATE TRIAL CUUNTERS AND EFFICIENCY IF PARAMETERS 192 C ARE WITHIN THE ADMISSIbLE DOMAIN 193 IF(V(IND).LT.CV)GO TO 100 194 NTRaNTR+1 195 NTRTmNTRT+I 196 VSUMmVSUIM+V ( ND) 197 IF(I ND IE;.NPOP) E"VSUM/FLAT (NTRT) 198 C WRITE INDIV,VALUEANO PARAMETERS INTO PFILE IF IPAP m 1 199 C OR IPBP a 1 AND VALUE OF INDIVIDUlAL EXCEEDS VALUE 200 C OF ALL PRECEUING INDIVIDUALS 201 100 IF(IPBP,EQ,1)GO TO 101 202 IF(IPAP.EQ,1)GU TO 102 203 GO TO 110 204 11C IF(v(IND).LE.HIV)GQ TO 110 20-5 HIVwV(lND) 206 102 IF(NPAR.LE.8) wRITE(7,105)INDIV V(IND), (X(I), I1.NPAR) 207 105 FORMATC1X,I5, F1.3,8I7) 208 IF(NPANH GT.8)iRITE(7.106)TNDIVV(IND) X(I),Il, INPAR) 209 116 FORMAT(lX, ISFlo,3,8I7/(16X,8I7)) 210 110 IKaP 211 C STORE FIRS1 NSEL GENOTYPES 212 IFCIND.GT.NSEL)GO TO 115 213 KWINU+ISTOR 214 WRITE(rt' ) ((CP(I,J,3),S(I.J,3),Im1,NSEG),J1,2) 215 VS(IND) V (IND) 216 IF(ITOG(1).EU.1)GO TO 125 217. G TO 13~ 218 C REPLACE LOWEST-VALUED GENOTYPE STORED SO FAR DURING 219 C F2 CYCLE IF VALUE OF THIS INDIVIDUAL EXCEEDS 220 C THE LOWEST VALUE 221 115 LOwal 222 00 120 I1, NSEL 223 IF (vb(I) LT.vS(LOiW) LOW$I 224 120 CONTINUE 225 IF(V(TNPD)LT.VS(LOW))GO TO 130 226 K=LOw+ISTUR 227 wRITE(I'K) ((CP(IJ,3),S(I.J3),IilNSEG),JPl,2) 228 V$(LOW)iV(IND).29 C PRINT CYCLE, INDOIVIOUAL, VALUE, AND LOCATION IF 230 C GENOTYPE IS STORED IN Fl 231 125 IF(ITOG(i),.1) wRITE(6, 126) ICYCINDV(IND),K 232 126 FORMAT(2I6,F 11.3,6) 233 IK=l 234 C PRINT CYCLE, INDIVIOUAL, AND VALUE 235 130 IF (ITOG 1).E. 1.AlD.IK.E.0) WRITE6,126) ICYC INO, V(ND) A-37

236 IF(INDEU.NPOP)GO TO 140 237 INOD I 1 238 GO TO 65 239 C END CYCLE ICYC 240 C LIST INDIVIDUALS ACCORDING TO PHENOTYPIC VALUE 241 140 CALL LIST(VSN8ELR) 242 C AVERAGE VALUE AND STANOAWO DEVIATION OF SELECTED INDIVIDUALS 243 CALL ASD(VS NSELAVGS STDS-) 244 C AVERAGE VALUE AND STANDARD DEVIATION OF POPULATION 245 CALL ASD(V,NPOP,AVGSTD) 246 C STORE ICYC,-EAVG,STOAVSSTOS~NIZZNTR IN F2 247 K( tIRUN-l )*LCYC+ICYC 248 WRITE(2'K, 15$) ICYCE,AVG,STOAVGSSTDSNIZNTR 249 150 FORMAT(lX, I3,SFI0.32I10) 250 C TEST FOR END OF RUN 251 IF (ICYC.EQLCYC)GO TO 160 252 C BEGIN NEW CYCLt 253 ICYC=TCYC+l 254 IDRAr IDRAW+NSEL 255 IF(IDRAM.GT.NSEL) IDRAWm0 256 ISTOR=ISTOR+NSEL 257 IF (ISTU.GT NSEL) ISTQORm0 258 GO TO 6i0 259 C TEST FOR END OF REPLICATE RUNS 260 160 IF(CIUN.EQ.NREP)GO TO 170 261 IRUN IRUN+1 262 GO TO bP 263 C MEAN AND EXTREMFS OF REPLICATE RUNS 264 170 CALL PRR (LCYCNREP) 265 C CLOSE FILES 266 CALL CLOSE(1) 267 CALL CLOSEC2) 268 CALL CLOSEC3) 269 CALL CLOSE(7) 270 C TEST FOR STOP 271 IF (COATAC ),EQ TnP)STOP 272 C PRI4JT NAME OF NEXT OATA FILE IN SEQUENCE AND PAUSE 273 C IF ITOG(2) a 2 274 IF(ITOGC2, EQ.2) WRITE (6,18g)COATA(l) 27:i 18 FOQMATC1X,'RESTART AT',A5) 276 IF TOGC(), to2)PAUSE 277 C CONTINUE USING INPUT DATA IN FILE CDATA 278 CALL StEK (,COATA) 279 GO TO 10 280 END A-38

Simple Recurrent Selection 2 (SRS2) EDP-9 CHAIN/EXECUTE System D (IS - 15 i 1A,SB3 P R DO-1 5 V I } j i`I A Di)< A - 1 - 4/ IC i I,1 t.HAI,9 i7 Ci H A I N)7 A iNAME XCT FILE > S:." S' 2 >CSRS LIST O PTI FS A' OA E'.E?:' S >NM )'E F II NE F R ES ID;T\JT C OD 3 > MS R S2 I. \,T F ANS F ZY 0, C..!.., M.'UT AT7, J,'T.,: I a.BA, LI S T. - ASDU! RN,! I A N.D E V E'N T I'P AC, PAC!, DS CA, SA D..ESFCR IBE L IN'\1K S R ST;UCTr RE > C 1 =SGA1 t PG A-1 >G2=SGAS P.P A2 > G3 S3 =SA. 3 PG A3 >..7 4=-SG A/P..?GA >G6=SG A6,PG A6 >G 7 =SG(A7?, PG.A7 > G 8=SG-A S. PGA8 > 9 SGA9, PG A9 > G. 1 =S G.A 1.0,PGAi >G1 = S GA 1 I,P.iA 11 >G 12= S'GA 2P PGA 12 >G -1: G2: G 3:.G 4:G 5: G6: G7:G'8:G69: 1 0: r 1. 11: 61G.: PD FSV >V:I V2.: V3: \A:V SV6 CORE REO' ) 1 5"06-0-57636 DOS.-15 VIA $SEXIT A-39

Input Data 80001 SRS2 7/12/73 NDVLP 4 NV.LU I PINV 0. 0010 PTRA 0. 0000 PCROS Q,5000 PCROL 0 5000 PMUT 0,90000 CV 0.00 00 NPOP 32 NSEL 8 LCVC 10 NPAR 8 NSEG 32 NYAR 5 IX I IPAP I IPBP 0 IP AF 0 IPCS 0 STOP Main Program (MSRS2) 001 C MSRS2 VI 002 C SIMPLE RECURRENT SELECTION 2 003 C MAIN PROGRAM OF GENETIC PROGRAMMING SYSTEM SRS2 01.4 INTEGE.R CP.(26, 62, 3). S (256i 2, 3) R ( 100), X (256) 005 1,TCP(256,2), TS(256,2) 00$ LOGICAL EVENT, VIA8 007 DIMENSION A(12),COATA(2(2 F(2) F2(2) F3(2) PFILE(2) 00.8 1,VC003)VS (10),VVC2) 009 COMMON /CPS/CPS illa DATA Fli 1). F2C.,F3(1)/5HFl,5HF2 p5MF3 / 011 1,Fl(2),F2C2),F3(2),PFILE(2)CODATA(2)/5*4H SRC/ 012 1,STOP/H5STOP /wPFILE(l)/5HSRS2 / 013 C READ PFILE N VILPNVALU P INV,PTRAPCROSPCROL PMUT,CV 014 C NPP, NSEL.LCYC NPARNSEG NVAR IX, IPAP, IPPw IPAF IPCS 015 C COATA(1) FROM DISK FILE a11 IF(ITQ Tt2.)..,.. GO TQ 6 017 WRITE(6, 1) 018 i FORMAT Ci X,.DATA F ILE' ) o19 READ(5,5)PFILEC1) 020 S FORMAT(AS) A-40

021 6 CALL SEEK(1,PFILE) 22. 1i0 RE AD. C. 1 5)PF I n C 1 ). A, NO VLP NVALU, PIN. PTRA 023 1,PCROSPCROLPMUTCV 124 15 FORMAT(9XtA5/12A5,2C/9X.I6),5(/9XFS64)/8XF7.4) 025 READ ( P 20) NPUP NSEL,LCYC 02 20 FORMAT(9X,I6,2(/9X,Io)) 027 READ (l 25) NPAR, NSEG NVAR TX 028 25 F RMATC(9X I6, ( /9 I 6)) 029 READ(C,30iIPAPIP8P,IPAF IPCSCDATA(l) 030 30 FORMAT(9X I6,3(/9X, 6)/9X,A5) 031 CALL CLOSE(l) 032 C ELETE AND RECREARTE PRINT FILE 033 CALL OLETE(7,PFILE,I) 034 CALL ENTER(7,PFI.L~) 035 C WRITE PFILENDVLP NVALU,PINV,PTRA,PCROSPCROLPMUTtCV, 036 C NP.OP,NSE.LLCYCNPARNSEG,NVAR, IX IPAP,IPBP IPAF IPCS 037 C COATA(l) INTO PRINT FILE PFILE 038 WRITE (7,40)PFILE(1),A,NDVLPNVALUPINVPTRA 039 1,PCROS,PCROLPMUTCVNPOPNSELLCYCNPAR 040l, N8&eG.NVAR, I X, I P A PA, T P T P AFIPCS, CAD O T A ( 1 ) 041 40 FORMATC(OX,A5/lX,12A5/1 NDVLP',I10/' NVALU',t10 04.2 1/' PINV',F1.4/1 PTRAI,Fl.4 043 1/' PCROS',F10.4/' PCROL',F10.4/1 PMUT',FIl,4 044 1/. Cvi,F1.3.4/ NPOPII,111/ NSELI,I1l 045 1/1 LCYC',Ill/' NPARI11/' NSEGI',1/' NVAR' 11l 046 1/' iX.I13/' IPA P.t1/l IPBP,! i /' IPAF,I1 047 1/' IPCS',Il1/10X,A5) 0.48 C DELETE AND REDEFINE DIRECT ACCESS FILE Fl USED TO STORE 049 C UP TO 2*NSEL.2 CHROMOSOME ARRAYS 050 CALL DLETEC(,F1,I) 051 CALL DEFINE(1 4*NSEG,2*NSEL*2,F1l, IVl?0,00) 052 KV 2*N$EL 053 C OELETE AND REDEFINE DIRECT ACCESS FILE F2 USED TO STORE 054 C EFF, AVGp STO, AVGS, STOS, NIZ, NTR FOR EACH CYCLE 055 CALL DLETEC2,PF2,I 056 CALL DEFINE(2,8tNVAR*LCYCF2,IV2, 1,t,0) 057 C DELETE AND REDEFINE DIRECT ACCESS FILE F3 USED TO COUNT 058 _..T. NUMBER OF "." ALLELES IN THE POPULATION AT EACH LOCUS 059 C AND CYCLE 060 CALL DLETE(3,F3,I) 061 CALL DEFINE (3, 16 NSEGF3, V30, 0 0) 062 C START RANDOM NUMBER GENERATOR AT IX 063 IX~ZIX 064 CALL URN(I XU) 065 C INITIALIZE VARIETY COUNTER AND BEGIN VARIETY IVAR 066 IVARRi 067 50 INDIVO0 068 NTRTs0 069 V.SUM o. 070 Emo. 071 ICYCal 072 HIVo0. 073 ISTOReO 074 IDRAiWNSEL A-41

075 C BEGIN CYCLE ICYC 076 60 INOm. 077 NIZ"0 078 NTRm0 079 Njli 080 N2l1 081.C SELECT PARENTAL GENOTYPES AND LOAD ARRAYS CP AND S 082 61 IFCICYC.GT.I)GO TO 67 083 IF(CVAR.GT.2).GO TO 3 084 C FORM RANDOM HETEROZYGOTES OF SOURCE POPULATION 085 DO 62 1"1,NSEG 086 CALL URNCIXU) 087 00 62 J l r,2 088 N~(I'1)/d+1 089 MmI-(N"I)*8 090 CP(TJ,3) IPAC (N, M 091 IFt(J.E.l )StI,J,3) IX 092 IFCJ.E.2)S CI,J, 3)-IXw1 093 62 CONTINUE 094 GO TO 74 095 C FETCH PARENTS OF VARIETAL CROSS 096 63 K.KV+1 097 REAOD(lK)((CP(IJ, l),S(I, J, 1, I1, pNSEG),Jl,2 098 KmK+1 0r99.REAO.( 1 K) (CCP(I,J,2) S(I,J, 2),l 1,NSLG), J1,2) 100 GO TO 73 101 C DETERMINE PARENTS OF DIALLEL CROSS 102 67 N2~N2*1 103 IF(N2,LENSEL).GO TO 68 104 N1Nl1li 105 IF(N1.EQNSEL)N1si 108 N28Nl+l 107 C PRODUCE FIRST PAREtT OF OIALLEL CROSS BY SELFING AN 108 C INDIVIDUAL SELECTED FROM THE SOURCE POPULATION OR 109 C PREVIOUS CYCLE 118 68 ItNNI+IDRAW.1.1 READ (I' l ) (CP I, J,, 1 S (I, J, ) I l 1 NSEG) Jml, 2) 112 READ(1lI1) (CCP(I,J,2),S(IJ2,2,I1,NSEG),Jl1,2) 113 CALL INVER(CPNSEG,PINV) 114 CALL TNANS(CPNSEG,PTRA) 115 CALL FZYGO(CPS,NSEG,PCROSPCROL) 116 CALL MUTAT(S,NSEGPMUT) 117 C STORE..FIRST PARENT IN TCPTS 118 69 DO 7. Jl, 2 119 DO 70 I.I,NSEG 120 TCPCIJ) CP(I,J,3) 121 70 TS(IJ) S(I,J,3) 122 C PRODUCE SECOND PARENT OF OIALLEL CROSS BY SELFING AN 123 C INDIVIDUAL SELECTED FROM THE SOURCE POPULATION OR 124 C PREVIOUS CYCLE 125 I2uN2,IDRAW 126 READ('lI2) ((CP(I,J,1),SCI,J,1),ISlNSEG),JUl,2) 127 READ(1'12) C(CPCI,J,2) S(I,J,2) IulNSEG) w,JI,2) 128 CALL INVER(CP,NSEGPINV) A-42

129 CALL TRANS(CPNSEG,PTRA) 130 CALL FZYGO(CP,,NSEGPCRO8,PCROL) 131 CALL MUTAT(SNSEGPMUT) 132 C PRINT PEDIGREE IF REQUESTED 133 IF(TTOU(1).EU. 1)WITE(6,71)N,N2, I,2 134 71 FORMAT(29X 4I6) 135 C DIALLEL CROSS OF SECOND-YEAR PROGENY OF PREVIOUS CYCLE 136 DO 72 Jl1.2 137 DO 72 1,NSEG 138 CP(IwJ, 1) TCP(lJ) 139 S(IJ,vl)TS(lJ) 140 CP(I#J,2) CP(I#J,3) 141 72 S(I,J,2)3S(IJ,3) 142 73 CALL INVER(CP NSEG,PINV) 143 CALL TRANS(CPNSEG,PTRA) 144 CALL FZYGO(CP,,NSEGPC P PCPCROL) 145 CALL MUTATC(,NSEG,PMUT) 146 C PRINT CHROMOSOME STRUCTURE DURING LAST CYCLE IF IPCS = I 147 IF ICYC.EQ.LCYCANO IPCS. EgQ )CALL DCS(IND,CPNSEG) 148 C ABORT INDIVIDUAL AND RETURN TO SELECT NEW PARENT IF 149 C ZYGOTE IS INVIXALE 150 74 IF(VIAI(SNSEG))GO TO 75 151 NIZ"NIZ+1 152 GO TO 1 153 C INCREMENT COUNT OF "1" ALLELES AT EACH INDIVIDUAL AND 154 C PRINT NUMBER OF "1" ALLELES AT EACH LOCUS AT END OF EACH 155 C CYCLE IF IPAF x 1 156 75 IF(IPAF.EQ.O0)GO TO 8 157 CALL CA(ICYCLCYCINO NPOPNSEG) 15.8 C OEVELOP PARAMETER VALUES USING GENE ACTION SPECIFIED 159 C BY NDVLP 160 80 GO TO 8,82,83 84,85,86,87, 8,89 8t 1,81 1 2) NDVLP 161 81 CALL SGA1(NSEG$,3NPARX) 162 GO TO 90 163 82 CALL SGA2CNSEG,SNPARX) 164 GO TO 90 165 83 CALL SGA3(NSEG, SNPA, X 166 GO TO 9e 167 84 CALL SGA4(NSEG,S,NPARX) 168 GO TO 90 169 85 CALL SGAS(NSEGSNPARX) 170 GO TU 9V 171 86 CALL SGAd (NSEG, SNPAR X) 172 GO TO 9V 173 87 CALL SGA7 NSEG,SNPARX) 174 GO TO 90 175 88 CALL SGAC8NSeG,SNPARX) 1. 76 GO TO 90 177 89 CALL SGA9(NSEG S,NPARX) 178 GO TO 90 179 810 CALL SGA1 (NSEG,S,NPAR X) 180 GO TO 90 181 a81. CALL SGA11(NSEG,S,NPAR,X) 182 GO TO 90 A-43

183 812 CALL SGA12(NSEG, S NPAR, X) 184 C EVALUATE INDIVIDUAL PHENOTYPIC VALUE USING TEST 185 C FUNCTION SPECIFIED 8Y NVALU 186 90 GO TO(91,92,93,94,95,96) NVALU L8O7 91 CALL VlCNPAR,X,V(IND)) 188 GO TO 97 189 92 CALL V2(NPARXV(INOD) 190 GO TO 97 191 93 CALL V3(NPAR, XV(IN0)) 192 GO TO 97 19 94:CALL V4 CNPAR X.V( IN)) 194 GO TO 97 195 95 CALL V5(NPAR,XV(IND)) 196 GO TO 97 197 96 CALL V6(NPARX,V(INO)) 198 C INCREMENT INDIVIDUAL COUNTER 199 97 INDIV[INOIV*I 200 C UPDATE TRIAL COUNTERS AND EFFICIENCY IF PARAMETERS 201 C ARE WITHIN THE ADMISSIbLE DOMAIN 202 IF(V(IND).LT.CV)GO TO 100 203 NTRaNTRl1 2084 NTRTNTRT+l 205 VSUM"VSUM+V(INO) 206 IF(IND, EGNPOP)EmVSlM/FLOAT(NTRT) 207 C WRITE INDIVVALUE,AND PARAMETERS INTO PFILE IF IPAP 1 208 C OR IPBP a 1 AND VALUE OF INDIVIDUAL EXCEEDS VALUE 209 C OF ALL PRECEDING INDIVIDUALS 218 100 IFc(IPBPEQ1)GO TO 101 2_11 IF(IPAPEOQ1)GO TO 102 212 GO TO 110 213 11 IF(V(lND).LE.HIV)GO TO 110 214 HIVNVCIND) 215 102 IF(NPAHLE.8)WRITE(7,1C~5)IDIV,V(IND), (X (I) I1,NPAR) 216 t10 FORMATC(XI5,F10.3,8I7) 217 IF(NPAR.GT.8)WRITEC(7,16)INDIVV(IND), (X (I), I NPAR) 218 106 FORMATCI(XI5,F10.3,8I7/ (16X,8I7).) 219 110 IKiR 220 C STORE FIRST NSEL GENOTYPES 221 IF(ND.GT.NSEL)GQ TO 115 222 K"IND*ISTOR 223 WRITE(1'K) C(CP(I,J,3)SC(I,J,3),Ilm,N8E6),JgJI2) 224 VS(IND) V(INO) 225 IF(ITOG(1),E0.1)GO TO 125 226 GO TO 130 227 C REPLACE LOWEST-VALUED GENOTYPE STORED SO FAR DURING 228 C F2 CYCLE IF VALUE OF THIS INDIVIDUAL EXCEEDS 229 C THE LOWEST VALUE 230 115 LOW=l 231 00 120 ItINSEL 232 IF(VS(I).LT.VS(LOW) LwI 233 120 CONTINUE 234 IF(VCINLD)LT.VS (LOW))GO TO 130 235 KILOW+ISTOR A-44

2.3 WRITE 1 K) ((CP(IJ,),S(IJ,3), Il1,NSEG ),J 12) 237 VS(LOW)V( INU) 238 C PRINT CYCLE, INOIVIOUAL, VALUE, AND LOCATION IF 239 C GENOTYPE IS STURED IN Fl 240 125 IF(ITOG(t).EU.W WRITE(6,1 ICYCIND, V (IND) K 241 126 FORMAT(2I6,F 113,oI6) 242 IK 1 243 C PRINT CYCLE, INDIVIDUAL. AND VALUE 244 130 IF (TOUC I.E i, ANDOIK.E.0) WRITE6,l126) ICYC IND V CIND) 245 IFCIND.EQ.NPOP)GO TO 140 246 INOuINO.*1 247 GO TO 61 248 C END CYCLE ICYC 249 C LIST INDIVIDUALS ACCORDING TO PHE NOTYPIC VALUE 250 140 CALL LIST(VSNSELpR) 251 C AVERAGE VALUE ANO STANDARD DEVIATION OF SELECTED INDIVIDUALS 252 CALL ASDCVS, NSL, AVGSSTDS) 253 C AVERAGE VALUE AND STANDARO DEVIATION OF POPULATION 254 CALL ASD(VNPOP,AVGSTO) 255 C STORE ICYCpEAVGSTOAVGS,STOS,NIZNTR IN F2 256 K3(IVAR1l) *LCYC+ICYC 257 WRI'TE(2 K, 150) ICYC, EA AAGS AVGSSTOS NIZNT 258 150 FORMAT.(I1X, I3,5F10.3,2110) 259 C TEST FOR END OF VARIETY 260 IF(ICYC.EQ.LCYC)GO TO 160 261 C BEGIN NEW CYCLE 262 ICYC=ICYC+l 263 IDRAWKIDRAW+NSEL 2f_4 IF( I RA. GT.NSEL) ID RA W 265 ISTOR ISTOR+NSEL 266 IF(ISTOR.GT.NSEL)I$TORI0 267 GO TO 60 268 C TEST FOR END OF RUN 269 160 K R 1 ) 2.70 IF (IT0 C1),E 1) WRITE C6, 11) VS K) VV 271 161 FORMATC1X, VS$rtFl,3/1 VVa=2F10,3) 272 LOWmIVAR 273 IF(IVAR.LE2) GO TO 163 274 LOW,1 275 DO 162 I1I,2 276 IF(VV CI) LTa V (LO)) LOOWI 277 162 CONTINUE 278 163 IFCVS(K).LT.VV(LOs))GO TO 164 279 VV (LOW) VS(K) 280 KK+.ISTOR 281 REA) ( 1 iK) ((CP(IJl ) S(IJ,,I NSEG) J 1,2) 282 KaKV+LOW 283 WRITCtK) ((CP(IJt) SCI,J,), I 1,NSEG), Ja, ) 284 164 IF (IVARFEQNVAR) GO TO 170 285 IVARuIVAR+1 280 GO TO 5!. 287 C PRINT DATA FROM SUCCESSIVE VARIETIES 288 170 CALL POFSV(LCYCfNAR) 289 C C CLOSE FILES A-45

290 CALL CLOSE(l) 291 CALL CLOSE(2) 292 CALL CLOSE(3) 293 CALL CLOSE(7) 294 C TEST FOR STOP 295 IF(COATA(1).EQSTOP)STOP 298 C PRINT NAME OF NEXT DATA FILE IN SEQUENCE AND PAUSE 297 C IF ITOG(2) * 2 298 IF(ITOG(2).EQ,2)wRITE(6, 180)CDATA ) 299 1.8 FORMAT(IXwRESTART AT I,A5) 300 IFCITOG(2).EQ.2)PAUSE 301 C CONTINUE USING INPUT DATA IN FILE CDATA 302 CALL SEEK(1COCATA) 303 GO TO 10 304 END A-46

Reciprocal Recurrent Selection 1 (RRSI) PDP-9 CHAIN/EXECUTE System DOS-15 \ vA $,; PR DO'$-.5 IJ -1A $1,$ J()Ve D-KA. - 1 -./ $C HA ILN CH.AIN V7A NA.M-.E XCT F I-LE > RRP S 1 L IST OPT IO'iS & PHARAMETFE~IRS >.NM DE'FINE RFSIDENT CODE >'M R R 1 IN'V E.R T RANS F 7 YrnC fO rW S; M1 UTAT,MIT:..I-T I A''v L ST, - ASD, URlRN, I RAND EVENT, I'PAC IPA C, DS,CA' A SA D:E'SCRI-.B'E L INKS & ST'U RCTURE >6'2 t=.SG, A PGA 1 > G 2' SSG- A2 P.Gr A2 >G3 = SGA3, P GA3 >G4 =SGA.^,P'RGA >3:r 5 -SG A5, P GA 5 >G6 =.SG'A6. PGA6 >G7-=.SGv.A7 J PGA7 > G.7'=. S-GA- 7 PC.? A 7 >G8= SGA8., PG'AS >G 9 SGiA9, PG-A9 >-G 1 I=SGA1. I, PGrA10I G 1 1 =S. A4 1 PGA1 1 >G 12 =S'G Al 2- PGA: 12 >G t 2: G3:G4 G 5- G:6 G7.8:G 9: Gl 0:0. 1:;61':. 2:MERR >V.:V2:V3:V4:V5:V6 CO.RE REQO'D 1 5532-57636 D.O-S- I VIA $$EXIT A-47

Input Data fj'i A t RRSj 6/25/73 NOVLP 1 NV AL.U PINYV.0 / ICA PTRA 0 ^ PCROS. 5', - PCROL -,5 -n PMUT. Mc NPOP' NSEL 4 NSA1P 2 LCYC 1I' NPAR 8 NSEG 32 NREP I IX 1t IPAP I IPBP IPAF I.PCS. $ T OP Main Program (RRS1) Q001 C MPRS1 Vi 002 C RECIPROCAL,,tCUk.'.T SELECTION 1 w043 C MAIN PROGFAM nF.,E1IIt P1O(GRAMMING SYSTEM RHS1 ad4 INTF GtER CP (25t,2.,3)- S(256,23), 3RA (10) RB(I10,0), 26) 00 5.LOGTC O L EVF, r, VI A 006 DIMENSION A(ia,COAT (2,Fl (2) F2(2) F3(2),PFILE(2) 307 1 V A 1'),Vb 1 09i) a08 coMtNI! /CPS/,CP, 009 OA rA F 1f),F2(1),F3 (1)/5HPF,5HF2,5HF3 -10 1,F'. (1.),F2 (2),.'f 3 (2), PFILE (C2) COATA'(2)/5*4H SRC/ o011 1,STTOP/ HSTt(,P /,PFII.E (l)/5HRRS1 / 012 C REAO PFILF,' ~VLP#, NViA4LiUPI V, PTRAPCROSPCROL,PMUTCV, i13 C NPOP, NSeiS.EL,v N pLC CNPA,NSEG.S NEPIX, IPAPIPBPIPAFIPCS 014 C COAT4(1) FKrii' UISK FILE 015 Tr(TTfir62).~i.) -.~E.)GO TO 6 016 WR.iTc 65, 1 017 1 FORmAT(1Xo, ~'.-ATA FiLE~) E18 REA (5, 5) PFILE 1) 919 5 FU;ATA (5) ia20 6 CALL $SEK((1,PFiLE) 621 1ei REI nCI( lb)PFXILL 1, A,NOVLP, NVALU, PINVPTRA A-48

22 1, PCh' f5, PCHt.-L, PMUT r. C 023 15 F'- k^"l (,AX /1 2Ab r 2 (/X P,I6,5 C/.gX w F6.s 4) /X, F7 4) 024 F.^i, ) vPU P,S SFL,NSAMP,t. YC 2 5 2C FtOR (X Ib,/ ) 026 W:Ar, ( 1, 5') NAt N,,, GN NREP TX 027 2 FOk T ( oX, It, C(/9X, 16 ) ) 028 P[Arl" ( s (3t) IPAPT tP, IPAFIPCCS CDATA () 029 3'0 FOPt'T (9X, I6 (/, 16) /9 X A5) l030 CALL CLOSE C(1) 0(31 C OFLET AHN; RLCH.FATIF PRIXIT FILE 032 CALL_ 3LFT(7,PFILF, F:) 1030 -CALl F.NTTf (7,PFIL-) 034 C Vi TE PFILC.,VLPNVALUJPINVPTRAPCkOSPCOLPMUTCV, 035 C NPOP,'!x$1Ft,s (F.aSA rP L;L Y L',N P A i.NSE Rs P lJME P P I X IPAP,PBPiP p IPAF, IPCS (036 C CrATA INTO PFINT FILl. PFILE 037WR I T. t(7, 4. 4)PF LE( ), A, NOVLP, NVALIJPINV PTRA 038 3, SPC.r(S, SPCR(L, rPMIUT,CV, NPOP, NSEL NSAMP, LCYC, NPAR 3391,iNFH-,NEP,,Ix, IPPIAP, IP, IPAF I PCS CTA 1 ) 040 4, F4OPAT)XA0/ IX,!12AS/1 ND.VLPpI^10/I NVALUI,10o 041 1/' PiVT.',F1 F,4/ PTRAFii.4 042 1/1 PLkOS',F1o.4/f PCROLfF.O0.4/1 PMUTF11.4 043 I/ r.V,,F135t.4/, NPOP'pI l/I NSEL'II11/ NSAMP, f1fi0 044 tI/ L-CCII11/' NPARsIt]/v NSEGIt1l/1 NREP,I!'_45I5 / J:/',Xt3/. X'PAPW,I11/1 IPBP'IllI/ IPAF',Ill 046I/ 1/' IPCS' I 11/10XA 5 047 C OF.LETE ANi, Ktnr.EFIK,t DIRECT ACCESS FILE Ft USED TO STORE a48 C UP TO 4*Npr FP CHO". OSLUMt ARRAYS i 49 CALL f'LFT(1 I F1, I ~'350 ~ CALL, i-F lNt ( 1,4N$G, A*NPnflP, F I, IVI, ), ) 051 C jFL.ETF AN^. F-EFIN- Lt OREtTCT ACCESS FILE F2 USED TO STORE 052 C FF, AVG, STL, AV-(,, STOS, NIZ, NTR FOR EACH CYCLE'J53 CALI U LFT C.( F2,P i) 054 CAL L r..F IE -.2, 3 (NREP,3) *LCYC F2,IV2, 1 00) 055 C O!FLETE AN,'EDEF INb OiK ECT ACCESS FILE F3 USED TO COUNT a56{ C rTH NtiMtF.P.R [OF "I" aLLELES IN THE A AND b POPULATIONS 057 C A'T FCH LU( C..i ANL) CYCLE 058 CkALL )L6T (3,FiI) o59 CALl. (tFI'.I l(,I6,NSGF3,,V30,,,J) 06 C START RA.:i.i NU'jlMbt: iENERATOR AT IX 061 Ix=-i 062 CALL L Xu i ) 063 C I.kITITLTIZ LL:('i)NITt A ANt) BEGIN Ni.lE IRUN 064 MNR P; P +i P P 065 N Y F::UP P S AMP 066 I kJLID,= 1 kit7 5~ X~~S~~ 0b 7 5 IN T v 06d NTRT=e, 069 V 5 ti- t~'1 =:. 071 ICvCci 07 2 H I vs =l.. 073 In, F~ F' 1 074 I STO-c r^,!hi 075 C FOZ; rANI)IC.: ~ETF!Hi.ZY GOuS SOURCE POPULATIONS A-49

076DO 9., IN\POP 077DO O lIlN$ISG 078 CALl. tN(C X, U) 079DO.c J"1,2 081 T (i- ) 082 CP(Ir,J13) ]IAC(N, ) a83IF CJ,, H 1)S(I,J 3) IX IF ( J, F JZ,, 084 IF f F. u.W2S ( J, ^IX-1 065 54 CONT 1iU' lF 066 Rirl t (II I) ( CRcP(I,J,31$ t IJ,3) I1, NSEG),J1,?2).87 C I.tCReMENT CirlhNT OF "1" ALLFLES AT EACH LOCUS OF INDIVIDUALS 088 C IN THs SOtiiC.e PlPUL4TIU)S TF IPAF M I 089 TF (IP;E. F'E".) iO Tn I5 090 IF (K, L E;-POP).K=K ^1i9 rttr IF C, tT.NPOF) aF, K -NP0P 092 C ALL (ACYC. LCYC, K, NPOP, SSEG) d93 55 CO,T INUE 094 C E6IN CYCLE iCYC 095 6 I i) 1 096 NI Z =' 097 NTR =? (09 C OFIT'RINME PtrENtS Ir RECIP4OCAL CROSS 099gI F F cv 100 1. P 1'01 Vaf 1) ri) aSi. I2 65 IFA=Mc iM+ 3 i IF O. iT F L.N SP) ('; rTO 70 I Pt 4 1s 1 I'.5 I F (o,',1.T, TPOP) Ni P;Nsl INPOP 1^'06I l L& PnP) A^ 1) 1NP PCA I' I 07 I F p v G T o Pf' ) V B t "Ib ) =- 10' 2 p 107 IF(1l, GT..pnP)V81 ):-l0P. 108 TFFM 109 70> IF 1..LE tCP) N2= AN(NPnOP+l, NPOP) 110 IFC-('"I iGT, s-iPOP)N2 Ir AND( 1 POP) 111 C FOP' Hv Y83PTO'oWiJTYPF OF CROSSBPED ZYGOTE 112IlsXGIDw 112 I! ^i+iORAW 1 1 X I I: = h " I [R 2 a 114'EA(l Il) CCCPCI,Jl,S(tIJ,1,IaNSE),Jml,2) 115 RE.rl (1 I23 C(C:(I, J,? ~8(IJ~2) t I= rNSNEG),J1, 2) 116 CALl'X VE f!;: (CP, NSEf, P NV) 117 CALL TKANS(P, NSEGIPTRA) l 16 CALL FZY (ct v C. P, S,SE 3, CPCROU, PCRUL 119 CA L.L. L,.uTAT (ST, iSE (',PML UT 120 C PPIST CHPCt'o: nsni ST*UCT JRE DURING LAST CYCLE IF IPCS I 1 121 IF: (iCYC.,El,' LCYC.,ANO. IPCS.E. ) CALL pCS(IND, CP NSEG) 122 C PRINT PELTGPFc E IF krtJUESTED 123 IF(IrGftl1 l )'Ql ITE(6,71)N1,N2,Ili,I2 124 71, FnP.T(29x,4i6) 125 C AABOT INDTIVi1AL AN) R'.tTURN TO SELECT NEW RANDOM PARENT IF 126 C ZYGCOTTt 1. it.vIAbLE 127 IF(Vi o t($,NSG ))G TO'r 1286 NI27I/+1 129 Gj T! 7v A-50

130 C UEVfEL.tP F,:,,,T, l VALUJS JUSING GENF ACTION SPECIFIED 131 C tY NjDVLP 132 8 GO T(^,,, R.,B,7p,6, 8,10 R1, 82),NDVLP 133 $1 CALl SiAt f (4.ieG S,'JPA,X) 134 GO TLY'V 135 82 CALI. St., 2 t.i;,w S, iPAA ) 137 83 CALL t S,A3(tNSI ^ S,t PAR ) X 13a GO TLu 139 84 CALL 4 (N, S, P4, X 1a453 86 C. A I. $I; AL ( b r- [, L S, "iP/, + XA ) 144 GO r t^ 141 9 8 C aL I $, A A ( L $.,S A 4 S,, P A R c X ) 142 Gi t Gjn T t. 143 85 7 CALL SGA f (NS,, ^ PAR'Y) 14452 0 TLU 9r 146GO N A 15 4 Gr T i.l. 1478 CALti S;A1( f NSG, S, NPAR,) 149 d^ CALL S'GAY(NSc;G,SNPARY) 1 57 C FUt NCT ",CFiE[; 3Y NVALU 159 9i CALl. vI/. ( N PA, X V I PA, i) 152 GO TU 7^ 153 911 CALL. L l, (1C S,CS PA", Ax 1562 GO TO 7 156 C rALUAT& Ir -IVlIOHAL PlHfcOTyPIC VALL~ USING TEST 157 C FUNCTiON SPhCIFIELi tY NVALU 159 91 CALlI V1(NPAFPXIVV4U) 16. GO TO Q7 161 93 CALL. V ( tPAR X VI U) 1i6 GO TO 9'7 163 93 CAL.I` (NPAPLxVII) 1657 9 CALL (;, AL, V( P;,v 4 Ul) 16 GCO TU 97 i69 CALI \V! b fPA', x, \/'d )) 17 v) C I,CREE NT lr:LJuIVJOliAL CO.NTER 171 97 iNC ITV=J'UIV+i 172 C R(f'Crwi' HItdMiST PiRL;,GNY VALUJE COF WECURRENT PARENT 173 IFf.1.GT.NP(OP)O'TO 9 174 IF (v\I, GE VIA (rY ) V.A A(1) I1VIN0 175 G' 9. 176 9B N9B i-P'UP 177 IF (vsi,-.E V, (Nb) ) VfNS) VIND 17' C JUP'ATEr TRtI'L CJULrT4tiHS AitJ FFFICTENCY IF PARAMETERS 179 C ARt WITXHIN THE AO:ISSI'LE )OMAIN 18 9k I,laF( fI'u.LT.C')Go TO 10I 181 NTFrNT +1 182 hNTRTkTFT+PTI 183 VSL s V i4+V T iN A-51

18 4 F ( t N r), e. N e y H ) E t v $ I 1 / F L J h T ( N T R T I 184 IF Tf a...NH Y ) E'vS'JM/FLOAT(NTNT) 185 C MRITE IMPTIV,VALUlE,.A4O PARAMETERS INTO PFILE IF IPAP m 1 186 C OR IPB3P s I AU VALUE OF IlNDIVIDUAL EXCEEDS VALUE 187 C OF ALL'PREC.FIiNG INOIVJOUALS 188 1l IF (XIP.Pc* L. r)G TI] 1.1 189 IF(IPAP.EO..*)GO To 1'2 190 GO TO l13 191 101 IF CvINrL).LLE.IV)GO TO i 13 192 HIVV 1JrP 193 1 2 IF (h,. Le. ), I T (7, 5) IIVV INO w (CI),INP A R) 194 15 FOriAT (1X, 5,F1.3,^17) 195 F(F (,.!PA.l:T.)TI'r() rI 7, 1i?6) I OIV6,VINO, (XCI),I, NPAR) 196 1. FOFMAT (lX,I, Fl:, I7/(t y,817)) 1i97 C PRINT CYCLF-, IiIvX V')OUAL, AND VALlE 198 13A IF (TT C I 1) P..t ) w 6ITE (6 l3l IICYC., IND, VINO 199 131 FO A (t I, F 1 3) 200?'TF(TINE.EQ*.NmHY)GO TrO 140 201 I N i)sl. 202 GO n lo 65 203 C ENOI CYCLE I YCr 204 C LTST INfOV)!iU1tLS ACCiURING TO PHENOTYPIC VALUE.0.5 1.40 CALL LtST(VA,NiuP,R4) 206 CALL I ST(V', POPP, R) 207 C AVERAGE VAii l AND STANDaARU DEVIATION OF A PROGENY 2PI08 CALL 4Si. (AVA, NPP, AV GA,fSTOA) 209 C AVERAGE VAt!lH. AND S'rANL)ARf DEVIATION OF b PROGENY 210 CALL ASD CV, NPOP, AVGS STOR) r21 C STU.PE ICYC,EAV;GA, 3T)A,AVGASTO0bNIZNTR IN F2 212 K (T iN- 1) *LC YC+ICYC 213 WRIT C2 ( K:, 15 ) ICYC,E, AVG, STDA,AVGB, STDNB IZNTR 214 15' FORAT ( 1 X, t35F10,q32I1l9) 2"15 C TEST FOR Ei'r OF RWli4 216!F( TYC.EQ.L.CfC)G o TO 16a 217 C EI,;IN N El iYCLE 21d TCYC. STCYC+ 21- C SELF NSEL A iOIVITODALS wITTH HIGHEST PROGENY VALUE 220 C Tro PROPAGATF P OPULATIONS A AND 8 221 NI.t7 222 DO J b5 Ka I, PUP 223 Ni N1 + 224 IF('1 j..T.NSL) Ntal 225 IF (K.* L..NPOPj I 1=C(N )+IOPAW 226 IF (K.;T.NPPP) I 1 R C(N1) +NPOP+IDRAW 227 2= r i 228 REAn(1 I1) ((C(I,JI,1),S I,J,1),I,NSEG),Ji, ) 229 REAnC C'I2) CP(I,J, 2),S(IJ,2),I 1,NSE G,J1,2) 233 CA L. IVC P,NS P I NV) 231 CALL TWANS(CP, NSE,W PTRA) 232 CALL F Y G (CPS, NSSE ^ P ,ROSPCROL) 233 CALLI hiUTAT CSNSE,G P 1;UT) 234 I3=K+ rTO 235 hRlTt.(l TI33 ((CPClI,J 3 S S(fJA3), Il, NSG6),Jl 2) A-52

236 C;iCR FT.;'r:J "1, ALLEL S AT CACH LOCUS OF INDIVIDUALS 237 C T,, TE, IF.', A A I) 0^ P PULAT J.ONS IF IPAF * 1 238 IF (r'AF.^v&.E.U. ru TO 155 239 F ( < L_. P)P) < K s 240 TF (~.' *T.u uFe=s-sNr' P 241 CAL.L. ( Y(C C, LCY(C, s, NPOP, - SEG) 242 15 Cr,T! i T IJ 243 C FS%.-T BA4S Li3CjAT Il'^S OF Ft 244 T)A' A ^ I' O N + P 0 P 245 IF (T.k, 4!?.'T,,T i POP) I)'RAW='; 24 dI S T T r.; = T:') J P 247 Ir'T.iT' P )P ) ITOrBfP? 2493 G;i T. t 249 C TfST FOP C K!'F rF t'PLICTf'C RUNS 25 10..) IF C T,'.~,~',.'.",' )Gr ro 17? 251 @I^~Jr I tltf84 l 252 G6O TU db 253 C M- FAN -Nj F:T;'fE.Mi1S r)F REPLICATE RUNS -254 17 CALL t C LCYC, Ni EP) 255 C CLU)SE FILFS 255 CALL CLOSE(CI 257 CALL fCLOSt5 (?) 258 CALL C LUSCE.C3) 259 CALL CtL.OE(7) 260 C TEST r0' S P:r 261 IF cf()OAT A ( ).C 3 STOP) STOP 262 C PRINT NAME or NEXT OATA FILE IN SEQUENCE AND PAUSE 263 C IF ITO.G(2) s 2 264 IF (I TO1 (2)r..2) r IrE C(6 1 8() COAT A 1) 265 li) FOfAT4 ( IX,'R'SrART AT,AS) 26 IF ( T TO ( 2) 2 ) )USe 267 C CONTINUIF w1SI,,r INPu)T QATA IN FILF CDATA 268 CALL SCt FK (COATA) 269 GO 1t ti 270 E N F A-53

Resident Subroutines: INVER,TRANS,FZYGO,CWS,MUTAT,MUT,VIAB,LIST, ASD,URN, IRAND,EVENT, IPAC,NPAC,DCS, CA, SA C INVER VI SUBROUTINE INVER CP NSE, PINV1 INTEGER CP(256,2,3) LOGICAL EVENT IP(PINV.EQ..) RETURN 00 20 K.l,2 00 20 Jw1,2 00 20 I1,NSEG IF(,NOT.EVENT(PINV))G0 TO 20 CALL NPAC (CPCI(.. J- K),IC M) PF(M*EQ.*1GO TO 20 NaIRAND CMI ) IF ITOG(),Eg l) WRITE (6,5) lCNMKJ S FORMAT ( I X NVERSIONf5!.6 00 10 L"1,NSEG CALLI NPAC CCP CL, Jj K) J LC., P) FP(LCNE9tICGO TO 10 P(IFP.LT.NOR.XP.GT.M)GO TO 10 CP.L JK) IPAC(CCC, M*NIP) Is CONTINUE 20 CONTINUE RETURN END C TRANS VI SUBROUTINE TRANS(CPNSEGPTRtA) INTEGER CP(256t2~3) LOGICAL EVENT I.F. (PTRA, Eg.0..RETURN 00 120 K.I,2 00 120 Jl1.2 00 120 It1,NSEG IFC(NOTEVENT(PTRA))GO TO 120 CALL NPAC(CP(ICX J K)NCNP) I.XIRANO C 1. NSEG). CALL NPAC(CPCL, JK J, ),MCMP) CP(MCEQNC.GO TO 120 NwIRAND(1,4) IC(ITOGCl).EQ.l)WRITEC(6t5)N,NCNPMCMPKJ 15 FORMATCitXTRANLOCATION',7I6) GO TO C20,40, 6090).. N C EXCHANGE UPPER ARMS 20 00 30 LeI,NSEG A-54

CALL NPAC(CP(L, JK), LC LP) IF(LC.EQ.NC.AND.LP.LE NP) IC"MC IFCLC.EQOMC.AND.LP.LEMP) IC"NC IF (LC.EQ.,NC. ANLO.LP.GT.NP) IPLP"NP*MP IF (LC.EO. MC.AND.LP.GTMP) IPeLP"MP*NP CP(LoJ,K) IPACCIC, IP) 30 CONTINUE GO TO 120 C EXCHANGE LOWER ARMS 40.0. 50 L NSEG CALL NPAC(CP(CL JK),LCLP) IF(.NOT.LC.EQ.NC.AND.OP.GE.NP)GO TO 45 CP(L J,K) mIPAC (MC, LPNPMP) 45 IF(.NOT.LCEQ.MC.ANDiLP.GEMP)GO TO 50 CP(L J,K) IPAC(NCLP"MP+NP) 5e CONTINUE GO TO 120 C EXCHANGE UPPER ARM OF NC CHROMOSOME WITH LOWER ARM OF MC CHRPOMQS:' 6B MXO0 00 70 Le1,NSEG CALL NPAC(CP(LwJK),LCtLP) XF LCEQMC.ANO,LPGT.MX) MXLP 70 CONTINUE 00 80 L1, NSEG CALL NPAC(CP(L J K),I C, LP) IF(.NOT.LCEQ.NC.ANDOLP,LEeNP)GO TO 75 CP(L, J K) IPAC(MCNP*MPwLP) t IFP(LC EQNC AND.LPGTNP)CP(LJ~K).IX1PAC(LCLP-NP+MX"MPe ) IFP(NOT.LC.EQ.MC.ANO LP',GEMP)GO TO 80 CP(L JK) IPACCNCMXwLP*l) 80 CONTINUE GO TO 120 C IXCHANGE LOWER ARM OF NC CHROMOSOME wITH UPPER ARM OF MC CHROMOSC4 g9 NXJ0 00 100 LlINSEG CALL NPAC(CP(L JK),LCLP) F C(LC.EQ.NC. AND.LPGTNX)NXwLP 108 CONTINUE 00 110 Le1,NSEG CALL NPAC(CP(LJK),LC, LP IF(.NOT.LC.EQ.NCANDOLP.GE.NP)GO TO 105 CP(L JiK) wIPACCMCNX.LP*) 10S IXF(.NOTa.LCEQeMCANO,,LPLLE MP)GO TO 106 CP(LJK) IlPAC(NCMP+NP.LP) 106 IF LC.EO.MC.ANOLP.SGTMP) CPL JK< )IPACCLCLP-MP*NX-NPIl) 1 1 CONTINUE 120 CONTINUE RETURN END A-55

C PZ.Y0O VI SUBROUTINE FZYGO(CP,,NSEGPCROSPCROL) INTEGER CP(256,2,3), (256,2,3),H(32,4).p F 2), LP (256,RP (256) LOGICAL EVENT OATA ftl),P(2)/2,l/ C ZERO ZYGOTE ARRAY 00 10 Jl,12 00 10 LaINSEG CP(LvJ,3)3 10 SLJ,3)5"~ C GENERATE GAMETE FROM EACH PARENT DO 120 Kl.,2 C ZERO DATA ARRAy 00 20 J.1,4 00 20 I"1.32 2a HZIJ),0 C UNPACK DATA AT LOCI IN BOTH GENOME9 AND IXLL ARRAY H NSCw0 00 40 IwINSEG CALL NPAC(CP(I, 1K), ICl, IPl) CALL NPAC(CP(I 2,K),XC2 IP2) PrC(XICl l).EQ.OOR.HCIC1 l.),EG.2)H(ICt, tl)H(Cl, )*1 IP CH(C2, 1).EOQeOR.H(IC2 ),EO.)nH(IC2, l) wH(C2, )*2.F(IPl.GT.H(ICl2,)2()HCl,2)QIPl F (IP2*GT.H(CC2,3) ) HtC2,3) IP2 iF(ICtEQ.IC2)GO TO 40 iP(H(CIC14)*EQ.oAND.H(IC2,4)EQO0g)GO TO 30 XF(H(ClCp4) EO0oe.ANDH(IC2C4). NEoa)H(ICl,4) HeC2~w4) F(CHCXCI l4). NE.0,ANDeMCIC2,4).EO0) H(IC2,4) HCICl,4) XFP(HIC1,4),EQoH(IC2,4))CO TO 40 00 25 Jw.I32 P (JmNEIC2.ANDOHCJ,4),EQI.MC2,4 )HCJ4) H(lClt,4) 25 CONTINUE H(CC2,4).H(IZCI4) 0 TO 40 30 NSCwNSC+l M( Cl,4)NSC HCZC2,4)s NSC 40 CONTINUE C AS3IGN SOURCE GENOMES TO EACH CHROMOSOME I IN H(I,1) 00 50 wt1,32 IP(H(tX,).EQ.e)GO TO 50 IP(CHCI, ) EQ,3)H(I, ) IRANDC,2) 00 45 JwI,32 tZ(H(J,l1).EQ*O ORH(J,4).EQO)GO TO 45 IF (H(J,4.EQH (I 4) )H(Jl) n W(I, ) 45 CONTINUE 50 CONTINUE C SEGREGATION WITH CROSSOVER INHIBITED BY INVERSION AND C TRANSLOCATION DO 120 ri",32 XP(H(I,Z1).EQ.0)GO TO 120 JH(CI,l) A-56

JHwF (J) C ARRANGE LOCI ON SOURCE CHROMOSOME BY POSITION 00 60 LCINSEG CALL NPAC(CP(LIJ,K),LC M) IF(LC.NEI)GO TO 60 LP (M) L 68 CONTINUE C IDENTIFY SECTION OF SOURCE CHROMOSOME $YNAPSED WITH ANOTHER C CHROMOSOME Nl1l N2,H(,IJ*1) 70 LIlLP(Nl) DO 80 NiNiN2 LNSLP(N) CALL NPACCCP(LN.JH,K),LINCLNP) CALL NPAC(CP(LI.JHK),LICLIP) IF(LNC.NEL1C) GO TO 90 RP(N) IABS(LNP"L2P+NI) 60 CONTINUE 90. NFNI1 C SELECT GAMETE SEGMENTS FROM PARENTAL CHROMOSOMES WITH PCROS C PROBABILITY OF FUNCTIONAL CROSSOVER SETWEEN SEGMENTS JCeJ 00 110 NwNINF IF CEVENT(PCRS0) ) JCmF CJC) IF(RP(N),NE.N)JCaJ IF(N,GT,.NIANDRP(N1),NE*.N.)JCSJ 100 L LP (N) CP(L K, 3) CP(LJK) JCHsF (JC) Mm0 JCC1l 00 105 KKmI.16 IF CEVENT CPCROL) ) JCCPF CJCC*+ 1) 105 MPM*2*JCC CALL CWSCS(LwJCK),S(LIJCHtK),M,S(LK,3)) 110 CONTINUE IF(NFEQ,N2)GO TO 120 Ni iNF* GO TO 70 120 CONTINUE RETURN END /CWS VI /SUBROUTINE CWS(SJCSJCHMSK3),TITLE CWS *GLOBL ODA.CWS CWS 0 JMS.DA A-57

JMP.*5 SJC DOSA a SJCM,DSA 0 M,OSA 0 SK3,OSA. 0 LAC* M CMA O.AC MBAR LAC* SJC ANO* M OAC TEMP LAC* S.JCH AND MBAR TAO TEMP OAC* 8K3 JMP* CwS MBAR 0 T~HP 0. *END C MUTAT VI SUBROUTINE MUTAT(S, N$E6,PMUT INTEGER 8(256,2,35 LOGICAL EVENT F (PMUT.EQE..) RETURN DO 20 Jml,2 00 20 L1,NSEG M0O 00 10 Kul,17 -F(.NOTEVENT(PMUT))QO TO 10 MM*2*(K* ) t CONTINUE IF(M.GTo.0CALL MUT(S(LJS3),M) 20 CONTINUE RETURN END /MUT VI /SUBROUTINE MUTC(I M.TITLE MUT *GLOBL,DAMUT MUT 0 JMS*.DA JMP.*3 I,DSA 0 M ODSA 0 LAC* I A-58

XOR* M ANO C177777 OAC* I JMP* MUT *END C V2AB VI LOGICAL FUNCTION VIA(S,5NSEG) INTEGER 8(2S6,2,3) VIABs.TRUE. RETURN END C tIXS VI SUBROUTINE LIST(V,N,$) INTEGER S(t10) DIMENSION V(100) 00 10 ImIN 10 S(I)O! X NM1NN-1 00 20 ImlNMI 00 20 KIPI.N KSmS(K).XF(V(KS),LT.V(IS))GO TO 20 M.$CI) SCZ)S(1) 83()~S(K), (K.) PM 20 CONTINUE RETURN ENO C ASO VI SUBROUTINE ASO(V,N,AVGSTO) DIMENSION VC100) SwO 00 10 I1, N 10 S.S*VCI) AVGmS/PLOAT (N) STOm~. 00 20 IaloN 20 STODSTOD+V(I))AVG)**2 A-59

F (N*GT. l) STOSORT CSTO/FLOAT (N.l)) T (N,Eo, $sTDO0m. RETURN ENO /URN VI /SUBROUTINE URNI(XU) *TITLE URN.GL0OB. DA.OURN URN 0 JMS* DOA JMP *3 IX OSA, 0 U.DSA 0 LAC* IX SMA JMP START CMA TAD (I OAC I START LAC U TAOD ( OAC UPI LAC I CLL MUL /MULTIPLY BY 259 403 /DECIMAL 259 * OCTAL 403 ANO (77777 /MODULO 32768 OAC* IX OAC I RTL /POSZTION FOR IBI wT WORD CLQ NORM OAC* UP /DEPOSIT MANT$ISA IACS /GET STEP COUNTER TAD (.34 CMA TAO (t ANO (777 OAC* U /OEPOSIT EXPONENT JMP* URN UP ~UPI~ lIaA-60 A- 6

C XRANO VI FUNCTION IRAND(IL,'IU) OATA IX/l/ CALL URNCIXU) IRANOIL+IFTX (FLOAT (IUIL+I)*U) IF(IRANO.EQ.IU+t) IRANOmIU RETURN END C EVENT VI LOGICAL FUNCTION EVENT(PROB) QATA IX/l/ EVENTs FALSE, CALL URN(IX.U) IF(U.LT.PROB)EVENTr.TRUE, RETURN END /IPAC VI /FUNCTION IPAC(N,M) sTITLE IPAC *GLOBL,OAIPAC IPAC a JMS*,DA -JMP.3 M LAC* N TAD (-I LLS 10 AND (177400 OAC TEMP LAC* M TAO (1I AND (377 XOR TEMP JMP* IPAC TEMP a A-61

/N.PAC VI /SUBROUTINE NPAC(CP,CPP),TITLE NPAC,GLOLL.OA,NPAC NPAC a JMS* *OA JMP *+4 CP *OSA 0 C D.$A 0 P,DSA 0 LAC* CP AND (377 TAO (I OAC* P LAC* CP ItRS 10 ANO (377 TAO Ct OAC* C JMP* NPAC C OCS VI SUBROUTINE DC CNDOCPNSEG) INTEGER CP(256,2,3) WRITE(7,0) IND lOe FORMAT(IX, t NOIVIOUAtL X3) 00 60 Jl1,2 WRI(?7,20) J 2B FORMAT( IX. GENOME'1 2) Nel 25 IPMAXm0 00 30 L l,NSEG CALL NPAC(CPCLJa3),ICZP) IF(IC.NE.N)GO TO 30 CP(. P, 1,) L F (IP.GT, PMAX) IPMAXvIP 30 CONTINUE IFC(PMAX*EO.0)GO TO 60 WRITE(7,40)N 48 FORMAT(IX,'CHROMOSOME' f,3) R TE (7, 50) CP( l C, t )I, IIMAX) 50 FORMATCtX,10I4) GO TO 25 60 CONTINUE RETURN END A-62

C CA V2 SUBROUTINE CA(IGENLGENINONPOP,N8EG) INTEGER CP(256,2.3) S(256w,23) A(tl6) B(16 COMMON /CPS/CPS IF(INDOGT.1lGO TO 30 NF IX2,NPOP NFLs0 00 10 K"1,is 10 A(K)0O 00 20 K,1.NSEG 20 WRITEC(3K) (ACI)#1,X116) 30 00 50 KmINSEG CALL SA(S(K,1,3),S(K,2,3),B()) REAO(31K)A 00 40 Ilt,l6 40 ACI)A(CI)+'BI) WRITE(C3K)A 50 CONTINUE IF (INDLT.NPOP) RETURN WRITE (C7. 6) IGEN 60' FORMAT( / X GENERATIONIIX4/ X,1 EGI 24X, NUMBeR OF I ALLELES 0. 80 K31,NSEG REAOC3~K)A WRITE f7,70) K (A (w17) I 16)?0 FORMAT (lX, 33X, 614) DO 80 Jm,116 IF(A(J).EO,0. R.A J).EQ,.NIX)NFLUNFL+I 60 C ONT.INUE WRITE(7,90)NFL 90 FORMATC1X,' NFL'I4) NFLO0 RETURN ENO /8A VI /8UBROUTINE SA(S 82, ).TITLE SA.GLOLL,DASA A 0 JMS* *DA JMP.44 Si 0.A 0 82,DSA 0 8 *OSA 0 LAC 8 TAO (-t OAC POINT LAC* S1 XOR* 82 OAC ONE A-63

LAC* SI AND* S2 QAC TWO 6AC (=20 OAC CNT DO0 ZZ POINT LAC TWO ANO (C CLL RAL OAC TEMP LAC ONE ANQ (tC XOR TEMP OAC* POINT LAC ONE RAR QAC ONE LAC TWO RAR DAC TWO ISZ CNT JMP 00 JMP* SA POINT a CNT 0 TEMP 0 ONE a ~END A-64

Linked Subroutines: SGA1,PGA1;SGA2,PGA2;SGA3,PGA3;SGA4,PGA4;SGA5,PGA5;SGA6,PGA6; SGA7,PGA7;SGA8,PGA8;SGA9,PGA9;SGA1O,PGA10;SGA1.,PGA1l; SGA12,PGA12;SGA2A,PGA2A;SGA5A,PGA5A;SGA8A,PGA8A; SGAllA,P'(GA L;A; MERR:PDFSV:V1,V2,V3,V4,V5,V6 C SGA1 VI SUBROUTINE SGAI(NSEG,$wNPARX) INTEGER S(256,2,3),X(256)eW(4) OATA W/2lt120,1920/ L,0 N9Q O0 2Q jol4NPAR 00 10 J0l,4 CALL PGA1C S (L I 3) S (L,2, 3),M) PF(JEO. 1) MM*15/32 F(J*.EQ.)MM* 15/2 IS NoN*M*W(J) 320 X(I ) ON RETURN END /POQA VI /SUBROUTINE PGA(CS1,S2,M),GLOBL,DAPGAI PGAI 0 JMS*,DA JMP.+4 1,OS.A 0 2,DSA 0 M *09A 0 LAC (-20 OAC CNT OZM N LAC* S1 XOR* S2 OAC A #1 ANO (I TAO N OAC N LAC A RAR OAC A ISZ CNT JMP Wt LAC c(20 OAC CNT A-65

I.AC* S8 ANO* 82 CLL RAL. OAC A W2 ANO (2 TAO N OAC N LAC A RAR OAC A lSZ CNT JMP W2 LAC N OAC* M JMP* PGAI CNT 0 C..N.T. A.O N a0 A 0 O.EN C SGAv VI SUBROUTINE SGA2(NSEG,SNPARX) INTEGER S(256,2,3),X(256) 00 10 LxI,NPAR CALL PGA2(SCLl 3),S(L,2~3) X(L)) 10 CONTINUE RETURN END /PGA2 VI /SUBROUTINE PGA2($ S2, M).GLOBL. *DA,PGAP 2 0 JMS* *OA JMP,+4 S1.SA 0 82 8SA 0 M,DSA 0 LAC* Sl XOR* S2 CLL RAR OAC TEMP LAC* Sl AND* S2 A-66

TAO TEMP AND (177777 OAC* M JMP* PGA? TEMP 0.END C SGA3 VI SUBROUTINE SGA3(NSEG6SNPARX) INTEGER S(256,2, 3),XC256) 0O 10 L"INPAR CALL PGA3 C$ (L.,3), S (L, 23), x (L) 10 CONTINUE RETURN END /PGA3 VI /$UBROUTZNE PGA3(S1,S2,M) -GLOBL.OAPGA3 PGA3 0 JMS*.DA JMP,4 S1 *OSA 0 $2 D$OA A M *DSA 0 LAC* S1 XOR* S2 9AC HET LAC* S AND* S2 XOR HET AND (177777 JMS CONV OAC TEMP LAC* St ANO* S2 JMS CONV TAO TEMP RAR ANO (177777 DAC* M JMP, PGA3 HET 8 TEMP 0 /SUBROUTINE TO CONVERT ACC PROM GRAY TO BINARY CODE CONV 0 A-67

OAC N /SAVE ACC LAC (-20 /SET COUNTER OAC CNT OZM A LAC N /RESTORE ACC RTI ROT.A RAI /ROTATE BITS LEFT INTO POSITION OAC N /SAVE ACC ANO (t XOR A DAC A tAC N /RESTORE ACC ANO (777776 /CLEAR LS8 XOR A I8Z CNT JMP ROTA CLL ANO (177777 JMP* CONV N 0 CNT 0 A 0.END C SGA4 VI SUBROUTINE SGA4(NSEGw9SNPAR X) INTEGER S(256,2,3) X(256) W(4) ATA W/l l,.20,1. 92 / L*0.00 20 l:,NPAR Ns0 00 10 Jml,4 CALL PGA4 (S (L 1, S (L 2. ), M) IFCJEQ. ) MwM*15/32 F (J.EQ.2)M M*t5/2 10 NN*M*,W(J) N,N. 1 6384 F (NLT B) NwN I.(N. CN GT. 32.7.67). N65535SN 20 XCIX)N*2 RETURN KNO A-68

/PGA4 VI /SUBROUTINE PGA4(S1,S2,M),GLOBL.DAPGA4 PGA4 0 JMS* *DA JMP 4.+4 Si.OSA 0 S2 aDSA 0 M DOSA 0 LAC (20. OAC CNT OZM N LAC* St XOR* S2 OAC A WI ANO t( TAO N OAC N LAC A aAR OAC A ISZ CNT JMP WI LAC (:20 OAC CNT LAC* St -NQ* S2 CLL RAL OAC A W2 ANO (2 TAO N.AC N LAC A RAR OAC A ISZ CNT JMP W2 LAC N OAC* M JMP* PGA4 CNT 0 N 0 A 0.END A-69

C SGA5 VI SUBRU'.JTINE SGA(NSEG,S, NPARX) INTEGER S(256,2,3),X(2S6) 00 10 Lsl,NPAR CALL PGA5(S(L, 1,b),S(L2,3), N) NmN-16384 IF(N.LT.0) NuN IF (N.GT,32767) Nmb553wN 10 X (L) mN*? RE URN ENU /PGA5 VI /SUBROUTINE PGA5(S1,S2,M).GLnBL 9DA,PGA5 PGA5 ) JMS* *DA JMP.+4 $1,OSA M2.OSA 0,M,OSA 0 LAC* S1 XOR* S2 CLL RAR DAC TEMP LAC* S1 ANO* S2 TAO TEMP AND (177777 OAC* M JMP* PGA5 TEMP a,END C SGAS VI SUBROUTINE SGA6CN$EG, NPAR X) INTEGER (256,2, 3),X(256) D0 10 LItwNPAR CALL PGA6(S(L, 13),w(L,2,3.,N) NNwt96384 F (N.LT0) NrwN Fr (N.GT. 32787) Nsd65535N 10 X(L),N*2 ~RETURN ENO A-70

/PGAG VI /$UBROUTINE PGA6(S1.S2,M), LOL.DAPGAG PGAl 0 JMS*,DA JMP.*4 S1.DSA ( S2.DSA 0 M *DSA 0 IAC* Si XOR* 82 OAC HET IAC* S1 ANO* 52 XOR HET ANO (177777 JMS CONV DAC TEMP LAC* Sl ANDO 82 JMS CONV TAO TEMP RAR ANO (177777 OAC* M JMP* PGA6 HET 0 TEMP 0 /SUBROUTINE TO CONVERT ACC FROM GRAY TO BINARY CODE SONY 0 OAC N /SAVE ACC LAC (-21 /SET CQUNTER OAC CNT OZM A LAC N /RESTORE ACC RTL RAL ROTA RAL /ROTATE BITS LEFT INTO POSITION OAC N /SAVE ACC AND (C XOR A DAC A,LAC N /RESTORE ACC AND (777776 /CLEAR LSB XOR A ISZ CNT JMP ROTA CLL AND ( 177777 JMP* CONV N 0 CNT 0 A 0,END A-71

C $GA7 V SUBROUTINE SGA7(NSEG,S NPARX) INTEGER S (256, 23), X (256, W4) OATA, /1, l20,.92a/, X/1/ Le-! La. I 00 20!t1,NPAR No0 00 10 Jwi,4 LPL#2 LD sLv CALL URNC(XU) CALL PGA7CS(CL,, i,S3), (L,23),C(L0,,3) 8(LO,2#3) ZXM) IF(CJ,EOQ,) MM*l5/32 Ir(J.eo.2 ) M.M*18/2 10 NIN*M*W(J) a0 X (15N RETURN END /PGA7 V /SUBROUTINE PGA7(SI.S2,Sl1,DS2D0IX, M) GLOdL *DAPGA7.GA.. JMP,.7 31 DOSA 0 32,DSA 0 310 *9DA 0 IX,OSA 0 I. D DSA 0 M DOSA 0 LAC C(20 DAC CNT OZM N AND* S2 OAC A LAC* 81 XOR* 82 OAC B.LAC* Si1 0 ANDO S20 DAC C LAC* 810 XOR* S20 AND* IX XOR C ANO B XOR A CLL A-72

RAL OAC A W2 ANO (2 TAO N OAC N LAC A RAR OAC A ZSZ CNT JMP W2 IAC N ANO (177777 OAC* M JMP* PGA7 CNT 0 N 0 A B 0 C 0 *END C SCGA Vi SIJURO!. TINE $GA (NSEG,SNPAR X) NTEGER S (25.2, 3) XC256) OATA IX/1/ 00 10 Iu1,NPAP L.L+2 LDL+ i CALL URN(IX,U) CALL PGA8(S(L, 1,3),S(L, 23) S(LD, 1,3),S(LD,2,3),IXM) 10 X(I),M RETURN ENO /PGA8 VI /SUBROUTINE Pr,A SCSl,S2, S S20,IX, M) *GL0tL,DA,PGA$ PGA8 0 JMS* *OA JMP.+7 S1,DSA 0 S2,DSA 0 S10,DSA S20,DSA ~, IX,OSA F, A-73

M *DSA LAC* St AND* S2 OAC A LAC* St XOR* 82 OAC LAC* S$O AND* $20 OAC C LAC* S D XOR* $20 ANID* X XOR C AND B XOR A ANU (177777 OAC* M JM p PGAg A 0 C *END C SGA9 VI SUBROUTI NE GA9 (NSEG SNPAR X ) INTEGER S(256,2,3)wX(t5a6 DATA IX/l/ L3 I 00 10 ISl.NPAR L._L2 LD OLv I CALL URN(CX,U) CALL PGA9gCSL, 1.3).S(L,2,3).S3LD, 1.3),(LaO2,3), xXM) 10 X(I)UM RETURN ENO /PGA9 VI /SUBROUTINE PGA9 CS1,82,S10,S20,IX,M) *GLOB4L *ODAPGAi PGA9 0 JMS* *DA JMP,*7 S1 *OSA 0 S2.DSA 0 St.DSA 0 A-74

S20.OSA 0 IX DOSA 0 M.OSA 0 LAC. S AND* S2 DAC AA LAC* SI XOR* S2 OAC B LAC* SiD ANOD $20 OAC C LAC. S$D XOR* S2D AND I X XOR C AND B XOR AA JMS CONY AND (177777 DAC* M JMP* PGA9 iA 0 B 0 e a /SUBROUTINE TO CONVERT ACC FROM GRAY TO BINARY CODE CONV 0 OAC N /SAVE ACC LAC (-20 /SET COUNTER OAC CNT OZM A LAC N /RESTORE ACC RAL ROTA RAL /ROTATE BITS LEFT INTO POSITION DAC N /SAVE ACC AND (1 XOR A DAC A IAC N /RESTORE ACC AND (7777776 /CLEAR LSB XOR A ISZ CNT JMP ROTA CLL AND (177777 JMP* CONV N 0 CNT 0 A 0.END A-75

C SGtA1 VI SUBROUTINE SGA1 t(NSEG, S,NPAR, X) INTEGER S(256,2,3),X(256),W(4) A. TA W/, 1 120, 219210/ ]fX/l/ L"-l 00 20 II1,NPAR Nw0 00 10 J1,4 LuL*2 LDIL+l CAILL URN(IXU) CALL PGAI0(.C(L, 1) tS(L,2,3) s(LO,,3)w$(CLD,2,3:), X,M) XF(JEQ. 1 M.M*15/32 F(JEQ.2) MsM*15/2 t1 N'N*M*W(J) NPNwj6994 XF N. LT.03 NwN IF (NGT.32767) N655358N 20 X (I)N*2 RETURN INO /PGA10 VI /SUBROUTINE PGA l0(el, 2, SO, 820, IX,M).GL0BL,OAPGA10 PGA1.0 0 jMS* *DA JMP.*7 SI..D8A 0 -2 *08A 0 S10.0$DSA 0 $20 0DSA 0 IX DOS 0 M *DSA 0 LAC (-20 OAC CNT OZM N LAC* St AND* S2 OAC A LAC* $1 XOR* 82 DAC B LAC* S10 ANO* S20 OAC C LAC* Si0 XOR* 820 ANO* IX XOR C ANO B A-76

XOR A CLL RAL OAC A W2 ANO (2 TAO N OAC N LAC A RAR OAC A ISZ CNT JMP W2 LAC N ANO (177777 OAC* M JMP* PGAI0 CNT a N 0 A t j 0 gEND C SGALj VI S!UtROIUT NE SGA I (NSE G,bNPA X ) iTNTFIER S(25,2,3,),X(256) LATA IX/1/ La-Il )0O 10 Xtu1NPAk LmL+2 iD"L+1 CALL U1JN(IX,U) CALL PGAtIS (Ll 1,),b(L,2,3),S(LO1,3),$CLDw2,3) IXM) M= M-1(38 4 IF CM LT.O ) M= F (M.GT. 327 67) rMO5535-r 10 X (CI) *'? REtTURK ENU /PGAll VI /SUBROUT INM' PGA 1l (SlS2, S 1 ), S20 I X, M), fLO'L DA, PGAI 1 PGA11 SO 4MS*.i)A JMP,+7 A-77

S1 *OsA P S2,OSA.~ S10 OSA' 520 DSA 0 IX *DSA M,DSA 6 LAC* Si AND* S2 OAC A LAC* S.I XOR* S2 OAC. LAC* S1 ANO* SD20 OAC C L AC* SiD XORt S20 ANO* I X iOR C AND. Ah1D B XOR A ANO (177777 OAC* M JMp* PGA 1 A 0 8 0 C ENI) C SGA12 VI SUBROUTINE SGA12(N3EGSNPARX ) INTEGER S(256,2, ),X(256) DATA IX/l/ Ll 00 10 Itl.NPAR LwL*2 CALL URN(IXU) CALL PGA12CSC(Ll3),$CL,2,3),$(LDO.I,3) SCLDO2,3!,tX,M) MlM Ie384 It C(M. LT. 0B MusM IF (M9.GT. 32767) Mm6S535wM 10 XC(I) tM*2 RETURN END A-78

/PGA12 VI /SUBROUTINE PGA12(SlS2S10,S20,IX,M).GLOBL.DAPGA12 PGA12 0 JMS*,DA JMP,* St DSA 0 82.OSA 0 S1D s.DSA 0 S20 ODSA 0 IX OSA 0 M DSA 0 LAC* Sl AND* $2 DAC AA LAC* S$ XOR* S2 DOAC B LAC* StO AND* S20 OAC C LAC* SO1 XOR* 82D ANO* ZX XOR C AND B XOR AA JMS CONY AND (: 177777 OAC* M JMP* PGA12 AA 0 a C 0 /SUBROUTINE TO CONVERT ACC PROM GRAY TO BINARY CODE C.NV 0 OAC N /SAVE ACC LAC (w20 /SET COUNTER DAC CNT OZM A LAC N /RESTORE ACC RTL RAL ROTA RAL /ROTATE BITS LEFT INTO POSITION DAC N /SAVE ACC ANDO ( XOR A OAC A LAC N /RESTORE ACC AND C777776 /CLEAR L88 XOR A ISZ CNT JMP ROTA CLL A-79

AND (177777 JMP* CONV N. CNT 0 A 0.END C SGA2 V2 SUBROUTINE SGA2(NSEGSNPARX) INTEGER S(256,2,3),XC256) 0 10 L ltNPAR CALL PGA2(S(L, lC,3),S(,2,3),M) 10 X(L)~M RETURN ENO /PGA2 V2 /SUBROUTI NE PGA2 (CS,.82, M),GLOBL.DAPGA2 PGA2 a JMS* *OA JMP,*4 3t,DSA 0 52.,D.A 0 M,DSA 0 LAC* 81 ANO (177777 OAC A ANO C(i0000 SNA JMP,*5 LAC A CMA ANO (177777 DAC A LAC* S2 AND (177777 OAC B NO t(100000 SNA JMP,*S LAC B CMA ANO (177777 OAC B LAC A TAO B A-80

OAC* M JMp* PGA2 B 0 SEND C SGA5 V2 SUBROUTINE SGA5(NSEGS NPARX) INTEGER S (256,2,3),X (25) 00 10 LtlNPAR CALL PGAS(S(L,1,3),S(CL,23),M MNMeM IF (MGE.65536) MmM-65536 10 X(L) "M RETURN ENO /PGA5 V2 /SUBROUTINE PGA5CSl.S2 M).GLOBL,OAPGA5 PGA5 0 JM*, DA JMP.+4 Sl sOSA 0 32.OSA 0 M ODSA 0 LAC* Si AND (177777 OAC A AND (1 i000 SNA JMP,+5 LAC A CMA AN. (C177777 OAC A LAC* $2 AND (177777 OAC B ANO (100000 S.lNA. SNA JMP,+S LAC B CMA ANO C 177777 OAC B A-81

LAC A TAO B OAC* M JMp* PGAS A 0 a 0.END C SGA8 V2 SUBROUTINE SGA8 NSEGSINPARX) INTEGER S(256,2,3),X(26) OATA IXX. / O0 10 ImI,NPAR LL*2 LDL* 1 CALL URN(IXiU) CALL. PG A8(I.S CL 3) (L. 2.). ILD 1 3) 8(LD, r3)! X,M) 0 XX(I)sM RETURN END /PGA8 V2 /SUBROUTINE PGASCS1, 2S1D.20, ZX, M).GLOI0L.DA PG6AS PGA8 0 JMS*.DA jMP,+ SI *o$AA S2,OSA 0 10.....A 0 820 ODSA 0 IX 0AD$AS 0 M DSA 0 LAC* 81 AND. 82.OAC A LAC* SI XOR* 82 DAC B LAC s310 LAC. S1D XOR* 520 AND* IX A-82

XOR C ANO B XOR A ANDO (177777 OAC A ANO (100000 SNA JMP.*5 LAC A CMA AND (177777 OAC A LAC A CLL. AL AND (177777 OAC* M JMP* PGA8 A 0 c,END C SGAII V2 -UBROUTINE SGA11 NSEQ, SNPAR,X) iNTEGER S(256,2, ),X256) DATA IX/t/ 00 10 I1lNPAR 1..L42 LnL*2 CALL URN(IXU) CALL PGA l CS (L, 1 3), L S(L., a23), S (L. t, 3) S (LO, 2,3) IX, M) MMs*M x (M.GE.,65S6) MM1605556 10 X(I;~M RETURN END /PGA1 V2 /SUBROUTINE PGA1l(Sl2,S2SlD,S20IX,M).GLOL,DA.PGA1l PGAtI 0 JM$S *DA JMP, *7 SI.DSA 0 A-83

82 O0DA 0 S O.,OSA S20 eDSA 0 IX DOSA 0 M. OSA 0 LA.C* S1 ANO* S2 OAC A LAC* S1 XOR* S2 DAC B LAC* SOD ANO* S2D DAC C LAC* SiD X.OR* 820 ANOD IX XOR C ANO B XOR A AND.(177777 OAC A ANDO (1000 SNA JMP, 5 LAC A CMA A.ND (177777 OAC A I4AC A CLL RAL ANO (177777 OAC* M JMP* PGAll 8 o C @ *ENO C MERR VI SUIROUJTIN MERt(LGENNRNP) DIMENSION A(7) AMAX(7),AMINC7),R(7),IR(2) O0 60 J1,LGeN 00 10 I"1,7 A(I).,* AMAX CI) I210O0. 10 AMIN(I)i 000. 00 30 I, 1NREP K.B (I-I ) LGEN + J READ(C2K,20)IGEN, CR(L),Lw, 5),IR(),IR(2.) A-84

20 FOR AT(I3,5Fl(0,32IlK) R(6) FLOAT (I (1) ) R(7) eFLOAT(I (2)) On 30 K,17 A (KI A (K) R (K) IF (R (K).GTAMAX (K)) AMAX CK) mR (K) IF(R(K) LT.AMIN K) ) AMIN(K) R(K) 30 CONTINUE tdfFLOATCNREP) 00 40 Ix.,7 40 A(I) AC() / KxNREP*LGEN+J WRITEC2l'KI5 )JA 50 FORMAT( X, I3,7F10.3) KvK+LGEN KvK+LGEN 60 WRIT (2' K,5) JAMIN *RIT (7,770) 70 FORMATC/1X, AVERAGE VALUES' 1/1X,'GEN,7X, IEFFl 7X, IAVG',7X ISTD'6X, AVCS 6X i!STOSI,7X, NIl'7X, NTR') 00 90 JmlLGEN K mNREP*LGENJ READ(2'K, ) IGEN, R 80 FORMAT(I3,7F 103) 90 WiRITE (7, 50) IGEN, IF NREP.EQ 1) RETURN WRITE 7, 1P0) 100 FORMAT(/1XlMAXIMUM VALUES' /l1X,'GEN,7X, EFF,7Xt AVG',7X, STO,6X, AVGS 6X i'STUS',7X, NIZ',7X, lNT;R) 00 110 Ju",LGEN K. (NNEP 1) *LGEN+J READ (21K, 80) IGEN, IR C) lIFIX (P (6)) I (2) FTX fR(7 )1 11 wRIT(EC7,12) IGEN, (R CK) K,5) IR C 1) IR(2) 120 FOCMAT( X, I3,5Fl1.3,2I10) wRITE(7~ 130) 130 FOR MAT(/1 X MINIML M VALUES' 1/IX,'GEN,7X,' EfFl,7Xt A XV G 7XISTO 6X, IAV$It6X, 1'STUSL,7XN tIZ,7X,' NTR') 00 140 Jl1,LGEN K (NREP+2) *LGEN+J REA (2 K,80) IGEN,R IR C( ) IFIX( (P ()) IR (2) aIFIX (R(7) 140 wRITE 7,120) IGEN, (R K(),K,5),IR,IR(2) RETURN END A-85

001 C PDFSV VI 002 SUBROUTINE PDFSV(LGEN,NVAR) B03 DIMENSION A(7)R (7),IR(2) 6.4 00 406 IfNVAR 00S WRI'TE(7,1)IX 00 1 x FORMAT X IVARIETY' I 3/1XGEN7X'EPFFI7XIAVGI7XiSTO 007 I AVG8 6X STDS t7X NIZ 7X NTR ) 008 00 40 J"1,LGEN 009 Kw CI-l)*LGENsJ 01Q REA (2 K 20) IGEN, CR L) Ll Si ) R (1) IR C2) 011 20 FORMAT (I3#5,F1a3,2I.1) 01a WRITEC(7 30)IGEN, (RC) L,S), IRC(), IRC(2 013 30 FORMAT(lXI3S5F10.3,2It0) 014 40 CONTINUE 015 RETURN.01 END C VI V2 SUBROUTINE VI(N,XV) INTEGER XC(26) 00 20 IP2,N.2 XI FLOAT (X C( 1 ) )/65535. X2mPLOAT CX (I) )/65353 20 VsV*50,*((CCl*X)+ X2) V"V/FLOAT CN/2) RETURN END C V2 VI SUBROUTINE V2CN,X,V) INTEGER X(25)6 00 20 I2, N.2 X1 tFOAT(X C( l)) /65535 X2.FL.0AT (XI)) /65535S V V1ila,10.AB8S(X2. X * 2 1i35s.2*SRT( Cl."Xl) **2+C(l.X2)**2 20 CONTINUE mVV/FLOAT N/2) RETURN END A-86

C V9 VI SUBROUTINE V3(NXV) REAL MIM2 INTEGER XC256) G(PlP2, Ml, M2 SI S2, RHO) EXP (w (82**2* (PtM)**2.2* 181*S2*RHO* (PlMl) * (P2=M2)* 1St**2* P2-M2)**2) / (2.*Sl**2*S2**2* (l.RMHO**2)) V.0. D0 20 I"2,N,2 XlPLOIAT(X (IlX))/655,35 X2wlLOATCX (I)) /655,3 V.V*60S*G,(Xt w X2,0. wSa,, 1,,~ t w,e) IttI00*G(Xl X2,75.,75., tl0. l.,.95) l+40.*G CX tX, X2,4Q. i, 10., 1.,.0) 20 CONTINUE V.V/FLOAT (N/2) RETURN END C V4 VI SUBROUTINE V4(N,X,V) REAL MI,M2 INTEGER X(256) G(pI, P2 Ml, M2, Sl82RHO) EXP( C82**2* (PlwM) **22,* i 8*S2*RHO* (P1w-M) * (P2wM2) 18t**2* CP2wM2)**2) / (2.*Sl**2S2**2* (."RHO**2 )) V.0. DO 20 I2,N,2 XvrPFLOAT(X(lt))/655,35 X2'0L.OAT X (I)) /655,3 im60.*G (Xl, X2,75, 75,, 10,, 10,,.95) 1+48.*G (X1, X2,40, 10., 1.,,l10,,.0) 20 CONTINUE V V/FFLOAT (N/2) RETURN END C VS VI SUBROUTINE VSCN,XYV REAL MlM2 INTEGER XC256) G(Pl P2 Mt,M2 S, S2,RHO) EXP("C 2*2* (PtlMl) **2,2., 1St*S2*RHO* (P1-M1) * CP2-M2)+ 1Sl**2* CP2"M2) **2) / C2..*S1**2*.82*2*. C.wRHO**2) 00 20 Im2.N.2 A-87

XlwFLOAT(X (tl))/655.35 X2tFLOAT (X (CI )/655,35 V"V*.0,*G(X1X2, r0* w 1. 1., 0 l. * l.4Be. G.XiAX.~7E.,?75.?,,0~1.e.,..,,95) Ili00.*GCXI,X2,40*., I0I,,, 16.,.0) 20 CONTINUE VV/FLOAT (N/2) RETURN END C VS V2 SUBROUTINE V6CNXV) INTEGER X(25S6 00 20 IZm,.N SIFLOAT(X (I)"327687)/32767. 2. VYVS.*S. Vi0..wlt00,*V/FLOAT (N) RETURN ENO A-88

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