http://hdl.handle.net/2027.42/49534 Wed, 22 May 2013 20:07:49 GMT 2013-05-22T20:07:49Z http://deepblue.lib.umich.edu:80/bitstream/id/184747/ummz_logo.jpg http://hdl.handle.net/2027.42/49534 http://hdl.handle.net/2027.42/94109 Fourier shape analysis and fuzzy measure shape group differentiation of Great Lakes Asterionella Hassall (Heterokontophyta, Bacillariophyceae) Pappas, Janice; Stoermer, Eugene Species separation of character-poor Asterionella, an abundant Great Lakes diatom, is difficult to accomplish by visual inspection alone. Diatom shape is an inherited property which is measurable. Quantifiable variation is mostly the result of genetic influences, while qualitative changes in valve morphology are mostly the result of environmental influences. Asterionella valve shape and shape group separation was studied using principal components analysis (PCA) and fuzzy measure theory. To quantify shape, Fourier coefficients were calculated from arc lengths and tangent angles around the periphery of the valve outline. Polar Fourier coefficients resulted from an orthogonal polynomial N regression of Phi*(t) = a sub 0 + sum from n to N of A sub n times cos(nt +a sub n), where a sub 0 is the zero'th Fourier coefficient, A sub n is the nth amplitude, and a sub n is the n'th phase angle. One-hundred x,y coordinates were used to calculate 22 shape coefficients to get a best fit closed curve in a least squares sense. Standardized PCA of mean-corrected, square root transformed amplitudes produced seven Asterionella shape groups. Classification integration and fuzzy measures were used to determine degree of shape group overlap and degree that specimens belonged to an assigned shape group. Fuzzy measures were based on morphometry of head pole, foot pole, and mid-valve widths or a combination and scaled and ordered on the interval [0,1). Sugeno's or the fuzzy integral, E= fuzzy integral of h(x)o g(•),where E is the evaluation of h(x) (partial evidence) and g(•) (importance or possibility measure), was used. Partial evidence was fuzzy average overlap. Degree of shape group membership was evaluated as degree of certainty (partial evidence) and Sugeno's measure (importance measure). Complete overlap or specimen inclusion was equal to one, complete lack of overlap or specimen exclusion was equal to zero, and the crossover point was 0.5. Two exceptions, shape groups II-III and shape groups IV-V atE= 0.6 exhibited overlap. Two specimen assignments were slightly questionable at E= 0.49 and E = 0.57 for shape groups II and VI, respectively. All other specimen assignments were E > or = 0.6. Overall, shape group differences were evident and may indicate different species of Asterionella Hassal. · Mon, 01 Jan 2001 00:00:00 GMT http://hdl.handle.net/2027.42/94109 2001-01-01T00:00:00Z http://hdl.handle.net/2027.42/94108 Asterionella Hassall (Heterokontophyta, Bacillariophyceae) Taxonomic history and quantitative methods as an aid to valve shape diffrentiation Pappas, Janice; Stoermer, Eugene The taxonomic history of the diatom genus Asterionella is sketchy at best. At present, delimitation of the genus, and species within it, are unclear. This is presented in a compilation of the taxonomy of Asterionella. In regard to species determination, valve shape variation is important. With the proliferation of splitting diatom taxa at the species level, the need for revision of Asterionella is apparent. We have provided some initial results concerning application of quantitative methods to valve shape variation in Asterionella. Seven shape variants may be present in the Great Lakes. Sat, 01 Dec 2001 00:00:00 GMT http://hdl.handle.net/2027.42/94108 2001-12-01T00:00:00Z http://hdl.handle.net/2027.42/93636 A new approach to problems in taxonomy and ecology Stoermer, Eugene; Pappas, Janice Diatom systematics and ecology, two of Frank Round's major research interests, contain much uncertainty. This derives from several sources. The taxonomic diversity of diatoms appears to be much greater than previously thought. Recognition of this diversity has led to realization that popula-tion-based ecological studies, although perhaps made more difficult by increased taxonomic resolution, will also likely become even more powerful. There have been significant advances in objective "quantitative" tools useful in understanding diatom taxonomy and parallel advances in tools that allow us to reduce and analyse large, complex, data sets. However, at least partly due to the limited number of in-vestigators involved in research on diatom taxonomy and ecology, these new sources of information have proven difficult to systematize into new and improved understanding. This has served, in some instances, to sharpen the inherent conflict between ecologists, who need a stable taxonomic framework and taxonomists most interested in exploring and explaining biodiversity, biogeography, and their underlying systematic relationships. We suggest application of methods from the rapidly advancing field of fuzzy logic to diatom studies. These methods allow explicit recognition of uncertainties and systematized incorporation of qualitative information and verbal descriptions into analysis of taxonomic and ecological problems. Original research Thu, 01 Jun 2006 00:00:00 GMT http://hdl.handle.net/2027.42/93636 2006-06-01T00:00:00Z http://hdl.handle.net/2027.42/85394 QUANTIFYING AND ANALYZING SURFACE FEATURES IN FOSSILS USING 3D DATA Miller, Daniel and Pappas, Janice QUANTIFYING AND ANALYZING SURFACE FEATURES IN FOSSILS USING 3D DATA MILLER, Daniel J. and PAPPAS, Janice L., University of Michigan Museum of Paleontology, The University of Michigan, 1109 Geddes Ave, Ann Arbor, MI 48109-1079, djmill@umich.edu Characterizing the surface features of organisms can be useful for addressing a wide range of questions in paleontology and neontology. The ability to do so in a quantitative and explicit way permits analysis both within and across data sets. In this study, we use digital close-range photogrammetry to extract 3D coordinates that are then used to characterize surfaces. We use standard statistical parameters used in metrology, such as general surface roughness (average), degree of surface roughness (root mean square), preponderance of either peaks or valleys present on the surface (skewness), and degree of peakedness (kurtosis), as well as direction of change in surface roughness (root mean square slope). All of these parameters incorporate height and spacing information about the peaks on the surfaces of specimens. In addition, we also explore the potential application of spatial series analyses to characterize surfaces where spatial series take the form of sequential changes in surface features of a specimen. All calculations can be performed at different scales and on single or multiple patches from each specimen’s surface. Degree of continuity between patches or matching patches on a specimen surface is another potential way to quantitatively characterize surface features. We characterize the surfaces of a variety of fossil invertebrates from different phyla and demonstrate the use of these metrics in quantitatively comparing surfaces in different specimens regardless of their taxonomic position. Surface statistics are also used to explore features and patterns at a variety of spatial and size scales. Although these metrics are statistical summaries of surface features, they nevertheless provide a more precise quantitative means of comparing widely disparate morphologies when compared to qualitative approaches. The use of explicit and easily compared surface statistics potentially facilitates the exploration of a wide variety of hypotheses pertaining to biomechanics, development, biogeography, systematics, and taphonomy. 2010 GSA Denver Annual Meeting (31 October –3 November 2010) Geological Society of America Abstracts with Programs, Vol. 42, No. 5, p. 140 Published abstract with citation. Sun, 31 Oct 2010 00:00:00 GMT http://hdl.handle.net/2027.42/85394 2010-10-31T00:00:00Z