Dimensions of Sedimentary Lithotopes and Taxonomies of Fishes

Abstract

The size of subgroups among larger taxonomic units, as measured by the number of taxa within them, is a metric of fundamental importance to the appreciation of causes of change in biodiversity in both time and space. Central to such evaluations is an understanding of the expected and observed variation in the numbers and sizes of groups comprising various taxonomic levels. Here we show that numbers of fish taxa within subdivisions (memberships) of any supertaxon in a Linnaean taxonomy are virtually identical to areas of patches of like sediment (lithotopes) that are distributed across various depositional surfaces. Both sedimentary surfaces and Linnaean taxonomies are closely approximated by functions that generally describe random divisions of geographic and/or shape-space. We describe a ‘broken plate’ model for taxonomic membership that is akin to Robert MacArthur’s (1957) classical ‘broken stick’ model for abundance distributions, where species abundances in an ecosystem are described by an exponential function of abundance (segment length) frequencies reflecting the random subdivision of resources. In a taxonomic context, the broken plate presumes that the amount of morphospace realized at any taxonomic level is proportional to the numbers of subtaxa of which it is comprised. A hypothetical transect across the morphospace associated with any higher taxon would comprise a ‘broken stick’, or exponential, distribution of square roots of the number of contained subtaxa. Taxonomic membership (occupied morphospace) within the higher taxon is therefore randomly partitioned among subtaxa, analogous to the sizes of fragments of the broken plate. Thus, just as the broken stick distribution is well-described using only the length of the stick and the number of segments into which it is broken, the partitioning of taxa into subtaxa within any supertaxon is random and adequately described using only the number of taxa and the number of subtaxa into which they are partitioned.

Such ‘broken plate’ functions yield excellent agreement for membership partitioning among classes, orders, families, and genera of fishes. Quantification across all taxonomic levels provides several insights related to the biodiversity of this important group: (1) Membership of taxonomic groups of fishes is self-similar among all levels of Linnaean division (e.g., families per order, genera per family, species per genus) and is almost entirely independent of levels of taxonomic separation between groups being considered, with an average of seven to eight members within any taxonomic group. (2) The ‘broken plate’ representation implies that divisions within one taxonomic level are independent of all other divisions; a similar partitioning of species among genera belonging to both diverse and depauperate families supports the supposition that little ‘memory’ exists between levels of taxonomic membership. (3) Special explanations for the generation of apparently extreme polytype may be largely unnecessary; taxonomic diversities expected from the ‘broken plate’ model suggest that observed disparity in numbers of fish species comprising many clades is no greater or less than one would expect from a random fragmentation of morphospace.