The fractal dimension of taxonomic systems

Abstract

The hypothesis that biological diversity has a fractal geometry is tested through the examination of size-frequency distributions of taxa with different numbers of subtaxa. Data used derive from 44 checklists and catalogues of species concerning protists, fungi, plants and animals, and from three synoptic classifications of protists, plants and animals. Distributions give hyperbolic curves whose log-log plots are almost linear, with negative slopes. Long tails of distribution curves due to very large taxa call for skew variants of hyperbolic curves. The positive values of log-log regression line slopes correspond to the fractal dimensions D nof the taxonomic assemblages, characterizing their diversity. Non-random occurrence ofn D nvalues among groups suggests a relationship with true biologic diversity patterns, rather than an effect of taxonomic criteria. Differences in fractal dimension among the examined lists are discussed, the more relevant being the higher differentiation of marine groups with respect to continental ones. The fractal geometry of diversity is viewed as an evolutionary pattern possibly related to scaling evolutionary processes, suggested by the finding of hyperbolic trends at different taxonomic levels.