A Simple Explanation for Taxon Abundance Patterns

Abstract

For taxonomic levels higher than species, the abundance distributions of number of subtaxa per taxon tend to approximate power laws, but often show strong deviationns from such a law. Previously, these deviations were attributed to finite-time effects in a continuous time branching process at the generic level. Instead, we describe here a simple discrete branching process which generates the observed distributions and find that the distribution's deviation from power-law form is not caused by disequilibration, but rather that it is time-independent and determined by the evolutionary properties of the taxa of interest. Our model predicts-with no free parameters-the rank-frequency distribution of number of families in fossil marine animal orders obtained from the fossil record. We find that near power-law distributions are statistically almost inevitable for taxa higher than species. The branching model also sheds light on species abundance patterns, as well as on links between evolutionary processes, self-organized criticality and fractals.