Natural taxonomic categories of angiosperms obey Benford's law, but artificial ones do not

Abstract

Benford's phenomenological law gives the expected frequencies of the first significant digit (i.e., the leftmost non-zero digit) of any given series of numbers. According to this law, the frequency of 1 is higher than that of 2; this in turn appears more often than 3, and so on decreasing until 9. Similarly, Benford's law can also be applied to the first two significant digits (i.e., from 10 to 99), and so on. We applied Benford's law to sets of taxonomic data sets consisting of the number of taxa included in taxa of higher rank. We chose the angiosperms (Magnoliophyta) as a model case, because they are very diverse, are monophyletic, and a consensus on taxonomy of orders and families has been achieved (classification APG III), and we used as sets of data the number of species, genera, families, and orders. Only the number of species per family and per order are Benford's sets, but the remaining data sets do not obey Benford. Furthermore, in the case of the analysis of the first two significant digits of species per genus, the deviation from Benford was very large, but they fit to a power law. Given that the conformity to Benford's law is fulfilled for ‘natural' taxonomic categories of angiosperms (i.e., species and family), but not for those with more artificiality (genus), we speculate, ‘the more natural, the more Benford'.