OLM11.5 Species-abundance distribution under neutral dynamics

In a finite population of neutral variants without new ones occurring, drift eventually clears away all but a single variant (Ch11.2, p.240). However, if new variants can pop up from time to time, then an equilibrium number and distribution of variants may ensue (Ch 11.3, p.246). This OLM demonstrates that, assuming a high number of completely neutral variants, abundance of the variants follow Fisher’s log-series distribution. It should be noted here, however, that Fisher did not propose this distribution for modelling abundance distributions (Fisher et al. 1943) on the basis of some principle, but for technical reasons (OLM 11.6). The postulates of the model (a high number of absolutely neutral variants) can be approximately true for alleles, but not for species (Note 7.1, p.141), so the occurrence of new variants will be termed “mutations” hereafter.


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