Introduction to probability distributions: probability flux

Abstract

We have shown that, for the neutral theory to work, effective population sizes must be very much smaller than was supposed by most workers during the ‘pan-selectionist’ era of population genetics. For example, the mean fixation time for a neutral mutation, even in the absence of population subdivision, is 4N_e generations. While this mean is somewhat inflated by cases in which, by chance, fixation takes an exceptionally long time, it can be shown that fixation before 0.8N_e generations is very unlikely to occur (Kimura 1970a, Kimura & Ohta 1971a). Hence, if N_e were very large, very little neutral evolution would occur in the time available. (This does not contradict the notion that the rate of neutral evolution over a long time period equals the neutral mutation rate, since in this context a ‘long time period’ means a time period that is long compared with the mean fixation time; the latter must be short, on a geological timescale, for the neutral theory to account for the rate of molecular evolution.) The neutralist, therefore, must assume relatively small values of N_e.

For precept must be upon precept, precept upon precept; line upon line, line upon line; here a little, and there a little.

Isaiah 28,10