Polyallelic random drift in relation to evolution.

Abstract

The number of alleles that are maintained at a locus in a population of givenl size by a given mutation rate is important in evolutionary theory. The possible number of alleles is enormous. At a locus consisting of only 1000 nucleotide pairs, each with four alternatives, the number differing from the type gene by a single substitution is 3000 and by two substitutions, nearly 4.5 X 106. The total number from substitutions alone is 41000. The actual number present at any given time in a population of size N obviously cannot exceed 2N and may be expected to be very much less. It is instructive to determine the steady-state distribution of frequencies of alleles under the simplifying assumption that all alleles, except perhaps one or more specified ones, have the same properties. The number of such similar alleles present at any time is the reciprocal of the mean frequency, multiplied by the portion of the total frequency which they constitute. The composition of this array is continually changing with turnover 2Nu where u is the mutation rate. The first attempt at such estimates was for the case of self-incompatibility alleles (Wright') in which it was known that rather large numbers actually occur in very small isolated populations.2 Because of the peculiar mode of selection-inhibition of any pollen grain that carries the same allele as either of those in the cells of the style-any novel mutation is subject to maximum favorable selection. There is an equilibrium frequency toward which gene frequency tends to move from either direction. Unfortunately this equilibrium frequency is not constant. It shifts especially with changes in the number of alleles. It was recognized that only an approximate solution could be obtained. Approximate relations between number of alleles (n), effective size of population (N), and rate of mutation from any allele (u) were presented which seemed adequate for most biological purposes. Discussion of the subject3'7 has introduced rather more confusion than clarification, but some improvement of the formulas has emerged, and more is probably possible. The present paper will deal with simpler cases.