MAINTENANCE OF GENETIC VARIABILITY UNDER THE JOINT EFFECT OF MUTATION, SELECTION AND RANDOM DRIFT

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Abstract
Formulae are developed for the distribution of allele frequencies (the frequency spectrum), the mean number of alleles in a sample, and the mean and variance of heterozygosity under mutation pressure and under either genic or recessive selection. Numerical computations are carried out by using these formulae and Watterson's (1977) formula for the distribution of allele frequencies under overdominant selection. The following properties are observed: (1) The effect of selection on the distribution of allele frequencies is slight when 4Ns ≤ 4, but becomes strong when 4Ns becomes larger than 10, where N denotes the effective size and s the selective difference between alleles. Genic selection and recessive selection tend to force the distribution to be U-shaped, whereas overdominant selection has the opposite tendency. (2) The mean total number of alleles in a sample is much more strongly affected by selection than the mean number of rare alleles in a sample. (3) Even slight heterozygote advantage, as small as 10-5, increases considerably the mean heterozygosity of a population, as compared to the case of neutral mutations. On the other hand, even slight genic or recessive selection causes a great reduction in heterozygosity when population size is large. (4) As a test statistic, the variance of heterozygosity can be used to detect the presence of selection, though it is not efficient when the selection intensity is very weak, say when 4Ns is around 4 or less. A model, which is somewhat similar to Ohta's (1976) model of slightly deleterious mutations, has been proposed to explain the following general patterns of genic variation: (i) There seems to be an upper limit for the observed average heterozygosities. (ii) The distribution of allele frequencies is U-shaped for every species surveyed. (iii) Most of the species surveyed tend to have an excess of rare alleles as compared with that expected under the neutral mutation hypothesis.