MAINTENANCE OF GENETIC VARIABILITY UNDER THE PRESSURE OF NEUTRAL AND DELETERIOUS MUTATIONS IN A FINITE POPULATION

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Abstract
In order to assess the effect of deleterious mutations on various measures of genic variation, approximate formulas have been developed for the frequency spectrum, the mean number of alleles in a sample, and the mean homozy-gosity; in some particular cases, exact formulas have been obtained. The assumptions made are that two classes of mutations exist, neutral and deleterious, and that selection is strong enough to keep deleterious alleles in low frequencies, the mode of selection being either genic or recessive. The main findings are: (1) If the expected value () of the sum of the frequencies of deleterious alleles is about 10% or less, then the presence of deleterious alleles causes only a minor reduction in the mean number of neutral alleles ir, a sample, as compared to the case of = 0. Also, the low- and intermediate-frequency parts of the frequency spectrum of neutral alleles are little affected by the presence of deleterious alleles, though the high-frequency part may be changed drastically. (2) The contribution of deleterious mutations to the expected total number of alleles in a sample can be quite large even if is only 1 or 2%. (3) The mean homozygosity is roughly equal to (1-2)/(1+λ 1), where λ 1, is twice the number of new neutral mutations occurring in each generation in the total population. Thus, deleterious mutations increase the mean heterozygosity by about 2/ (1 +λ 1). The present results have been applied to study the controversial problem of how deleterious mutations may affect the testing of the neutral mutation hypothesis.