The evolution of selective advantage in a deleterious mutation.

ISHER (1928) put forward a theory of dominance that is still the subject of Fcontroversy. If a deleterious mutation is continually occurring, it will appear mainly as a heterozygote. FISHER suggested that the fittest of these heterozygotes would be selected and ultimately become as fit as the wild type. The wild type would then be dominant to the deleterious mutation. The fitness of the heterozygote must therefore be subject to genetic variations which are selected for their effects as modifiers. This idea has been criticised because the selection of single genes modifying the expression of the mutant heterozygote is very slow (WRIGHT 1929a, b; CROSBY 1963; EWENS 1965, 1966). But as SHEPPARD and FORD (1966) point out, a very great deal of time may have been available for this selection. They suggest that several recessive mutations may have a very long history-for example chat albinism may have a longer history than man and have been occurring for millions of generations. Even so 'we should really be thinking not of the selection of single modifiers, but of selection acting on a genetic variance in the fitness of the mutant heterozygote. This problem has been formulated by D DONALD (1967) in a very simple way. Consider MENDEL'S tall and short peas. Both phenotypes have very different means; but no doubt there is variation within each phenotype around its mean and if the population consisted of only one of the phenotypes we should then observe a simple quantitative character and would want to know its variance and heritability. Therefore, when we observe a polymorphism, we ought surely to consider the variance and heritability of each of the phenotypes. Thus we should consider the problem of the natural selection of the selective coefficient of a particular genotype whose fitness has a given variance. Following O'DONALD (1967), let the fitness of an individual be 1 s, where fitness is to be regarded as the probability of survival. Let s have the relative frequency density f(s) with mean i and variance V . An individual will therefore have the selective coefficient s 'with the probability f (s )ds . After selection the probability will be (1 s ) f ( s )ds and the total frequency will be 1 i. Thus in the distribution of the selected individuals, the probability of an individual with the selective coefficient s is (1 s)f(s)ds/(l i). The mean of the selected distribution is therefore