Article,
The number of mutant forms maintained in a population
(1967)
Abstract
Experimental and empirical studies appear to indicate the existence of large
numbers of polymorphisms in wild populations. It is desirable to formulate a
model which qualitatively explains the relative importance of the pressures of
selection, mutation and random drift in maintaining these polymorphisms. An
equivalent problem investigated by Fisher 3 concerned the rate of mutation
necessary in order to maintain a sufficient number of heterozygous loci which
thus contribute toward genetic variance.
In recent years there has been much interest in the related problem of deter-
mining the number of alleles (alternative gene types) that can be maintained by
mutation. It is this problem that the subsequent analysis is primarily aimed at;
however, it directly adds insight into the question of clarifying the reasons for
the large numbers of polymorphisms observed. Kimura and Crow 11 and
Ewens 2 have investigated quantitatively the situation when each mutant
form that arises is different from previous forms. Either due to selective dis-
advantages, mutation or migration pressures, or random sampling effects due
to finite population size, the resulting subpopulation generated by each mutant
form ultimately becomes extinct. The reasons for studying these models are set
forth in Kimura and Crow at length and are not repeated here. For further
bibliographic references on this subject we refer to Wright 14.
