CORRIGENDUM

Abstract

IOCHEMICAL studies of certain proteins have recently shown that the rate of evolution or gene substitution is much higher than that previously thought (KIMURA 1968; DAYHOFF 1969). This high rate of gene substitution has aroused a great deal of controversy about HALDANE’S (1957; 1960) theory of the cost of natural selection. HALDANE postulated that the genetic deaths needed to secure gene substitution by natural selection lower the average fitness of a population, so that there is an upper limit to the number of gene substitutions per unit length of time, depending on the fertility of the species in question. In this case the fitness of a genotype was assumed to be constant. HALDANE’S theory was accepted by KIMURA (1960; 1967) and CROW (1968) but questioned by a number of authors. Among others, SVED (1968) and MAYNARD SMITH (1968) have argued that if the population size is regulated in a density-dependent manner and gene substitution occurs by competitive selection, the mean fitness of the population would not necessarily be reduced. They produced a model of threshold selection in which gene substitutions may occur at a much higher rate than HALDANE’S computation allows. Recently, MATHER (1969) developed an interesting model of competitive selection and showed that many classical formulae for the change in gene frequency hold true under competitive selection. He, however, argued that the cost of natural selection should be re-examined, taking into account competitive selection and the effect of selection on population size. He thought that the cost of selection would be much less than HALDANE’S computation suggests. Another type of model for competitive selection was developed by SCHUTZ and UZANIS (1969). In this model, however, neither the cause and process of competition nor the mechanism of population regulation was studied in detail. The purpose of the present paper is first to develop mathematical models for natural selection in regulated populations and then examine the adequacy of the theory of the cost of natural selection. The cost of natural selection will be looked at from a slightly different angle, and the fertility excess or genetic variance of fitness necessary for a given rate of gene substitution will be studied. It will be shown that competition itself does not lead to threshold selection and HALDANE’S conclusion is essentially correct.