On the Biological Significance of the Cost of Gene Substitution

If gene substitution is a response to unfavorable changes in the environment, there will be a lag in the population's response to those changes. The cost of gene substitution can be defined as the reproductive excess necessary to prevent extinction when the population is at a low density. Two simple derivations of the cost in a haploid population are presented. The cost is a function of the initial gene frequency of the favored alleles and the rate of occurrence of the environmental changes. The exact expression obtained is compatible with Haldane's (1957) result. The occurrence and substitution of favorable mutants in the absence of environmental change does not impose any cost, but makes the population better able to bear the cost. It is argued that this definition of the cost makes it independent of the exact mode of population size regulation. Too high a cost leads, not to a slowing of substitution, but to extinction. Models of natural selection by truncation are discussed, as are limits on the rate of substitution calculated from the genetic variance of fitness.