Theory of fitness in a heterogeneous environment: Part III. The response to selection☆

A method is presented for estimating the average fitness of a population which is responding to selection in a fluctuating environment. The environment is assumed to be a stationary Markov random process of the type described by Uhlenbeck & Ornstein (1930), and the genotype is restricted to a single locus with two alleles. The fitness of each genotype depends on the deviation of its phenotype from the optimal phenotype in the given environment. Finally the fitness of the population is expressed as a function of the parameters of the genetic system (average phenotypic effect of a gene substitution, mutation rate) and of the environment (mean, variance, and autocorrelation). Conditions were found under which it is advantageous for a population to be polymorphic (that is, under which the average phenotypic effect of a gene substitution should differ from zero for maximum fitness). These conditions are of two very different kinds. First, regardless of whether the environment is autocorrelated or not, phenotypic diversity is advantageous if the environment is sufficiently heterogeneous compared to the tolerance of an individual for non-optimal conditions. When W(Cz) is the fitness of a genotype whose phenotype differs from the optimum phenotype by z, the tolerance is defined as the distance from the peak (at z = 0) to the point of inflection of W(Cz). Since W(z) has its inflection at some z0, the tolerance of each genotype is z0C, and C is an inverse measure of homeostasis. If the environment consists of discrete niches or is bimodal with modes (or optimal phenotypes in the niches) further apart than z0C, it is sufficiently heterogeneous for polymorphism to be optimal. This kind of polymorphism is stable. The different genotypes should be retained in the same frequencies without responding to selection, so that the optimal genetic system will be one in which there is large genetic variance due to epistatic interactions but a minimal additive component. The second kind of optimal polymorphism occurs when there is a high autocorrelation in the environment. Here the advantage of genetic variance is only that it permits response to selection. Thus it will consist mostly of additive variance. These two kinds of optimal polymorphism have very different consequences for speciation. In the first case, recombination between populations will result in F2 breakdown, so that natural selection will tend toward the establishment of isolating mechanisms. Therefore we expect that groups in which there is low individual tolerance of suboptimal environment will have high levels of static polymorphism based on epistatic complexes, a high degree of F2 breakdown, and a high rate of speciation. In the second case, where additive variance predominates, F2 between populations is more or less intermediate and there is not any strong selection for isolation. Hence a high individual tolerance of non-optimal environments will be accompanied by genetic systems with more additive variance, fewer inversions holding epistatic blocks, low F2 breakdown, and a low rate of speciation. It is suggested that the willistoni group of sibling species and Drosphila melanogaster are representatives of these alternative systems of adaptation.