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Initial Increase of New Mutants and Some Continuity Properties of ESS in Two-Locus Systems

In a random mating, diploid population with viability determined by the genotype at two or more linked loci, natural selection does not guarantee an increase in the average viability of the population. Since it was first pointed out by Moran (1964), this apparent contradiction to the Darwin-Fisher-Wright expectation has been shown to occur in most multilocus nonadditive fitness regimes (Ewens 1969; Karlin 1975). As a result, even in a constant environment, it cannot be generally true that natural selection on genotypes distributed among phenotypes operates to maximize the average individual adaptation to the environment, i.e., to produce an optimal population strategy. When selection is considered to be frequency dependent, as in the models leading to the theory of evolutionary stable strategies (Maynard Smith and Price 1973), it is far from obvious that average fitness should be locally maximized when more than a single locus is involved. In this case, unlike that with a single gene, for a random set of genotypes and randomly chosen parameters relating these genotypes to the phenotypes, genetic equilibria are most unlikely to determine an ESS distribution of phenotypes. (See, e.g., Lessard 1984. Of course, one can question whether such parameters are indeed distributed at random.) The long-term effects of natural selection should not be considered in the context of changes in frequencies of a fixed set of genotypes. Even if nonneutral mutations occur at random, they do not succeed at random so that the set of extant genotypes in a population should not be regarded as random. As has been demonstrated for the sex ratio (Eshel and Feldman 1982) for the Mendelian segregation ratio under unlinked control (Eshel 1985), and for a one-locus twophenotype frequency-dependent system (Lessard 1984), criteria for success of new mutations may be different from and easier to interpret for genotypes than are the rules governing frequency changes of a given fixed set of genotypes. We know very little about the range of possible new mutations that may affect the course of evolution of a given phenotype. For this reason we call "long-term aspects of natural selection" those genetic criteria for the success of new mutations which can be interpreted in purely phenotypic terms.