Selection in a Cyclically Changing Environment
The classical selection model of population genetics describes a diploid population of infinite size. The individuals are assumed genetically identical with the exception of a single autosomal locus with two alleles A and a. Viabilities are attributed to the genotypes AA, Aa, aa. The state of the population can be described by the frequency of the allele A. In the case of separated generations the model assumes the form of a difference equation, for overlapping generations one obtains a differential equation (see Crow and Kimura 1975, Edwards 1977, Hadeler 1973, 1974, Nagylaki 1977). It is well known that in discrete time as well as in continuous time there are essentially four qualitatively different cases: if the heterozygotes are intermediate, then either the allele A or the allele a is superior; if both alleles are present initially then the frequency of the superior allele increases monotonely and converges to 1. If the heterozygotes are superior then there is a single polymorphism; every population in which both alleles are present converges to that polymorphism. If the heterozygotes are inferior, then the two pure states are locally stable and a unique unstable polymorphism acts as a threshold.
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