On the equilibrium states in certain selection models
SummaryThe Fisher-Wright-Haldane model describes the behavior of a diploid population with random mating and separated generations under selection. Similar models for overlapping generations have been investigated. The corresponding differential equations for gene frequencies are derived under the hypothesis that the population as a whole is in Hardy-Weinberg-equilibrium. This hypothesis cannot be satisfied in actual populations. A system of equations for the genotype frequencies is derived without this hypothesis. It can be shown that the equations for gene frequencies yield an appropriate description — at least in the neighborhood of an equilibrium — if the differences in fitness result from differences in fertility rather than mortality.