On the Equilibration of Fitnesses by Natural Selection

Abstract

Models of selection on a modifier locus affecting the degree of polymorphism in a population which has 2 or 3 distinct phenotypic classes are considered. Frequency-dependent interactions between the different types in the population and both internally and externally induced fluctuations in population size are also considered. Two types of models are analyzed, difference-equation models of populations with discrete, nonoverlapping generations and differential-equation models of populations with overlapping generations but no age structure. Under many circumstances natural selection at the modifier locus will tend to equilibrate the fitnesses of the phenotypic classes in the population to the extent possible given the genetic constraints of the character being analyzed. For the model of frequency-dependent interactions considered, the long-term evolutionary trend of the population would not be to maximize the total population size or the mean fitness of the population. This is a different result from that found in other models of selection, including models of density-dependent selection and models of selection on a modifier system, because of the frequency dependence caused by the interference of the different morphs. The evolution of parameters that directly affect the fitnesses of different morphs in a population will tend to maximize the total population size given that the fitnesses of the different morphs are equal at equilibrium.