Genetic Equilibrium and Population Growth Under Density-Regulated Selection

A maximization principle relating gene frequency changes and population growth is formulated for a simple model of density-regulated selection. The selective value of each genotype is altered by density in a way analogous to logistic population growth. The growth of the population as a whole is logistic, its maximal rate of increase being a weighted arithmetic mean of the genotypic rates, and its carrying capacity a weighted harmonic mean of the genotypic carrying capacities. A stable genetic polymorphism occurs at a maximum, and an unstable equilibrium at a minimum, of the mean genotypic carrying capacity.