Density-dependent selection in a random environment: An evolutionary process that can maintain stable population dynamics

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Abstract
A theoretical analysis of natural selection is presented in which fitnesses depend on population density and randomly varying environmental processes. The theory is based on a general, heuristic analysis of a pair of coupled, nonlinear, stochastic difference equations that describe the joint dynamics of allele frequencies and population size. Four main conclusions emerge from the investigation of a particular class of models: ( i ) growth rates at low population densities tend to increase; ( ii ) individual selection, given sufficient genetic flexibility, will mold growth rates at higher densities so that in spite of i , stable deterministic population dynamics are maintained; ( iii ) “more fit” genotypes cannot be simply characterized—in particular, the mean population size need not be increased; and ( iv ) genetic polymorphisms can be maintained in both haploid and diploid organisms.