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

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.