The Implications of Density-Dependent Population Growth for Frequency- and Density-Dependent Selection

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Abstract
The relationship between density-dependent population growth and frequency- and density-dependent selection was investigated. For the haploid asexual case, Malthusian growth leads to constant birth and death rates and constant fitness values. A more general Lotka-Volterra formulation leads to both density- and frequency-dependent selection. The more general formulation is necessary but not sufficient for polymorphic coexistence in asexual forms. For the diploid sexual case, Malthusian growth leads to frequency-dependent population trajectories, but the basic birth and death rates are constant. A density-dependent model, analogous to the Lotka-Volterra model of the asexual case, leads to both frequency- and density-dependent fitness values and selection differentials. If selective differentials are solely reproductive in origin, whether density dependent or independent, Hardy-Weinberg frequencies characterize the polymorphic equilibrium, when it exists. This is not the case when selection differentials involve survival components, whether density dependent or independent. Heterosis is not necessary to achieve stable polymorphism and the polymorphic condition can be maintained by certain types of intergenotypic competition as well.