Continuous models for frequency-density dependent selection

The growth of a panmictic monoecious diploid population with two alleles at one locus is modeled by making fitnesses depend on the genotypes' abundance. This implies an implicit dependence of fitnesses on both density and gene frequency. Equations are derived for the gene frequency and for the population size in the overlapping generation case. A diffusion model for the gene frequency is finally obtained, and the gene frequency transition probability density function is determined in the case of no dominance.