Abstract
This study analyzes a four dimensional system of time-autonomous ordinary differential equations which models density-dependent coevolution with interspecific competition and with fitnesses exhibiting partial dominance. There are two competing populations, each possessing two alleles. If each homozygote fitness is a linear function of the competing population density, then using techniques of dynamical systems we show that a type of ecological and genetic exclusion occurs for a wide range of parameters. For these parameters, the asymptotic behavior of bounded solutions is determined by the genotype carrying capacities, and the asymptotic behavior of unbounded solutions is determined by the genotype growth rates. Numerically, there appear to be no nonequilibrium, compact invariant sets where all four alleles are present for any parameter combinations.
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