Chaos from Linear Frequency-Dependent Selection

The simplest diploid form of frequency-dependent selection can generate periodic and chaotic trajectories for the allele frequency. The model is of a randomly mating, infinite diploid population with nonoverlapping generations, segregating for two alleles under frequency-dependent viability selection. The fitness of each genotype is a linear function of the frequencies of the three genotypes. The region in the space of the coefficients that yields cycles and chaos is explored analytically and numerically. The model follows the period-doubling route to chaos, as seen with logistic growth models, but includes additional phenomena such as the simultaneous stability of cycling and chaos. The general condition for cycling or chaos is that the heterozygote deleteriously affect all genotypes. The kinds of ecological interactions that could give rise to the fitness regimes producing cycling and chaos include cannibalism, predator attraction, habitat degradation, and disease transmission.

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