Complex dynamical behaviour of frequency-dependent viability selection: an example

The model of viability selection based on a one-locus, two-allele diploid population is considered. Frequency dependence is introduced through the fitnesses of three phenotypes (strategies) exhibited by the population. Both discrete and continuous dynamics are analyzed and contrasted with the classical results of frequency-independent selection and with the more recent results of frequency-dependent selection based on two-phenotype multi-allele systems. Cycling and chaotic behaviour are shown to be easily obtained in the discrete model. Intuitive biological conditions for stability are shown to fail as well as at general equilibria of the continuous model.