The Emergence of Complex Population Dynamics in Age-Structured Populations under Natural Selection for Fertility

The paper considers a microevolution model of two-stage population with limitation under the influence of natural selection regulating individual fertility. Analytical and numerical investigations of the model have been conducted, and parametric regions corresponding to different types of dynamic behavior have been identified. The final genetic composition of the population is shown to be determined by the reproductive potential values of heterozygotes and homozygotes. With higher productivity of heterozygotes, the model predicts stable polymorphism; under intermediate dominance, polymorphism transitions to monomorphism or the emergence of a new mutation. Reduced heterozygote reproductive potential leads to a bistability trap, when the system shifts to one of the possible monomorphic states depending on the initial allele frequency. Furthermore, it has been found that within a narrow range of parameter values, reduced heterozygote fertility can result in multistability, where both the bistability trap and stable polymorphism may emerge depending on initial allele frequencies. Consequently, variations in the current population structure can alter the direction of evolution. Additionally, an increase in average fertility destabilizes the population dynamics, with the nature of the resulting fluctuations being determined by ecological limitation.