Evolutionary dynamics of a two-stage population with density-dependent regulation of the survival of reproductive individuals

G. P. Neverova ; E. Ya. Frisman

Matematičeskaâ biologiâ i bioinformatika, Tome 19 (2024) no. 2, pp. 293-303.

Résumé

The paper studies an evolutionary model of natural selection in a two-stage population with autoregulation of the survival of adult individuals. The population breeds seasonally, and we assume that reproductive potential is determined genetically. The proposed ecological-genetic model is a combination of an ecological model of the dynamics of a stage-structured population and a microevolutionary model of the dynamics of its genetic structure when the adaptive trait of birth rate is controlled by a single diallelic autosomal locus with allelomorphs $A$ and $a$. We study the proposed model analytically and numerically and determine the parametric regions with different dynamic behaviors. We consider the possibility of changing the dynamic mode due to a variation in the genetic composition of the population. The study shows the genetic composition of the population, namely, whether will it be polymorphic or monomorphic, is mainly determined by the values of the reproductive potentials of heterozygotes and homozygotes. Reduced fitness of the heterozygotes leads to a “bistability trap” when both monomorphic fixed points are attractive, and the initial abundances of stage classes and allele frequencies determine the genotype that will be fixed in the population. However, with density-dependent regulation of the survival of adult individuals, displacement of one of the alleles can lead to the extinction of the population. In general, a change in the direction of evolution may be accompanied by a change in the population dynamics mode.