Ecological–genetic approach in modeling the natural evolution of a population: Prospects and special aspects of verification

• A set of evolutionary models are applied in order to explain the polymorphism in arctic fox populations.
• The set of previously developed models is extended by models with cyclically varying parameters.
• An effect of optimal harvest on these populations is discussed.

This study presents a complex approach for modeling the natural evolution of a population in terms of population number and dynamics of the genetic structure. A set of dynamic models that consider various types of natural selection was applied to describe possible mechanisms underlying the formation of existing genetic variations in litter sizes in coastal, inland, and farmed arctic fox populations (Alopex lagopus, family Canidae, order Carnivora). The r–K selection model for uniform population and the models with natural selection were assessed on various life cycle stages in a two-age population. The life cycle of arctic fox was fitted to the population model with two age stages. The different reproductive potentials and survivability of progeny on the early stage of life cycle were genetically determined using the model with a single diallelic gene. A monomorphism was obtained for a considered characteristic in a population of coastal arctic fox with constant food supply. Meanwhile, a polymorphism with cyclic fluctuations in population number and gene frequency was obtained in inland arctic fox populations, which could be due to cyclic fluctuations of prey. In farmed fox populations, the considered gene becomes pleiotropic (defines the survival rate of individuals on early and late stages of the life cycle) because of artificial selection performed by farmers to increase the reproductive success of breeders. The application of an appropriate model (with selection by pleiotropic gene) can be used to determine the elimination rate of low litter size alleles from the farmed populations. The possible applications of the proposed models for formulating and solving optimal control tasks in arctic fox populations are discussed too.