Mathematical Modeling of Selection by Sex-Limited Trait: To the Question of Maintenance of Litter Size Polymorphism in Natural Populations of Arctic Foxes

Abstract

This paper proposes a model of selection by a sex-limited trait expressed in females. The model was modified to describe natural selection for such a trait in ecologically limited populations with an age structure. Simulation results are aimed at explaining the existing genetic variety in litter size in different (natural and artificial) populations of Arctic foxes (Alopex lagopus). The model assumes that the maintenance of polymorphism in litter size is associated with periodic changes in availability of food for natural populations of Arctic foxes and significantly depends on a parameter describing the relative survival advantage of individuals from small litters during years with low food supply. The work shows that selection by a sex-limited trait maintains the litter size polymorphism in a wider range of values of this parameter than selection by a trait not limited by sex, which is described by the classical selection model for the case where the survival and fecundity of an individual are determined only by its own genotype, regardless of sex. It is known that the presence of an age or stage structure in a population significantly increases the chances of maintaining genetic variety in a nonstationary environment. A generalization of the proposed selection model for a population with two stages of development made it possible to show that polymorphism in litter size is possible within even wider ranges of values of the considered parameter.