Random and non-random mating populations: Evolutionary dynamics in meiotic drive

Abstract

Game theoretic tools are utilized to analyze a one-locus continuous selection model of sex-specific meiotic drive by considering nonequivalence of the viabilities of reciprocal heterozygotes that might be noticed at an imprinted locus. The model draws attention to the role of viability selections of different types to examine the stable nature of polymorphic equilibrium. A bridge between population genetics and evolutionary game theory has been built up by applying the concept of the Fundamental Theorem of Natural Selection. In addition to pointing out the influences of male and female segregation ratios on selection, configuration structure reveals some noted results, e.g., Hardy-Weinberg frequencies hold in replicator dynamics, occurrence of faster evolution at the maximized variance fitness, existence of mixed Evolutionarily Stable Strategy ($ESS$) in asymmetric games, the tending evolution to follow not only a $1:1$ sex ratio but also a $1:1$ different alleles ratio at particular gene locus. Through construction of replicator dynamics in the group selection framework, our selection model introduces a redefining bases of game theory to incorporate non-random mating where a mating parameter associated with population structure is dependent on the social structure. Also, the model exposes the fact that the number of polymorphic equilibria will depend on the algebraic expression of population structure.