A THEORETICAL FRAMEWORK RELATING TO EXPONENTIALLY FREQUENCY-DEPENDENT SELECTION MODEL IN POLLAK'S SENSE

Abstract

Allowing the exponentially frequency-dependent fitnesses and taking into consideration the viability effect on the fertility model, a deterministic mathematical model of selection in a one-locus two-allele genetic system has been developed in such a way that equilibrium frequencies of the three genotypes are the same as those of optimizing the mean fertility of the population. Under the consideration of both exponentially increasing and decreasing nature environments in the sense of viability and fertility selections to be opposite, degenerate optimization points have been calculated by verifying whether those equilibrium points are Kuhn–Tucker points or not. The Hadeler–Liberman symmetric fertility model has also been accounted for derivation of all sets of frequencies of this type. Assuming the Fundamental Theorem of Natural Selection, a mathematical expression has been derived to show the variation of mean fertility with generation.