Dynamics of Positive Frequency Dependent Selection Triggers Selection for Silence

Abstract

Positive frequency dependent selection is a natural selection regime where the fitness of a phenotype increases with its frequency in the population. Examples can be typically found in the spread of disease tolerance strategies in a population. A characterizing feature of PFDS is that the focal allele may experience favorable selection only when it becomes more frequent in the population, while being selected against when it is rare. In this paper, by applying a solution concept from evolutionary game theory, we hypothesize that the process of emergence of such alleles triggers selection for silence, where the emergence of alleles that can stay unexpressed for a period of time will be favored by selection forces. We illustrate our hypothesis using a mathematical model of a population of single locus diploid organisms with two alleles where a single mutant of an allele that experiences positive frequency dependent selection appears in a population where the other allele is a dominant. The model results show that the longer the silence interval of the new mutant before its expression, the better its chances of getting fixed in the population. However, this effect will be observable only to a certain limit after which further increase in the interval will not have an effect on the expected fixation rate. Two divergences from the simple scenario are also investigated: the nonsynchronous expression of the focal allele and its emergence in a spatial grid limited by a migration bottleneck. In all cases, it is shown that there is an evolutionary pressure inherent in the dynamics of positive frequency dependent selection on the genes to have a delayed expression. It is hypothesized that the regulation systems of such traits will be under selection for either internal silencing mechanisms or to be triggered by an external environmental condition.