"Genotype dynamics and Haldane’s familial selection"Garay, JózsefBased on mating table, genotype dynamics is introduced and it is shown that static evolutionary stability implies the stability of the corresponding interior rest point in genotype dynamics. We apply this result to Haldane’s familial selection in a panmictic, diploid population, where the survival rates of full siblings within monogamous families are determined by Prisoner's Dilemma, and defector and cooperator pure strategy is uniquely determined by an autosomal recessive-dominant or intermediate Mendelian allele pair. We distinguish two types of Prisoner's Dilemma: in collaborating Prisoner's Dilemma cooperation while in alternating Prisoner's Dilemma defector-cooperator strategy pair maximizes the siblings' survival rates. Based on the stability of the pure cooperator and defector states, we provide a potential classification of genotype dynamics. We find that the pure cooperator population cannot fixate in the alternating case. However, in the collaborator case, fixation is possible but not necessary, as bistability and coexistence can also occur due to the interplay between the phenotypic payoff function and the genotype-phenotype mapping, which collectively determine the outcome of natural selection. |
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