Abstract
The theoretical investigation of how spatial structure affects the evolution of social behavior has mostly been done under the assumption that parent-offspring strategy transmission is perfect, i.e., for genetically transmitted traits, that mutation is very weak or absent. Here, we investigate the evolution of social behavior in structured populations under arbitrary mutation probabilities. We consider populations of fixed size N, structured such that in the absence of selection, all individuals have the same probability of reproducing or dying (neutral reproductive values are the all same). Two types of individuals, A and B, corresponding to two types of social behavior, are competing; the fidelity of strategy transmission from parent to offspring is tuned by a parameter μ. Social interactions have a direct effect on individual fecundities. Under the assumption of small phenotypic differences (implying weak selection), we provide a formula for the expected frequency of type A individuals in the population, and deduce conditions for the long-term success of one strategy against another. We then illustrate our results with three common life-cycles (Wright-Fisher, Moran Birth-Death and Moran Death-Birth), and specific population structures (graph-structured populations). Qualitatively, we find that some life-cycles (Moran Birth-Death, Wright-Fisher) prevent the evolution of altruistic behavior, confirming previous results obtained with perfect strategy transmission. We also show that computing the expected frequency of altruists on a regular graph may require knowing more than just the graph's size and degree.
Highlights
Most models on the evolution of social behavior in structured populations study the outcome of competition between individuals having different strategies and assume that strategy transmission from parents to their offspring is almost perfect
While most studies on the evolution of cooperation assume an almost perfect fidelity of strategy transmission from parent to offspring, here, we explored the effect of arbitrary mutation on the evolution of social behavior in structured populations
We provide a formula (eq (10)) that gives the expected frequency of a given strategy, for any life-cycle, any fidelity of parent-offspring strategy transmission, and that is valid in populations of fixed size that are such that the reproductive values of all sites are equal
Summary
Most models on the evolution of social behavior in structured populations study the outcome of competition between individuals having different strategies and assume that strategy transmission from parents to their offspring is almost perfect (i.e., when considering genetic transmission, that mutation is either vanishingly small or absent) This is for instance illustrated by the use of fixation probabilities to assess evolutionary success (e.g., Rousset & Billiard, 2000; Rousset, 2003; Nowak et al, 2004; Nowak, 2006; Ohtsuki et al, 2006). We provide a formula that gives the long-term frequency of a social strategy in any such population, for arbitrary mutation rates, and for any life-cycle (provided population size remains equal to N ) This formula is a function of the probabilities that pairs of individuals are identical by descent. We illustrate our results with widely used updating rules (Moran models, Wright-Fisher model) and specific population structures
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