Abstract
Evolutionary game dynamics in finite populations assumes that all mutations are equally likely, i.e., if there are strategies a single mutation can result in any strategy with probability . However, in biological systems it seems natural that not all mutations can arise from a given state. Certain mutations may be far away, or even be unreachable given the current composition of an evolving population. These distances between strategies (or genotypes) define a topology of mutations that so far has been neglected in evolutionary game theory. In this paper we re-evaluate classic results in the evolution of cooperation departing from the assumption of uniform mutations. We examine two cases: the evolution of reciprocal strategies in a repeated prisoner's dilemma, and the evolution of altruistic punishment in a public goods game. In both cases, alternative but reasonable mutation kernels shift known results in the direction of less cooperation. We therefore show that assuming uniform mutations has a substantial impact on the fate of an evolving population. Our results call for a reassessment of the “model-less” approach to mutations in evolutionary dynamics.
Highlights
Evolutionary game dynamics can be used to study the evolution of phenotypes
To study non-uniform mutations, we introduce two mutation rates: mAB is the probability that an A type mutates into a B type, and mBA is the probability that a B type turns into an A type
If mutations are small enough [2], mutants arise whenever the population has fixated on a strategy, and the dynamics can be completely characterized by studying a Markov chain between monomorphic states [3,11]
Summary
Evolutionary game dynamics can be used to study the evolution of phenotypes. It usually considers the fate of a population of strategies playing a game, subject to selection and mutation. In this framework one of the most studied formalisms is the Moran process, it allows for studying the interplay between selection and mutation under demographic noise. The strategy that is copied changes its type to any of the other available strategies. This process results in an ergodic Markov chain. The effect of selection and mutation can be assessed by inspecting the average composition of the population in the long run
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