Global mutations and local mutations have very different effects on evolution, illustrated by mixed strategies of asymmetric binary games |
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Authors: | Takashi Uehara Yoh Iwasa |
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Institution: | Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan |
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Abstract: | We study the evolutionary effect of rare mutations causing global changes in traits. We consider asymmetric binary games between two players. The first player takes two alternative options with probability x and 1−x; and the second player takes options with probability y and 1−y. Due to natural selection and recurrent mutation, the population evolves to have broad distributions of x and y. We analyze three cases showing qualitatively different dynamics, exemplified by (1) vigilance-intrusion game, (2) asymmetric hawk-dove game and (3) cleaner-client game. We found that the evolutionary outcome is strongly dependent upon the distribution of mutants’ traits, more than the mutation rates. For example in the vigilance-intrusion game, the evolutionary dynamics show a perpetual stable oscillation if mutants are always close to the parent (local-mutation mode), whilst the population converges to a stable equilibrium distribution if mutants can be quite different from the parent (global-mutation mode), even for extremely low mutation rate. When common local mutations and rare global mutations occur simultaneously, the evolutionary outcome is controlled by the latter. |
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Keywords: | Evolutionary game Replicator dynamics Selection-mutation valance |
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