%0 Journal Article %1 citeulike:4082991 %A Hashimoto, Koh %A Aihara, Kazuyuki %D 2009 %J Journal of Theoretical Biology %K diploid, game %R 10.1016/j.jtbi.2009.02.004 %T Fixation probabilities in evolutionary game dynamics with a two-strategy game in finite diploid populations %U http://dx.doi.org/10.1016/j.jtbi.2009.02.004 %X Fixation processes in evolutionary game dynamics in finite diploid populations are investigated. Traditionally, frequency dependent evolutionary dynamics is modeled as deterministic replicator dynamics. This implies that the infinite size of the population is assumed implicitly. In nature, however, population sizes are finite. Recently, stochastic processes in finite populations have been introduced in order to study finite size effects in evolutionary game dynamics. One of the most significant studies on evolutionary dynamics in finite populations was carried out by Nowak et al. which describes “one-third law” Nowak et al., 2004. Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 646-650. It states that under weak selection, if the fitness of strategy αis greater than that of strategy βwhen αhas a frequency 1/3, strategy αfixates in a β-population with selective advantage. In their study, it is assumed that the inheritance of strategies is asexual, i.e. the population is haploid. In this study, we apply their framework to a diploid population that plays a two-strategy game with two ESSs (a bistable game). The fixation probability of a mutant allele in this diploid population is derived. A “three-tenth law” for a completely recessive mutant allele and a “two-fifth law” for a completely dominant mutant allele are found; other cases are also discussed.

@article{citeulike:4082991, abstract = {Fixation processes in evolutionary game dynamics in finite diploid populations are investigated. Traditionally, frequency dependent evolutionary dynamics is modeled as deterministic replicator dynamics. This implies that the infinite size of the population is assumed implicitly. In nature, however, population sizes are finite. Recently, stochastic processes in finite populations have been introduced in order to study finite size effects in evolutionary game dynamics. One of the most significant studies on evolutionary dynamics in finite populations was carried out by Nowak et al. which describes “one-third law” [Nowak et al., 2004. Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 646-650]. It states that under weak selection, if the fitness of strategy αis greater than that of strategy βwhen αhas a frequency 1/3, strategy αfixates in a β-population with selective advantage. In their study, it is assumed that the inheritance of strategies is asexual, i.e. the population is haploid. In this study, we apply their framework to a diploid population that plays a two-strategy game with two ESSs (a bistable game). The fixation probability of a mutant allele in this diploid population is derived. A “three-tenth law” for a completely recessive mutant allele and a “two-fifth law” for a completely dominant mutant allele are found; other cases are also discussed.}, added-at = {2009-05-19T18:00:18.000+0200}, author = {Hashimoto, Koh and Aihara, Kazuyuki}, biburl = {https://www.bibsonomy.org/bibtex/2150910490d2d73a5169338fbf71eec93/earthfare}, citeulike-article-id = {4082991}, description = {CiteULike: Everyone's library}, doi = {10.1016/j.jtbi.2009.02.004}, interhash = {ec19ea8b0e5c7ad20b5a9c7da3ef90db}, intrahash = {150910490d2d73a5169338fbf71eec93}, issn = {00225193}, journal = {Journal of Theoretical Biology}, keywords = {diploid, game}, month = {February}, posted-at = {2009-05-19 02:57:26}, priority = {2}, timestamp = {2009-05-19T18:03:27.000+0200}, title = {Fixation probabilities in evolutionary game dynamics with a two-strategy game in finite diploid populations}, url = {http://dx.doi.org/10.1016/j.jtbi.2009.02.004}, year = 2009 }