Abstract
Classical evolutionary game theory (EGT) focuses on competition among phenotypes while assuming asexual transmission of these phenotypes to the next generation. However, phenotypic selection and sexual recombination are not necessarily mutually reinforcing in populations with sexual reproduction. In particular, it has been long known that some of the evolutionarily stable strategies derived by EGT methods cannot be achieved by sexually reproducing, real-world, populations. Thus, the recently formulated polymorphic evolutionary game theory (PEGT), which adds underlying genetics and sexual reproduction to evolutionary games, has the potential to revolutionize game theoretical modeling of coevolutionary processes. To illustrate the advantages of PEGT over classical EGT, I analyze two of the best known EGT models: Hawk/Retaliator/Dove and Defector/Tit-for-Tat/Altruist, by PEGT methods. I show that if one admits non-Mendelian genetics—common in heritable behavior, both of these games exhibit the properties of moderated aggression and conditional cooperation as components of population-level polymorphisms.
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Notes
I prefer to defer modeling non-random mating to asymmetric PEGT games.
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Acknowledgements
Special thanks are due to Dr. Reuben Hiller for his invaluable technical assistance. I thank the unknown reviewers for suggestions that make this a better paper.
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Fishman, M.A. Polymorphic Evolutionary Games and Non-Mendelian Genetics. Bull Math Biol 82, 31 (2020). https://doi.org/10.1007/s11538-020-00705-2
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DOI: https://doi.org/10.1007/s11538-020-00705-2