title: A genetic approach to the rock-paper-scissors game.
abstract: Polymorphisms are usually associated with defenses and mating strategies, affecting the individual's fitness. Coexistence of different morphs is, therefore, not expected, since the fittest morph should outcompete the others. Nevertheless, coexistence is observed in many natural systems. For instance, males of the side-blotched lizards (Uta stansburiana) present three morphs with throat colors orange, yellow and blue, which are associated with mating strategies and territorial behavior. The three male morphs compete for females in a system that is well described by the rock-paper-scissors dynamics of game theory. Previous studies have modeled the lizards as hermaphroditic populations whose individual's behavior were determined only by their phenotypes. Here we consider an extension of this dynamical system where diploidy and sexual reproduction are explicitly taken into account. Similarly to the lizards we represent the genetic system by a single locus with three alleles, o, y, and b in a diploid chromosome with dominance of o over y and of y over b. We show that this genotypic description of the dynamics results in the same equilibrium phenotype frequencies as the phenotypic models, but affects the stability of the system, changing the parameter region where coexistence of the three morphs is possible in a rock-paper-scissors game.
authors.affiliation: Instituto de Física 'Gleb Wataghin', Universidade Estadual de Campinas, Unicamp, 13083-970 Campinas, SP, Brazil.
authors.forename: Wendell P
authors.initials: WP
authors.lastname: Barreto
authors.affiliation: Instituto de Física 'Gleb Wataghin', Universidade Estadual de Campinas, Unicamp, 13083-970 Campinas, SP, Brazil; Ecology and Evolutionary Biology, Princeton University, 08544 Princeton, NJ, USA.
authors.forename: Flavia M D
authors.initials: FMD
authors.lastname: Marquitti
authors.affiliation: Instituto de Física 'Gleb Wataghin', Universidade Estadual de Campinas, Unicamp, 13083-970 Campinas, SP, Brazil. Electronic address: aguiar@ifi.unicamp.br.
authors.forename: Marcus A M
authors.initials: MAM
authors.lastname: de Aguiar
mesh_terms: D000818:Animals; D005075:Biological Evolution; D005260:Female; D005716:Game Theory; D008116:Lizards / Q000502:physiology; D008297:Male; D010641:Phenotype; D011110:Polymorphism, Genetic; D012098:Reproduction; D012641:Selection, Genetic; D012726:Sexual Behavior, Animal
keywords: Diploidy; Evolutionary game theory; Population genetics; Sexual reproduction