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A genetic approach to the rock-paper-scissors game
Wendell P Barreto1, Flavia M D Marquitti2, Marcus A M de Aguiar1
1Instituto de Física 'Gleb Wataghin', Universidade Estadual de Campinas, Unicamp, 13083-970 Campinas, SP, Brazil.
Journal of Theoretical Biology
|April 8, 2017
Summary
Polymorphisms in side-blotched lizards (Uta stansburiana) influence mating and defense. Introducing diploidy and sexual reproduction into game theory models explains the coexistence of different male morphs, affecting system stability.
Area of Science:
- Evolutionary Biology
- Game Theory
- Population Genetics
Background:
- Polymorphisms typically affect fitness, making morph coexistence unexpected.
- Side-blotched lizards exhibit three male morphs (orange, yellow, blue) with distinct mating and territorial behaviors.
- Previous models treated populations as hermaphroditic, focusing solely on phenotype.
Purpose of the Study:
- To extend existing game theory models of lizard mating strategies.
- To incorporate diploidy and sexual reproduction into the dynamical system.
- To investigate how genetic structure affects morph coexistence and system stability.
Main Methods:
- Developed a genetic model for a single locus with three alleles (o, y, b) in a diploid system.
- Incorporated dominance relationships: o > y and y > b.
- Analyzed the dynamical system to determine equilibrium phenotype frequencies and stability.
Main Results:
- The genotypic model yields the same equilibrium phenotype frequencies as previous phenotypic models.
- Diploidy and sexual reproduction alter the stability of the rock-paper-scissors game.
- The parameter region allowing coexistence of the three morphs is modified by the genetic structure.
Conclusions:
- Explicitly modeling diploidy and sexual reproduction provides a more realistic framework for understanding morph coexistence.
- Genetic factors significantly influence the stability dynamics of polymorphic mating systems.
- This extended model offers new insights into the evolutionary maintenance of polymorphism in natural populations.