Abstract
It has long been known in the field of population genetics that adaptive topographies, in which population equilibria maximise mean population fitness for a trait regardless of its genetic bases, do not exist. Whether one chooses to model selection acting on a single locus or multiple loci does matter. In evolutionary game theory, analysis of a simple and general game involving distinct roles for the two players has shown that whether strategies are modelled using a single ‘locus’ or one ‘locus’ for each role, the stable population equilibria are unchanged and correspond to the fitness-maximising evolutionary stable strategies of the game. This is curious given the aforementioned population genetical results on the importance of the genetic bases of traits. Here we present a dynamical systems analysis of the game with roles detailing how, while the stable equilibria in this game are unchanged by the number of ‘loci’ modelled, equilibrium selection may differ under the two modelling approaches.
Highlights
Biological fitness typically depends on complicated phenotypes, which depend on multiple genetic loci
For a simple yet general evolutionary game theory model of social evolution, in which behaviour is conditioned on social role occupied, recent analysis has shown that the stable equilibria under selection are the same regardless of whether one considers selection acting on the entire strategy [2, 6], or acting on independent ‘genes’ for each role [9]
We have presented an analysis using the tools of dynamical systems theory, for the simple case of asymmetric non-additive donation games played between relatives
Summary
Biological fitness typically depends on complicated phenotypes, which depend on multiple genetic loci. To illustrate the global behaviour of the gene dynamics model (1), let us consider an example of a situation where the equilibrium (eÃ, eÃ) exists; as parameters, we choose b = 2, c = 0.5, d = 0.25 > 0, and r = 0.185.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
