title: Effect of Spatial Dispersion on Evolutionary Stability: A Two-Phenotype and Two-Patch Model.
abstract: In this paper, we investigate a simple two-phenotype and two-patch model that incorporates both spatial dispersion and density effects in the evolutionary game dynamics. The migration rates from one patch to another are considered to be patch-dependent but independent of individual's phenotype. Our main goal is to reveal the dynamical properties of the evolutionary game in a heterogeneous patchy environment. By analyzing the equilibria and their stabilities, we find that the dynamical behavior of the evolutionary game dynamics could be very complicated. Numerical analysis shows that the simple model can have twelve equilibria where four of them are stable. This implies that spatial dispersion can significantly complicate the evolutionary game, and the evolutionary outcome in a patchy environment should depend sensitively on the initial state of the patches.
authors.affiliation: School of Mathematical Sciences, Capital Normal University, Beijing, China.
authors.forename: Qing
authors.initials: Q
authors.lastname: Li
authors.affiliation: Key Lab of Animal Ecology and Conservational Biology, Institute of Zoology, Chinese Academy of Sciences, Beijing, China.
authors.forename: Jiahua
authors.initials: J
authors.lastname: Zhang
authors.affiliation: Laboratory of Mathematics and Complex Systems, Ministry of Education, School of Mathematical Sciences, Beijing Normal University, Beijing, China.
authors.forename: Boyu
authors.initials: B
authors.lastname: Zhang
authors.affiliation: Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada.
authors.forename: Ross
authors.initials: R
authors.lastname: Cressman
authors.affiliation: Key Lab of Animal Ecology and Conservational Biology, Institute of Zoology, Chinese Academy of Sciences, Beijing, China.
authors.forename: Yi
authors.initials: Y
authors.lastname: Tao
mesh_terms: D063147:Animal Distribution; D000818:Animals; D001522:Behavior, Animal; D005075:Biological Evolution; D004777:Environment; D005716:Game Theory; D005786:Gene Expression Regulation; D008957:Models, Genetic; D015233:Models, Statistical; D010641:Phenotype; D011157:Population Dynamics