title: Dimorphism by Singularity Theory in a Model for River Ecology.
abstract: Geritz, Gyllenberg, Jacobs, and Parvinen show that two similar species can coexist only if their strategies are in a sector of parameter space near a nondegenerate evolutionarily singular strategy. We show that the dimorphism region can be more general by using the unfolding theory of Wang and Golubitsky near a degenerate evolutionarily singular strategy. Specifically, we use a PDE model of river species as an example of this approach. Our finding shows that the dimorphism region can exhibit various different forms that are strikingly different from previously known results in adaptive dynamics.
authors.affiliation: Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA.
authors.forename: Martin
authors.initials: M
authors.lastname: Golubitsky
authors.affiliation: Department of Mathematics, Pennsylvania State University, State College, PA, 16802, USA.
authors.forename: Wenrui
authors.initials: W
authors.lastname: Hao
authors.affiliation: Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA. lam.184@math.ohio-state.edu.
authors.forename: King-Yeung
authors.identifier: 0000-0003-1004-0658
authors.initials: KY
authors.lastname: Lam
authors.affiliation: Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA.|Institute for Mathematical Sciences, Renmin University of China, Beijing, China.
authors.forename: Yuan
authors.initials: Y
authors.lastname: Lou
mesh_terms: D000818:Animals; D059001:Aquatic Organisms; D005075:Biological Evolution; D003198:Computer Simulation; D017753:Ecosystem; D005716:Game Theory; D056084:Genetic Fitness; D055641:Mathematical Concepts; D008954:Models, Biological; D011157:Population Dynamics; D045483:Rivers
keywords: Adaptive dynamics; Reaction–diffusion equation; River ecology; Singularity theory