title: Singularity theory of fitness functions under dimorphism equivalence.
abstract: We apply singularity theory to classify monomorphic singular points as they occur in adaptive dynamics. Our approach is based on a new equivalence relation called dimorphism equivalence, which is the largest equivalence relation on strategy functions that preserves ESS singularities, CvSS singularities, and dimorphisms. Specifically, we classify singularities up to topological codimension two and compute their normal forms and universal unfoldings. These calculations lead to the classification of local mutual invasibility plots that can be seen generically in systems with two parameters.
authors.affiliation: Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA.
authors.forename: Xiaohui
authors.initials: X
authors.lastname: Wang
authors.affiliation: Mathematical Biosciences Institute, The Ohio State University, Columbus, OH, 43210, USA. mg@mbi.osu.edu.
authors.forename: Martin
authors.initials: M
authors.lastname: Golubitsky
mesh_terms: D005075:Biological Evolution; D008954:Models, Biological
keywords: Adaptive game theory; Dimorphism; ESS; Fitness functions; Singularity theory