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Published on: July 30, 2019
Dimorphism by Singularity Theory in a Model for River Ecology
Martin Golubitsky1, Wenrui Hao2, King-Yeung Lam3
1Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA.
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.
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