Dimorphism by Singularity Theory in a Model for River Ecology

Martin Golubitsky; Wenrui Hao; King Yeung Lam; Yuan Lou

doi:10.1007/s11538-017-0268-3

Dimorphism by Singularity Theory in a Model for River Ecology

Martin Golubitsky, Wenrui Hao, King Yeung Lam, Yuan Lou

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1051-1069
Number of pages	19
Journal	Bulletin of Mathematical Biology
Volume	79
Issue number	5
DOIs	https://doi.org/10.1007/s11538-017-0268-3
State	Published - May 1 2017

All Science Journal Classification (ASJC) codes

General Neuroscience
Immunology
General Mathematics
General Biochemistry, Genetics and Molecular Biology
General Environmental Science
Pharmacology
General Agricultural and Biological Sciences
Computational Theory and Mathematics

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10.1007/s11538-017-0268-3

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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.",

author = "Martin Golubitsky and Wenrui Hao and Lam, {King Yeung} and Yuan Lou",

note = "Funding Information: This research was supported in part by the National Science Foundation Grants DMS-0931642 and DMS-1440386 to the Mathematical Biosciences Institute. The research of KYL and YL was supported in part by National Science Foundation grant DMS-1411479. We thank the referees for careful reading of the manuscript and constructive suggestions.",

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T1 - Dimorphism by Singularity Theory in a Model for River Ecology

AU - Golubitsky, Martin

AU - Hao, Wenrui

AU - Lam, King Yeung

AU - Lou, Yuan

N1 - Funding Information: This research was supported in part by the National Science Foundation Grants DMS-0931642 and DMS-1440386 to the Mathematical Biosciences Institute. The research of KYL and YL was supported in part by National Science Foundation grant DMS-1411479. We thank the referees for careful reading of the manuscript and constructive suggestions.

PY - 2017/5/1

Y1 - 2017/5/1

N2 - 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.

AB - 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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Dimorphism by Singularity Theory in a Model for River Ecology

Abstract

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