TY - JOUR
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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U2 - 10.1007/s11538-017-0268-3
DO - 10.1007/s11538-017-0268-3
M3 - Article
C2 - 28357615
AN - SCOPUS:85016426607
SN - 0092-8240
VL - 79
SP - 1051
EP - 1069
JO - Bulletin of Mathematical Biology
JF - Bulletin of Mathematical Biology
IS - 5
ER -