Equilibria of a predator prey model of phenotype evolution

Sílvia Cuadrado

doi:10.1016/j.jmaa.2009.01.002

Equilibria of a predator prey model of phenotype evolution

Sílvia Cuadrado

Department of Mathematics

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

7 Citations (Scopus)

Abstract

A selection mutation predator prey model for the distribution of individuals with respect to an evolutionary trait is considered. Existence of steady states is proved using the theory of positive semigroups. We show that these steady states tend to concentrate, when the mutation rate is small, at the so-called evolutionary stable value of the trait in the sense of adaptive dynamics of the corresponding ecological model. © 2009 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	286-294
Journal	Journal of Mathematical Analysis and Applications
Volume	354
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2009.01.002
Publication status	Published - 1 Jun 2009

Keywords

Evolutionarily stable strategy
Irreducible semigroup
Spectral bound

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10.1016/j.jmaa.2009.01.002

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title = "Equilibria of a predator prey model of phenotype evolution",

abstract = "A selection mutation predator prey model for the distribution of individuals with respect to an evolutionary trait is considered. Existence of steady states is proved using the theory of positive semigroups. We show that these steady states tend to concentrate, when the mutation rate is small, at the so-called evolutionary stable value of the trait in the sense of adaptive dynamics of the corresponding ecological model. {\textcopyright} 2009 Elsevier Inc. All rights reserved.",

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AB - A selection mutation predator prey model for the distribution of individuals with respect to an evolutionary trait is considered. Existence of steady states is proved using the theory of positive semigroups. We show that these steady states tend to concentrate, when the mutation rate is small, at the so-called evolutionary stable value of the trait in the sense of adaptive dynamics of the corresponding ecological model. © 2009 Elsevier Inc. All rights reserved.

KW - Evolutionarily stable strategy

KW - Irreducible semigroup

KW - Spectral bound

U2 - 10.1016/j.jmaa.2009.01.002

DO - 10.1016/j.jmaa.2009.01.002

M3 - Article

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VL - 354

SP - 286

EP - 294

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Equilibria of a predator prey model of phenotype evolution

Abstract

Keywords

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