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Equilibria of a predator prey model of phenotype evolution
Authors:Sílvia Cuadrado
Institution:Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
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.
Keywords:Spectral bound  Irreducible semigroup  Evolutionarily stable strategy
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