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.
- Evolutionarily stable strategy
- Irreducible semigroup
- Spectral bound