A mutation-selection model for evolution of random dispersal

Abstract

We consider a mutation-selection model of a population structured by the spatial variables and a trait variable which is the diffusion rate. Competition for resource is local in spatial variables, but nonlocal in the trait variable. We focus on the asymptotic profile of positive steady state solutions. Our result shows that in the limit of small mutation rate, the solution remains regular in the spatial variables and yet concentrates in the trait variable and forms a Dirac mass supported at the lowest diffusion rate. [Hastings, Theor. Pop. Biol. 24, 244-251, 1983] and [Dockery et al., J. Math. Biol. 37, 61-83, 1998] showed that for two competing species in spatially heterogeneous but temporally constant environment, the slower diffuser always prevails, if all other things are held equal. Our result suggests that their findings may hold for arbitrarily many traits.

References in corpus (2)

• On a model of a population with variable motility
• Rare mutations limit of a steady state dispersion trait model

Cited by in corpus (6)

• Ideal Free Dispersal under General Spatial heterogeneity and Time Periodicity
• Super-linear propagation for a general, local cane toads model
• Rare mutations limit of a steady state dispersion trait model
• Adaptation to a heterogeneous patchy environment with nonlocal dispersion
• Influence of a mortality trade-off on the spreading rate of cane toads fronts
• Asymptotic analysis of a quantitative genetics model withnonlinear integral operator