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      A mutation-selection model for evolution of random dispersal

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          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.

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          Journal
          2015-06-01
          2015-06-25
          Article
          1506.00662
          ca8f2240-41fa-4603-8386-35b29b916ef9

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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