| Abstract: |
| This talk will describe optimal dispersal, and how it could evolve in some integrodifference models for migratory populations. We formulate integrodifference models that describe seasonal migrations where the environment is heterogeneous in space and varies between seasons, and where the integral kernels describing movement can depend on conditions at the arrival and departure points. We consider the kernels as movement strategies and use pairwise invasion analysis to find which kernels correspond to evolutionarily stable strategies (ESS). As in many other modeling contexts, those are the ones that can produce an ideal free distribution, which can be characterized in terms of line sum symmetry. The analysis requires our operators to be strongly positive. Thus, in cases where the environment is partially occupied in both seasons, we need to use order unit norms to define spaces whose positive cones have a nonempty interior. Perhaps this approach may be useful in other applications of integrodifference models where dispersal depends on environmental quality.
We also describe a way that a population can learn how to migrate optimally from the experience of past migrations. |
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