| Abstract: |
| Understanding how organisms distribute themselves in heterogeneous environments is a central question in ecology. The classical principle of ideal free distribution (IFD) predicts that individuals move so as to equalize fitness across space, and such strategies are known to be evolutionarily stable in static environments. However, real habitats are often time-periodic, and the notion of optimal dispersal in such settings is far less understood.
In this talk, we study dispersal strategies in a time-periodic, patchy environment through a system of reaction-diffusion (or patch) models with multiple competing species. We introduce a natural definition of ideal free distribution based on pathwise fitness, and characterize when such distributions can exist. We then show that dispersal strategies leading to IFD are evolutionarily stable: populations converge to an IFD determined by the environment, and species that realize a (joint) IFD can outcompete all others. Our results extend classical theory to systems with multiple competitors or multiple prey and predator species in time-periodic environments. Our main tool is the construction of Lyapunov functions inspired by generalized relative entropy inequality. This is joint work with R.S. Cantrell (Miami), C. Cosner (Miami) and H. Zhang (Shanghai Jiaotong). |
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