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| In previous work, Chris Cosner, Yuan Lou and I (and others) have considered the question of when dispersal strategies that can be viewed as leading to an ideal free distribution at equilibrium are evolutionarily advantageous among some class of strategies. We have done so in numerous mathematical frameworks including reaction-diffusion, integro-difference and for this discussion most particularly, discrete diffusion of an arbitrary number of competing species in an arbitrary number of patches. A common feature in all these models is that dispersal and growth appear in separate terms. Of course, not all patch models (in discrete or continuous time) have such forms. In many cases dispersal and growth are intermingled. Kirkland, Schreiber and Li considered the evolution of conditional and unconditional dispersers for a general such class of multi-patch difference equations. In this work, we build on the work of Kirkland, Schreiber and Li in the discrete time multi-patch case utilizing the approach of Cantrell, Cosner and Lou in discrete-diffusion case and then address some continuous time multi-patch models in which dispersal and growth are similarly intermingled, namely the Mouquet-Loreau metapopulation model and a model with density dependent growth and dispersal studied by Schoener . The discrete results cover a generalization of Kirkland, Schreiber and Li but for this talk I will focus on the model from Kirkland, Schreiber and Li and on the Mouquet-Loreau model. This work is in collaboration with Chris Cosner, Yuan Lou and Sebastian Schreiber. |
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