| Abstract: |
| This talk will describe some results for reaction-diffusion models of populations with stage structure. Reaction diffusion models for populations in heterogeneous environments where all individuals are considered to be identical and subject to logistic type growth predict that there is selection for slower diffusion. For stage structured populations that is not always true. We consider a model introduced by Brown and Zhang (J. Math. Anal. Appl. 2003). We show that if the regions favorable for reproduction by adults and for survival by juveniles are sufficiently similar, then slow diffusion is still favored. However, if the regions are different, sometimes fast diffusion is necessary for survival of the population. When the model includes competition between juveniles and adults it is cooperative at low densities but competitive at high densities. Also, in many populations, either juveniles or adults do not disperse, so there is no diffusion in one of the equations. Both of those situations require some novel mathematical approaches. In the case of strong competition between adults and juveniles we do not know if it is possible for the system to have multiple equilibria, which might correspond to multiple spatial patterns if they exist. |
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