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Survival of the fittest: Asymptotic competitive exclusion in structured population and community models. (English) Zbl 0810.35003

Summary: McKendrick-von Foerster physiologically structured partial differential equation models are used to investigate asymptotic competitive exclusion, a nongenetic “survival of the fittest” for ecological morphs which are closed under reproduction. We consider both the age structured and the individual-based age-size structured settings, and allow birth, death, and individual growth rates to be time and density dependent in the general cases. Results suggest a good measure of “ecotypic fitness” is the product \(\beta L\) of the birth rate function \(\beta\) and survivorship function \(L\). Density dependence in mortality that uniformly affects the different morphs does not modify the characteristic behavior.

MSC:

35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
92D25 Population dynamics (general)
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