Abstract
We are interested in modeling the Darwinian dynamics of a polymorphic asexual population, as driven by the interplay of phenotypic variation and natural selection through ecological interactions. Our modeling is based on a stochastic individual-based model that details the dynamics of heritable traits characterizing each individual. We consider the specific scales of the biological framework of adaptive dynamics: rare mutations and large population. We prove that under a good combination of these two scales, the population process is approximated in an evolution long time scale by a Markov pure jump process describing successive equilibria of the population. Then we consider this polymorphic evolution process in the limit of small mutations. From a fine study in the neighborhood of evolutionary singularities, we obtain a full mathematical justification of a heuristic criterion for the phenomenon of evolutionary branching.
Mathematics Subject Classification (2000). 92D25, 60J80, 37N25, 92D15, 60J75.
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Méléard, S. (2011). Random Modeling of Adaptive Dynamics and Evolutionary Branching. In: Chalub, F., Rodrigues, J. (eds) The Mathematics of Darwin’s Legacy. Mathematics and Biosciences in Interaction. Springer, Basel. https://doi.org/10.1007/978-3-0348-0122-5_10
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DOI: https://doi.org/10.1007/978-3-0348-0122-5_10
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