# From Individual Stochastic Processes to Macroscopic Models in Adaptive Evolution

@article{Champagnat2008FromIS, title={From Individual Stochastic Processes to Macroscopic Models in Adaptive Evolution}, author={Nicolas Champagnat and R{\'e}gis Ferri{\`e}re and Sylvie M{\'e}l{\'e}ard}, journal={Stochastic Models}, year={2008}, volume={24}, pages={2 - 44} }

We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population of discrete individuals characterized by one or several adaptive traits. The population is modelled as a stochastic point process whose generator captures the probabilistic dynamics over continuous time of birth, mutation, and death, as influenced by each…

## 110 Citations

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A model of a finite population in continuous time, where each individual is characterized by a trait under selection and a completely linked neutral marker, shows the convergence of the stochastic individual-based process to a new measure-valued diffusive process with jumps that is called Substitution Fleming–Viot Process (SFVP).

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- Environmental Science
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A probabilistic model to study the effect of the sexual preference on the speciation of species and gives numerical results and a detailed biological behavior analysis around two issues: the co-evolution of phenotypic and spatial niches of mutualistic species and the invasion dynamics of a homogeneous space by these species.

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