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… 
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