ON WRIGHT-FISHER DIFFUSION AND ITS RELATIVES

Thierry Edmond Arnold Huillet (1)

1 LPTM - UMR 8089 - Laboratoire de Physique Théorique et Modélisation

We present a series of elementary stochastic models arising from population genetics. Various mathematical aspects are investigated at the intuitive level. Special emphasis is put on the diffusion method. Focus is on the Wright-Fisher diffusion model and its variations, describing the forward evolution of one colony undergoing random sampling, possibly under the additional forces arising from mutation, selection with or without dominance. Some aspects of their dual coalescents obtained while running the diffusion process backward in time are also investigated.

Mots clés: Phylogeny (Theory); Mutational and evolutionary processes (theory); Population dynamics (Theory); Phylogeny (Theory).

Domaines: Probabilités [math.PR]; Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]; Bio-Informatique, Biologie Systémique [q-bio.QM]; Bio-informatique [q-bio.QM]

Thierry Edmond Arnold Huillet. ON WRIGHT-FISHER DIFFUSION AND ITS RELATIVES. Journal of Statistical Mechanics: Theory and Experiment, 2007, pp.P11006, vol 11. ⟨hal-00181730⟩