On discrete-time multiallelic evolutionary dynamics driven by selection

Thierry Huillet (1)

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

We revisit some problems arising in the context of multiallelic discrete-time evolutionary dynamics driven by fitness. We consider both the deterministic and the stochastic setups and for the latter both the Wright-Fisher and the Moran approaches. In the deterministic formulation, we construct a Markov process whose Master equation identifies with the nonlinear deterministic evolutionary equation. Then, we draw the attention on a class of fitness matrices that plays some role in the important matter of polymorphism: the class of strictly ultrametric fitness matrices. In the random cases, we focus on fixation probabilities, on various conditionings on non-fixation and on (quasi-)stationary distributions.

Mots clés: Evolutionary genetics; Multiallelic fitness landscape; Strictly ultrametric fitness matrix; Polymorphism; Moran and Wright-Fisher models; Fixation probabilities; Multiplicative fitness; conditioning; (Quasi-)stationary distribution.; (Quasi-)stationary distribution

Domaines: Probabilités [math.PR]; Bio-Informatique, Biologie Systémique [q-bio.QM]; Bio-informatique [q-bio.QM]; Mécanique statistique [cond-mat.stat-mech]

Thierry Huillet. On discrete-time multiallelic evolutionary dynamics driven by selection. Journal of Probability and Statistics, 2010, 2010, pp.580762. ⟨10.1155/2010/580762⟩. ⟨hal-00525968⟩