On discrete-time multiallelic evolutionary dynamics driven by selection

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 nonfixation,and on (quasi)stationary distributions. copyright © 2010 thierry e. huillet.