On discrete-time multiallelic evolutionary dynamics driven by selection
Summary: 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.
scientific article; zbMATH DE number 5822159
scientific article