On Discrete-Time Multiallelic Evolutionary Dynamics Driven by Selection

الملخص EN

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.