Fast, slow convergence, and concentration in the house of cards replicator-mutator model

Bertrand Cloez (1) , Pierre Gabriel (2, 3)

1 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
2 IDP - Institut Denis Poisson
3 UT - Université de Tours

We propose a fine analysis of the various possible long time behaviours of the solutions of the replicator-mutator equation with so-called Kingman's house of cards mutations. In particular, we give what is to our knowledge the first concentration result for this model.

Mots clés: evolutionary genetics; selection-mutation; house of cards model; long time behavior; concentration phenomenon

Domaines: Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Bertrand Cloez, Pierre Gabriel. Fast, slow convergence, and concentration in the house of cards replicator-mutator model. Differential and integral equations, 2024, 37 (7-8), pp.547-584. ⟨10.57262/die037-0708-547⟩. ⟨hal-03608758v2⟩