KARLIN-MCGREGOR MUTATIONAL OCCUPANCY PROBLEM REVISITED

Thierry Huillet (1)

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

Some population is made of n individuals that can be of p possible species (or types). The update of the species abundance occupancies is from a Moran mutational model designed by Karlin and McGregor in 1967. We first study the equilibrium species counts as a function of n, p and the total mutation probability ν before considering various asymptotic regimes on n, p and ν. Running title: KMG Model with Mutations.

Mots clés: Species abundance; Karlin-McGregor-Moran Models; Muta- tional and evolutionary processes; Population dynamics Asymptotics

Domaines: Mécanique statistique [cond-mat.stat-mech]; Probabilités [math.PR]; Génétique des populations [q-bio.PE]

Thierry Huillet. KARLIN-MCGREGOR MUTATIONAL OCCUPANCY PROBLEM REVISITED. 2018. ⟨hal-01782164⟩