The Moran model with random resampling rates

The Annals of Applied Probability, vol. 35, pp. 1852–1868

Abstract

In this paper we consider the two-type Moran model with N individuals. Each individual is assigned a resampling rate, drawn independently from a probability distribution P on R+, and a type, either 1 or 0. Each individual resamples its type at its assigned rate, by adopting the type of an individual drawn uniformly at random. Let YN(t) denote the empirical distribution of the resampling rates of the individuals with type 1 at time Nt. We show that if P has countable support and satisfies certain tail and moment conditions, then in the limit as N→∞ the process (YN(t))t≥0 converges in law to the process (S(t)P)t≥0, in the so-called Meyer–Zheng topology, where (S(t))t≥0 is the Fisher–Wright diffusion with diffusion constant D given by 1/D=∫R+(1/r)P(dr).

Authors 2

1. Siva Athreya

   International Centre for Theoretical Sciences

   Affiliation as printed

   International Centre for Theoretical Sciences-TIFR

2. Adrian Röllin

   National University of Singapore

   Affiliation as printed

   Department of Statistics and Data Science, National University of Singapore