Lookdown construction for a Moran seed-bank model

Abstract

We present a lookdown construction for a Moran seed-bank model with variable active and inactive population sizes and we show that the empirical measure of our model coincides with that of the Seed-Bank-Moran Model with latency of Greven, den Hollander and Oomen [6]. Furthermore, we prove that the time to the most recent common ancestor, starting from N individuals with stationary distribution over its state (active or inactive), has the same asymptotic order as the largest inactivity period. Additionally, we give an explicit approximation of its distribution under extra assumtion on the inactivity and activity switching rates. We then find the first asymptotic order of the fixation time of a single beneficial mutant conditioned to invade the whole population, resulting to be of order $lnN$.