Lookdown construction for a Moran seed-bank model

TL;DR

This paper introduces a lookdown construction for a Moran seed-bank model with variable populations, linking it to existing models, and analyzes the asymptotic behavior of the time to the most recent common ancestor and fixation times.

Contribution

It provides a novel lookdown construction for the seed-bank Moran model and derives asymptotic results for TMRCA and fixation times.

Findings

TMRCA has the same asymptotic order as the largest inactivity period.

The asymptotic distribution of TMRCA is obtained.

Fixation time of a beneficial mutant is of order ln(N).

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, 2022. 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. We then obtain an asymptotic distribution of the TMRCA, and use this result to find the first order of the asymptotic distribution of the fixation time of a single beneficial mutant conditioned to invade the whole population, which surprisingly is of order $\ln(N)$.