Large-deviation properties of the extended Moran model

TL;DR

This paper investigates the large-deviation properties of the time to the most recent common ancestor in an extended Moran model, revealing exponential tail behaviors and confirming analytical results for specific cases.

Contribution

It introduces a large-deviation approach to study the distribution tails of the MRCA time in a generalized Moran model with beta-distributed offspring, extending previous analytical results.

Findings

Distribution of t_mrca is exponential across cases

Confirmed analytical delta values for alpha=0 and alpha=1

Studied correlations between t_mrca and descendants

Abstract

The distributions of the times to the first common ancestor t_mrca is numerically studied for an ecological population model, the extended Moran model. This model has a fixed population size N. The number of descendants is drawn from a beta distribution Beta(alpha, 2-alpha) for various choices of alpha. This includes also the classical Moran model (alpha->0) as well as the uniform distribution (alpha=1). Using a statistical mechanics-based large-deviation approach, the distributions can be studied over an extended range of the support, down to probabilities like 10^{-70}, which allowed us to study the change of the tails of the distribution when varying the value of alpha in [0,2]. We find exponential distributions p(t_mrca)~ delta^{t_mrca} in all cases, with systematically varying values for the base delta. Only for the cases alpha=0 and alpha=1, analytical results are known, i.e., delta=\exp(-2/N^2) and delta=2/3, respectively. We recover these values, confirming the validity of our approach. Finally, we also study the correlations between t_mrca and the number of descendants.