Large-deviation properties of the extended Moran model

The distributions of the times to the most recent common ancestortmrca 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(α,2-α) for various choices of α. This includes also the classical Moran model (α→0) as well as the uniform distribution (α=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 α∈[0,2]. We find exponential distributions p(tmrca)~δ^tmrca in all cases, with systematically varying values for the base δ. Only for the cases α=0 and α=1, analytical results are known, i.e., δ=exp(-2/N²) and δ=2/3, respectively. We recover these values, confirming the validity of our approach. Finally, we also study the correlations between tmrca and the number of descendants.