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) ∼δtmrca 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.