Largedeviation properties of the extended Moran model
Abstract
The distributions of the times to the most recent common ancestort_{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 (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 mechanicsbased largedeviation 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 (t_{mrca}) ∼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 /N^{2}) and δ =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.
 Publication:

Physical Review E
 Pub Date:
 October 2018
 DOI:
 10.1103/PhysRevE.98.042416
 arXiv:
 arXiv:1710.07504
 Bibcode:
 2018PhRvE..98d2416H
 Keywords:

 Quantitative Biology  Populations and Evolution;
 Physics  Biological Physics
 EPrint:
 8 pages, 8 figures