On the use of star-shaped genealogies in inference of coalescence times

Genealogies from rapidly growing populations have approximate "star" shapes. We study the degree to which this approximation holds in the context of estimating the time to the most recent common ancestor (T(MRCA)) of a set of lineages. In an exponential growth scenario, we find that unless the product of population size (N) and growth rate (r) is at least approximately 10(5), the "pairwise comparison estimator" of T(MRCA) that derives from the star genealogy assumption has bias of 10-50%. Thus, the estimator is appropriate only for large populations that have grown very rapidly. The "tree-length estimator" of T(MRCA) is more biased than the pairwise comparison estimator, having low bias only for extremely large values of Nr.