A Probabilistic Method for Estimating the Sharing of Identity by Descent for Populations with Migration

The inference of demographic history of populations is an important undertaking in population genetics. A few recent studies have developed identity-by-descent (IBD) based methods to reveal the signature of the relatively recent historical events. Notably, Pe'er and his colleagues have introduced a novel method (named PIBD here) by employing IBD sharing to infer effective population size and migration rate. However, under island model, PIBD neglects the coalescent information before the time to the most recent common ancestor (tMRCA) which leads to apparent deviations in certain situations. In this paper, we propose a new method, MIBD, by adopting a Markov process to describe the island model and develop a new formula for estimating IBD sharing. The new formula considers the coalescent information before tMRCA and the joint effect of the coalescent and migration events. We apply both MIBD and PIBD to the genome-wide data of two human populations (Palestinian and Bedouin) obtained from the HGDP-CEPH database, and demonstrate that MIBD is competitive to PIBD. Our simulation analyses also show that the results of MIBD are more accurate than those of PIBD especially in the case of small effective population size.