Using rare mutations to estimate population divergence times: A maximum likelihood approach

In this paper we propose a method to estimate by maximum likelihood the div ergence time between two populations, specifically designed for the analysi s of nonrecurrent rare mutations. Given the rapidly growing amount of data, rare disease mutations affecting humans seem the most suitable candidates for this method. The estimator RD, and its conditional version RDc, were de rived, assuming that the population dynamics of rare alleles can be describ ed by using a birth-death process approximation and that each mutation aros e before the split of a common ancestral population into the two diverging populations. The RD estimator seems more suitable for large sample sizes an d few alleles, whose age can be approximated, whereas the RDc estimator app ears preferable when this is not the case. When applied to three cystic fib rosis mutations, the estimator RD could not exclude a very recent time of d ivergence among three Mediterranean populations. On the other hand, the div ergence time between these populations and the Danish population was estima ted to be, on the average, 4,500 or 15,000 years, assuming or not a selecti ve advantage for cystic fibrosis carriers, respectively. Confidence interva ls are large, however, and can probably be reduced only by analyzing more a lleles or loci.