Estimating the age of the common ancestor of a DNA sample using the number of segregating sites.

The number of segregating sites in a sample of DNA sequences and the age of the most recent common ancestor (MRCA) of the sequences in the sample are positively correlated. The value of the former can be used to estimate the value of the latter. Using the coalescent approach, we derive in this paper the joint probability distribution of the number of segregating sites and the age of the MRCA of a sample under the neutral Wright-Fisher model. From this distribution, we are able to compute the likelihood function of the number of segregating sites and the posterior probability of the age of the MRCA of a sample. Three point estimators and one interval estimator of the age of the MRCA are developed; their relationships and properties are investigated. The estimation of the age of the MRCA of human Y chromosomes from a sample of no variation is discussed.