Ages of mutations on a coalescent tree

Using the coalescent process, DNA sequences of a sample of individuals can be used to study the phylogenetic history of the individuals. Under the infinitely-many-sites mutation model, the DNA sequence data can be summarized by the number of segregating sites (which is numerically equivalent to the number of mutations on the tree). A number of methods exist, including a recursive method presented in this paper, that obtain an estimate of the age of the most recent common ancestor (MRCA), given the number of mutations. This paper introduces a method for finding the ages of mutations, given the total number of mutations on the tree. While the result is not useful in estimating the age of a specific segregating site, it is useful in examining the underlying assumption of a relatively constant population over time. This utilization of the result is illustrated using DNA sequence data obtained from a sample of Amerindians of the Nuu–Chah–Nulth tribe.