The age of a mutation in a general coalescent tree

Kimura and Ohta showed that the expected age of a neutral mutation observed to be of frequency x in a population is We put this classical result in a general coalescent process context that allows questions to be asked about mutations in a sample, as well as in the population. In the general context the population size may vary back in time. Assuming an infmitely-many-sites model of mutation, we find the distribution of the number of mutant genes at a particular site in a sample; the probability that an allele at that site of a given frequency is ancestral; the distribution of the age of a mutation given its frequency in a sample, or population; and the distribution of the time to the most recent common ancestor, given the frequency of a mutation in a sample, or in the population