Coalescent models (branching linear birth-death process models)
For a neutral mutation in a population of constant size:
t = 2 N p
In the case of an exponentially expanding population or one where the mutant allele is undergoing selection,
t = log(2Np(r+s) + 1)/(r+s)
where r is the exponential growth rate parameter (approximately the proportional increase per generation), and s is the selection coefficient for heterozygotes.
A well-known example of such a calculation is for idiopathic torsion dystonia (locus DYT1) among the Ashkenazi Jews [Risch et al 1995]. In Eastern Europe, this population increased rapidly in size from approximately 105 in 1650 to 5 x 106 in 1900, giving us an estimated r of 0.40. Risch et al [1995] estimate the allele frequency in the current population at 1/6000 to 1/2000. This gives an estimate of the age of the first mutation at 16-19 generations ago (about the year 1550).