How old is the most recent ancestor of two copies of an allele?

An important clue to the evolutionary history of an allele is the structure of the neighboring region of the genome, which we term the genomic background of the allele. Consider two copies of the allele. How similar we expect their genomic background to be is strongly influenced by the age of their most recent common ancestor (MRCA). We apply diffusion theory, first used by Motoo Kimura as a tool for predicting the changes in allele frequencies over time and developed by him in many articles in this journal, to prove a variety of new results on the age of the MRCA under the simplest demographic assumptions. In particular, we show that the expected age of the MRCA of two copies of an allele with population frequency f is just 2Nf generations, where N is the effective population size. Our results are a first step in running exact coalescent simulations, where we also simulate the history of the population frequency of an allele.