When and where was the most recent common ancestor?

The structured coalescent is investigated for single-locus, digenic samples in the diffusion limit of the unidimensional stepping-stone model for homogeneous, isotropic migration and random genetic drift. Let T denote the scaled time to the most recent common ancestor (MRCA) of the two genes, and let Z designate the scaled deviation of the position of the MRCA from the average position of the two genes. The joint probability density of T and Z is evaluated explicitly. Both the marginal and conditional distributions of T have infinite expectation, as does the marginal distribution of Z. Conditioned on T = tau, the distribution of Z is Gaussian with mean zero and variance 2tau. The main results are extended to anisotropic migration. The results establish the existence of and define in the diffusion limit a retrospective stochastic process for digenic samples in one spatial dimension.