  We consider a single genetic locus which carries two alleles, labelled P and
Q. This locus experiences selection and mutation. It is linked to a second
neutral locus with recombination rate r. If r=0, this reduces to the study of a
single selected locus. Assuming a Moran model for the population dynamics, we
pass to a diffusion approximation and, assuming that the allele frequencies at
the selected locus have reached stationarity, establish the joint generating
function for the genealogy of a sample from the population and the frequency of
the P allele. In essence this is the joint generating function for a coalescent
and the random background in which it evolves. We use this to characterize, for
the diffusion approximation, the probability of identity in state at the
neutral locus of a sample of two individuals (whose type at the selected locus
is known) as solutions to a system of ordinary differential equations. The only
subtlety is to find the boundary conditions for this system. Finally, numerical
examples are presented that illustrate the accuracy and predictions of the
diffusion approximation. In particular, a comparison is made between this
approach and one in which the frequencies at the selected locus are estimated
by their value in the absence of fluctuations and a classical structured
coalescent model is used.
