  The stationary distribution of a sample taken from a Wright-Fisher diffusion
with general small mutation rates is found using a coalescent approach. The
approximation is equivalent to having at most one mutation in the coalescent
tree to the first order in the rates. The sample probabilities characterize an
approximation for the stationary distribution from the Wright-Fisher diffusion.
The approach is different from Burden and Tang (2016,2017) who use a
probability flux argument to obtain the same results from a forward diffusion
generator equation. The solution has interest because the solution is not known
when rates are not small. An analogous solution is found for the configuration
of alleles in a general exchangeable binary coalescent tree. In particular an
explicit solution is found for a pure birth process tree when individuals
reproduce at rate lambda.
