A new maximum likelihood method to simultaneously estimate the paramet
ers of any migration pattern from gene frequencies in stochastic equil
ibrium is developed, based on a model of multivariate genetic drift in
a subdivided population. Motivated by simulations of this process in
the simplified case of two subpopulations, problems related to the nui
sance parameter q, the equilibrium gene frequency, are eliminated by c
onditioning on the observed mean gene frequency. The covariance matrix
of this conditional distribution is calculated by constructing an abs
tract process that mimics the behavior of the original process in the
subspace of interest. The approximation holds as long as there is limi
ted differentiation between subpopulations. The bias and variance of e
stimates of long-range and short-range migration in a finite stepping
stone model are evaluated by fitting the model to simulated data with
known values of the parameters. Possible ecological extensions of the
model are discussed.