Inferring patterns of migration from gene frequencies under equilibrium conditions

A new maximum likelihood method to simultaneously estimate the parameters of any migration pattern from gene frequencies in stochastic equilibrium 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 nuisance parameter q, the equilibrium gene frequency, are eliminated by conditioning on the observed mean gene frequency. The covariance matrix of this conditional distribution is calculated by constructing an abstract process that mimics the behavior of the original process in the subspace of interest. The approximation holds as long as there is limited differentiation between subpopulations. The bias and variance of estimates 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.