Nonconvergence in Bayesian estimation of migration rates

The estimation of migration rates using molecular markers is an important aspect of many population genetic studies. Several different methods are available for estimating migration, but most of these make multiple limiting assumptions. One method that is relatively free from assumptions is bayesass, which uses assignment methods in a Bayesian framework. However, when tested using simulated data, this method was found to have problems with the convergence of the Markov chain Monte Carlo. Here, I perform a literature study to test whether these convergence problems are also present when bayesass is used to estimate migration rates from empirical data. A review of 100 studies that have used bayesass shows that this is indeed the case. The estimated proportions of nonmigrants were mostly either close to 2/3 or 1, indicating that the MCMC tends to get trapped near the bounds of the prior distribution. In addition, I found that the quality of the inference was negatively affected by the number of sampled populations, but increased with increasing numbers of sampled individuals and with the strength of the population structure as measured by F_ST. Based on these results, I give several recommendations that should help to reduce problems when using bayesass with empirical data. Most importantly, I argue that researchers should be more realistic about inferences of migration rates and that bayesass will give optimal results only when the experiment has been especially designed around its use.