Nearly all plant and animal populations consist of many populations among which genetic exchange is limited. Understanding the pattern of differences among human populations is of considerable medical importance. Both the epidemiology of complex disorders and the pharmacological effectiveness of certain drugs depend on the genetic background of the population in which alleles are expressed. Commonly used ethnic label often provide insufficient and inaccurate representations of the underlying genetic structure. Thus, we will extend Bayesian methods we have developed to allow investigators to describe patterns of genetic variation in complex, hierarchically structured populations. In addition to the direct medical importance of understanding population genetic structure, geneticists have long been interested in using the pattern of differences among populations to infer population size, migration rates, and mutation rates. Nearly all existing statistical methods allow only the product of population size and migration rate or the product of population size and mutation rate to be estimated. We will develop novel methods for inference that allow these parameters to be separated. Our method is statically novel in that it requires simulation of the first-stage priors in the context of a hierarchical Bayesian model for genetic data. Similar approaches have been used to provide insight into the past demographic history of human populations and for understanding patterns of selection on disease-associated alleles. In both phases of the project we will devote special attention to developing and evaluating methods of models choice. Moreover, we develop refinements to existing user-friendly software implementing the methods we develop and make the software and the associated source code freely available under the GNU General Public license.