Bayesian stochastic search variable selection. When GTR models find use modeling nucleotide substitution, most of the K(K{1)~12 possible transitions have non-neglible probability of occurring and are observed over the evolutionary history. Such is unlikely to be the case for geographical locations; given that there may be many sites and each taxon only has one location (the equivalent of just one single alignment site), we expect most transitions to rarely, if ever, occur. Consequentially, we suspect a priori that many infinitesimal rates are zero. From a statistical perspective, so many degrees of freedom fit to the limited data lead to extremely high variance estimates. These poor estimates arise not only for L, but, more critically, for inference of the unobserved ancestral locations and X root . We circumvent this sparse data problem by invoking BSSVS to select a parsimonious parameterization of L. BSSVS enables us to simultaneously determine which infinitesimal rates are zero depending on the evidence in the data and efficiently infer the ancestral locations. As a beneficial by-product of BSSVS, directly quantifying the evidence about which rates are non-zero furnishes both the most likely migration patterns and the ability to test between competing migratory hypotheses.