We approximate the joint posterior (8) and its marginalizations using MCMC implemented in the software package BEAST [43] . We employ standard transition kernels over the parameter spaces of F and w. To sample realizations of L, we consider random-walk operators on the continuous portions and a specialized ''bit-flip'' operator on the Bernoulli rate indicators d jk . [53] discuss this transition kernel further. Finally, in many situations, inference on the posterior distribution of the root and internal node states is of paramount interest. We implement a pre-order, tree-traversal algorithm in BEAST that allows researchers to generate realizations of the root and internal node states following [20] and produce posterior summaries. Importantly, this procedure is not limited to phylogeographic models, making general ancestral state reconstruction available in BEAST for the first time.