Spatial variation in biodiversity is the result of complex interactions between evolutionary history and ecological factors. Methods in historical biogeography combine phylogenetic information with current species locations to infer the evolutionary history of a clade through space and time. A major limitation of most methods for historical biogeographic inference is the requirement of single locations for terminal lineages, reducing contemporary species geographical ranges to a point in two-dimensional space. In reality, geographic ranges usually show complex geographic patterns, irregular shapes, or discontinuities. In this article, we describe a method for phylogeographic analysis using polygonal species geographic ranges of arbitrary complexity. By integrating the geographic diversification process across species ranges, we provide a method to infer the geographic location of ancestors in a Bayesian framework. By modeling migration conditioned on a phylogenetic tree, this approach permits reconstructing the geographic location of ancestors through time. We apply this new method to the diversification of two neotropical bird genera, Trumpeters (Psophia) and Cinclodes ovenbirds. We demonstrate the usefulness of our method (called rase) in phylogeographic reconstruction of species ancestral locations and contrast our results with previous methods that compel researchers to reduce the distribution of species to one point in space. We discuss model extensions to enable a more general, spatially explicit framework for historical biogeographic analysis.

rase_0.2-1.tarRange ancestral state estimation (rase) R package used for the analyses. The most up to date version can be found on https://bitbucket.org/ignacioq/rase.Online Appendix about Monte Carlo ErrorMathematical derivations for the Monte Carlo sampling routine used and analyses of Monte Carlo error for approximating the likelihood of a domain.online_appendix.pdf