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.

Department of Ecology and Evolutionary Biology Yale University 165 Prospect Street New Haven CT 06520 8106 USA;

Department of Ecology and Evolutionary Biology Yale University 165 Prospect Street New Haven CT 06520 8106 USA; Center for Theoretical Study Charles University and Academy of Sciences of the Czech Republic Jilska 1 11000 Praha 1 Czech Republic;

Department of Ecology and Evolutionary Biology Yale University 165 Prospect Street New Haven CT 06520 8106 USA; Department of Biostatistics Yale School of Public Health 60 College Street New Haven CT 06510 USA

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