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 co...