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A fundamental goal of evolutionary biology is to characterize the processes by which species traits evolve, and how those processes gave rise to the patterns of variation observed between species. Since interspecific variation often arises over millions of years, the tempo and mode of these processes cannot typically be observed directly or reproduced experimentally. Instead, they may be studied through a statistical framework called the phylogenetic comparative method. This dissertation focuses on phylogenetic models for two classes of traits: species geographical distributions (or biogeographic traits) and quantitative traits. The following contributions represent methodological advances that serve to render longstanding theoretical questions vulnerable to statistical analysis.