Biotic interactions are hypothesized to be one of the main processes shaping trait and biogeographic evolution during lineage diversification. Theoretical and empirical evidence suggests that species with similar ecological requirements either spatially exclude each other, by preventing the colonization of competitors or by driving coexisting populations to extinction, or show niche divergence when in sympatry. However, the extent and generality of the effect of interspecific competition in trait and biogeographic evolution has been limited by a dearth of appropriate process-generating models to directly test the effect of biotic interactions. Here, we formulate a phylogenetic parametric model that allows interdependence between trait and biogeographic evolution, thus enabling a direct test of central hypotheses on how biotic interactions shape these evolutionary processes. We adopt a Bayesian data augmentation approach to estimate the joint posterior distribution of trait histories, range histories, and co-evolutionary process parameters under this analytically intractable model. Through simulations, we show that our model is capable of distinguishing alternative scenarios of biotic interactions. We apply our model to the radiation of Darwin's finches-a classic example of adaptive divergence-and find limited support for in situ trait divergence in beak size, but stronger evidence for convergence in traits such as beak shape and tarsus length and for competitive exclusion throughout their evolutionary history. These findings are more consistent with pre-sympatric, rather than post-sympatric, niche divergence. Our modeling framework opens new possibilities for testing more complex hypotheses about the processes underlying lineage diversification. More generally, it provides a robust probabilistic methodology to model correlated evolution of continuous and discrete characters.