Summary1. A number of approaches for studying macroevolution using phylogenetic trees have been developed in the last few years. Here, we present RPANDA, an R package that implements model-free and model-based phylogenetic comparative methods for macroevolutionary analyses. 2. The model-free approaches implemented in RPANDA are recently developed approaches stemming from graph theory that allow summarizing the information contained in phylogenetic trees, computing distances between trees, and clustering them accordingly. They also allow identifying distinct branching patterns within single trees. 3. RPANDA also implements likelihood-based models for fitting various diversification models to phylogenetic trees. It includes birth-death models with i) constant, ii) time-dependent and iii) environmental-dependent speciation and extinction rates. It also includes models with equilibrium diversity derived from the coalescent process, as well as a likelihood-based inference framework to fit the individual-based model of Speciation by Genetic Differentiation, which is an extension of Hubbell's neutral theory of biodiversity. 4. RPANDA can be used to (i) characterize trees by plotting their spectral density profiles (ii) compare trees and cluster them according to their similarities, (iii) identify and plot distinct branching patterns within trees, (iv) compare the fit of alternative diversification models to phylogenetic trees, (v) estimate rates of speciation and extinction, (vi) estimate and plot how these rates have varied with time and environmental variables and (vii) deduce and plot estimates of species richness through geological time. 5. RPANDA provides investigators with a set of tools for exploring patterns in phylogenetic trees and fitting various models to these trees, thereby contributing to the ongoing development of phylogenetics in the life sciences.

Many classical ecological and evolutionary theoretical frameworks posit that competition between species is an important selective force. For example, in adaptive radiations, resource competition between evolving lineages plays a role in driving phenotypic diversification and exploration of novel ecological space. Nevertheless, current models of trait evolution fit to phylogenies and comparative data sets are not designed to incorporate the effect of competition. The most advanced models in this direction are diversity-dependent models where evolutionary rates depend on lineage diversity. However, these models still treat changes in traits in one branch as independent of the value of traits on other branches, thus ignoring the effect of species similarity on trait evolution. Here, we consider a model where the evolutionary dynamics of traits involved in interspecific interactions are influenced by species similarity in trait values and where we can specify which lineages are in sympatry. We develop a maximum likelihood based approach to fit this model to combined phylogenetic and phenotypic data. Using simulations, we demonstrate that the approach accurately estimates the simulated parameter values across a broad range of parameter space. Additionally, we develop tools for specifying the biogeographic context in which trait evolution occurs. In order to compare models, we also apply these biogeographic methods to specify which lineages interact sympatrically for two diversity-dependent models. Finally, we fit these various models to morphological data from a classical adaptive radiation (Greater Antillean Anolis lizards). We show that models that account for competition and geography perform better than other models. The matching competition model is an important new tool for studying the influence of interspecific interactions, in particular competition, on phenotypic evolution. More generally, it constitutes a step toward a better integration of interspecific interactions in many ecological and evolutionary processes.