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Abstract Phylogenetic comparative methods are a major tool for evaluating macroevolutionary hypotheses. Methods based on the mean-reverting stochastic Ornstein–Uhlenbeck process allow for modelling adaptation on a phenotypic adaptive landscape that itself evolves and where fitness peaks depend on measured characteristics of the external environment and/or other organismal traits. Here, we give an overview of the conceptual framework for the many implementations of these methods and discuss how we might interpret estimated parameters. We emphasize that the ability to model a changing adaptive landscape sets these methods apart from other approaches and discuss why this aspect captures long-term trait evolution more realistically. Recent multivariate extensions of these methods provide a powerful framework for testing evolutionary hypotheses but are also more complicated to use and interpret. We provide some guidance on their usage and put recent literature on the topic in biological rather than mathematical terms. We further show how these methods provide a starting point for modelling reciprocal selection (i.e., coevolution) between interacting lineages. We then briefly review some critiques of the methodologies. Finally, we provide some ideas for future developments that we think will be useful to evolutionary biologists. 

Abstract Sexually selected weapons, such as the antlers of deer, claws of crabs, and tusks of beaked whales, are strikingly diverse across taxa and even within groups of closely related species. Phylogenetic comparative studies have typically taken a simplified approach to investigate the evolution of weapon diversity, examining the gains and losses of entire weapons, major shifts in size or type, or changes in location. Less understood is how individual weapon components evolve and assemble into a complete weapon. We addressed this question by examining weapon evolution in the diverse, multi-component hind-leg and body weapons of leaf-footed bugs, superfamily Coreoidea (Hemiptera: Heteroptera). Male leaf-footed bugs use their morphological weapons to fight for access to mating territories. We used a large multilocus dataset comprised of ultraconserved element loci for 248 species and inferred evolutionary transitions among component states using ancestral state estimation. Our results suggest that weapons added components over time with some evidence of a cyclical evolutionary pattern—gains of components followed by losses and then gains again. Furthermore, our best estimate indicated that certain trait combinations evolved repeatedly across the phylogeny, suggesting that they function together in battle or that they are genetically correlated. This work reveals the remarkable and dynamic evolution of weapon form in the leaf-footed bugs and provides insights into weapon assembly and disassembly over evolutionary time.