Phylogenetic comparative methods for studying adaptation: the adaptation-inertia framework

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.