Likelihood-based parameter estimation for high-dimensional phylogenetic comparative models: overcoming the limitations of 'distance-based' methods

Recently, a suite of distance-based multivariate phylogenetic comparative methods has been proposed for studying the evolution of high-dimensional traits, such as morphometric coordinates, gene expression data, and function-valued traits. These methods allow for the statistical comparison of evolutionary rates, assessment of phylogenetic signal, and tests of correlated high-dimensional trait evolution. Simulations reveal that distance-based comparative methods exhibit low statistical power and high Type I error under various evolutionary scenarios. Distance-based methods are also limited to relatively simple model specification (e.g., Brownian motion evolution) due to the lack of a likelihood function for parameter estimation. Here I propose an alternative method for studying high-dimensional trait evolution which overcomes some of the statistical limitations associated with distance-based methods. This framework, based on parametric bootstrapping and maximum pseudolikelihood parameter estimation, opens up the ability to estimate alternative evolutionary models, combine multiple evolutionary hypotheses, and potentially allow missing data and within-species variation. Simulations reveal that pairwise composite likelihood methods demonstrate appropriate Type I error and high statistical power, thus providing a robust framework for studying high-dimensional trait evolution. These methods are implemented in the R package phylocurve.