Modeling the Phylogenetic Rates of Continuous Trait Evolution: An Autoregressive–Moving-Average Model Approach

The rates of continuous evolution plays a crucial role in understanding the pace at which species evolve. Various statistical models have been developed to estimate the rates of continuous trait evolution for a group of related species evolving along a phylogenetic tree. Existing models often assume the independence of the rate parameters; however, this assumption may not account for scenarios where the rate of continuous trait evolution correlates with its evolutionary history. We propose using the autoregressive–moving-average (ARMA) model for modeling the rate of continuous trait evolution along the tree, hypothesizing that rates between two successive generations (ancestor–descendant) are time-dependent and correlated along the tree. We denote PhyRateARMA(p,q) as a phylogenetic rate-of-continuous-trait-evolution ARMA(p,q) model in our framework. Our algorithm begins by utilizing the tree and trait data to estimate the rates on each branch, followed by implementing the ARMA process to infer the relationships between successive rates. We apply our innovation to analyze the primate body mass dataset and plant genome size dataset and test for the autoregressive effect of the rates of continuous evolution along the tree.