On the Application of the Autoregressive–Moving-Average Model for Studying Phylogenetic Rate of Trait Evolution

The rate of evolution plays a crucial role in understanding the pace at which species evolve. Various statistical models have been developed to estimate the rate parameters 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 evolution correlates with its evolutionary history. We propose using the autoregressive-moving-average (ARMA) model for modeling the rate of evolution along the tree, hypothesizing that rates between two successive generations (ancestor-descendant) are time dependent and correlated along the tree. We denote \texttt{phyrateARMA}$(p,q)$ as a phylogenetic ARMA($p$,$q$) model in our innovation. 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 rate of evolution along the tree.