This research aims to develop statistical models to estimate the pace at which species change over time. A key novelty of the approach is that it can model a large number of characteristics at the same time without a significant increase in model complexity. The new models will enable scientists to study entire sequences of traits, such as each developmental stage of an animal, and significantly increase the number of traits incorporated in comparative analyses, allowing the exploration of new dimensions of biodiversity. The researchers will make all models and algorithms developed as part of this research openly available to the public as software packages for the R statistical programming language (also free to use). The project will also implement a hands-on research-based course for undergraduate students that will train them in statistics, programming, data-driven research, and models of molecular substitution, which are fundamental skills for the STEM job market today and in the foreseeable future. The phylogenetic comparative methods proposed in this project will introduce several advances to facilitate the analyses of multivariate traits and significantly expand the use of phenotypic sequences as a context to study the phenome of organisms. The approach will incorporate rate heterogeneity using Gamma-distributed rate scalers and estimate the evolutionary correlation among traits with correlated bivariate Gamma distributions for neighboring states in the sequence. E