Rates of phenotypic evolution vary tremendously across the tree of life, generating vast disparities in phenotypic diversity across space, time, and taxa. Unfortunately, elucidating the factors driving such "rate heterogeneity" remains challenging due to various methodological limitations. In particular, most available methods for inferring variation in rates of continuous trait evolution assume rates are either influenced by only a few factors (i.e., variables hypothesized to affect rates) or change infrequently over the course of a clade’s history. However, rates of phenotypic evolution are likely affected by a dynamic, tangled web of countless environmental, life history, and genetic factors. By ignoring "residual" rate variation stemming from unobserved factors and assuming relatively simple rate variation patterns, available methods for modeling continuous trait evolution tend to underfit empirical data and mislead hypothesis testing by inflating support for complex models assuming spurious factor-rate associations. Here, to address these challenges, I develop, test, and apply new phylogenetic comparative methods capable of accurately inferring variation in rates of continuous trait evolution and robustly testing for factor-rate associations. In chapter 1, I develop a novel continuous trait evolution model whereby rates constantly and incrementally change over time and across lineages, resulting in continuous, stochastic rate variation across a clade with closely-related lineages more likely to exhibit similar rates. I implement a Bayesian approach for fitting this model to empirical data in an R package, evorates (https://github.com/bstaggmartin/evorates/), along with comprehensive tools for analyzing and visualizing model results. Through simulation, I demonstrate that this method yields accurate inferences and can more reliably detect general decreases/increases in rates over time (i.e., "early/late bursts" of trait evolution) than previous methods by accounting for residual rate variation around overall time-dependent trends. Additionally, I use evorates to show that rates of body size evolution among whales and dolphins have generally declined over time yet exhibit substantial residual variation, with oceanic dolphins and beaked whales exhibiting anomalously fast and slow rates, respectively. In chapter 2, I generalize stochastic character mapping or “simmapping”-based pipelines for inferring relationships between rates of continuous trait evolution and discrete factors (e.g., habitat, diet) to also accommodate continuous factors (e.g., temperature, generation time). Simmapping is a popular method for imputing the uncertain evolutionary history of a trait (or factor) by sampling probable histories along a phylogeny under a given trait evolution model. However, available simmapping implementations only work with discrete variables. Accordingly, I develop a new R package, contsimmap (https://github.com/bstaggmartin/contsimmap/), which implements both a scalable algorithm for simmapping continuous variables and methods for inferring relationships between simmapped continuous factors and continuous trait evolution dynamics. I go on to verify the accuracy and robustness of this new pipeline in estimating factor-rate relationships via an extensive simulation study, even devising a pragmatic new approach to account for residual rate variation, which was ultimately crucial for controlling the pipeline's error rates. Lastly, I use the pipeline to show that rates of leaf and flower evolution are heterogeneous yet unrelated to overall size in a clade of eucalyptus trees ranging from ~1 to nearly 100 meters in maximum height. In chapter 3, I devise a new approach for inferring associations between discrete factors and continuous trait evolution dynamics by jointly modeling the evolution of both discrete factors and continuous traits under a unified process. A key advantage of this method is that it allows the continuous trait data to directly influence the likelihood of different factor histories, enabling inference unobserved discrete factors or "hidden states" potentially driving residual rate variation in continuous trait evolution. I implement this method in an R package, sce (https://github.com/bstaggmartin/sce/), and show that the method can effectively detect and quantify heterogeneity in rates of continuous trait evolution driven by both observed and unobserved factors under a wide variety of simulated evolutionary scenarios. Further, I demonstrate the empirical utility of the new method by using it to rigorously show that tropical sage lineages exhibit elevated rates of flower size evolution compared to temperate lineages.
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