A fundamental goal of evolutionary biology is to characterize the processes by which species traits evolve, and how those processes gave rise to the patterns of variation observed between species. Since interspecific variation often arises over millions of years, the tempo and mode of these processes cannot typically be observed directly or reproduced experimentally. Instead, they may be studied through a statistical framework called the phylogenetic comparative method. This dissertation focuses on phylogenetic models for two classes of traits: species geographical distributions (or biogeographic traits) and quantitative traits. The following contributions represent methodological advances that serve to render longstanding theoretical questions vulnerable to statistical analysis.
Chapter 1 develops an inference method to efficiently estimate historical biogeographic patterns using data augmented Markov chain Monte Carlo. This strategy increases the feasible number of areas per analysis from the tens to the thousands. Taking advantage of this increased resolution, the work introduces parameterizations for distance-dependent dispersal effects to greatly reduce model complexity. Analyzing Malesian Vireya (subgenus Rhododendron) biogeography, the method recovers Wallace’s Line and Lydekker’s Line as important geographical dispersal barriers, as well as ancestral range estimates for the clade.
Chapter 2 presents a technique called biogeographic dating that leverages paleogeographical information to estimate speciation events in absolute time. To achieve this, I construct a time-heterogeneous continuous-time Markov chain for the dispersal process, whose rate matrix takes values that are empirically informed by paleocontinental adjacencies. For biogeographic evolution, the time-heterogeneous process restores rate-time identifiability, thus enabling the estimation of absolute speciation times. Informed by the current paleogeographical literature, I construct an empirical dispersal graph using 25 areas and 26 epochs between the Cambrian (540 Ma) and the present (0 Ma). Applying biogeographic dating to Testudines (crown turtles), I recover a root age concordant with fossil-based estimates (≈205 Ma) to validate the efficacy of the method.
Chapter 3 introduces a class of models of continuous trait evolution that permit bursts of evolutionary change (“jumps”). Darwin’s original conception of evolution proposed that species evolve gradually over time, which is typically modeled as a Brownian motion. However, many evolutionary mechanisms produce bursts in trait variation as punctuated change of large effect, such as rapid adaptation. I use Lévy processes to model these effects, which are a flexible class of stochastic processes that produce gradual and/or punctuational patterns of change. Applying a data augmented Bayesian method to primates, I show that body mass and endocranial volume measurements both bear the signature of evolution with jumps.
