Predicting the past: Mathematical models and numerical methods in molecular phylogenetics

Molecular phylogenetics is the study of phylogenies and processes of evolution by the analyses of DNA or amino acid sequence data. In this thesis we describe a computationally efficient Bayesian methodology for inferring species trees and demographics from unlinked binary markers. The new diffusion approach coupled with state-of-the-art numerical algorithms allow for analyses of datasets containing hundreds or even thousands of individuals. We demonstrate the scale of analyses possible using a SNP data sampled from 399 fresh water turtles in 41 populations. The method, which we call Snapper, is the successor of the coalescent based method Snapp. A reanalysis of soybean SNP data demonstrates that the two methods are hard to distinguish in practice. We also describe a Bayesian methodology for inferring niches of present and ancestral species of plants from environmental measurements and estimated phylogenies. Fitting the phylogenetic niche model to three conifer species endemic to New Zealand confirms that viable ancestral niches can be inferred. Lastly, in anticipation of even larger genomic datasets we look into graphical processing units as computational tools for efficient model fitting. We introduce a new graphical processing unit based algorithm designed to fit long chain Hidden Markov models, applying this approach to an Hidden Markov model for nonvolcanic tremor events. Our implementation resulted in a 1000-fold increase in speed over the standard single processing algorithm, allowing for a full Bayesian inference of model parameters