Phylogenetic Trees and Their Analysis

Determining the best possible evolutionary history, the lowest-cost phylogenetic tree, to fit a given set of taxa and character sequences using maximum parsimony is an active area of research due to its underlying importance in understanding biological processes. As several steps in this process are NP-Hard when using popular, biologically-motivated optimality criteria, significant amounts of resources are dedicated to both both heuristics and to making exact methods more computationally tractable. We examine both phylogenetic data and the structure of the search space in order to suggest methods to reduce the number of possible trees that must be examined to find an exact solution for any given set of taxa and associated character data. Our work on four related problems combines theoretical insight with empirical study to improve searching of the tree space. First, we show that there is a Hamiltonian path through tree space for the most common tree metrics, answering Bryant\u27s Challenge for the minimal such path. We next examine the topology of the search space under various metrics, showing that some metrics have local maxima and minima even with perfect data, while some others do not. We further characterize conditions for which sequences simulated under the Jukes-Cantor model of evolution yield well-behaved search spaces. Next, we reduce the search space needed for an exact solution by splitting the set of characters into mutually-incompatible subsets of compatible characters, building trees based on the perfect phylogenies implied by these sets, and then searching in the neighborhoods of these trees. We validate this work empirically. Finally, we compare two approaches to the generalized tree alignment problem, or GTAP: Sequence alignment followed by tree search vs. Direct Optimization, on both biological and simulated data

Statistical approaches to viral phylodynamics

The recent years have witnessed a rapid increase in the quantity and quality of genomic data collected from human and animal pathogens, viruses in particular. When coupled with mathematical and statistical models, these data allow us to combine evolutionary theory and epidemiology to understand pathogen dynamics. While these developments led to important epidemiological questions being tackled, it also exposed the need for improved analytical methods. In this thesis I employ modern statistical techniques to address two pressing issues in phylodynamics: (i) computational tools for Bayesian phylogenetics and (ii) data integration. I detail the development and testing of new transition kernels for Markov Chain Monte Carlo (MCMC) for time-calibrated phylogenetics in Chapter 2 and show that an adaptive kernel leads to improved MCMC performance in terms of mixing for a range of data sets, in particular for a challenging Ebola virus phylogeny with 1610 taxa/sequences. As a trade-off, I also found that the new adaptive kernels have longer warm up times in general, suggesting room for improvement. Chapter 3 shows how to apply state-of-the-art techniques to visualise and analyse phylogenetic space and MCMC for time-calibrated phylogenies, which are crucial to the viral phylodynamics analysis pipeline. I describe a pipeline for a typical phylodynamic analysis which includes convergence diagnostics for continuous parameters and in phylogenetic space, extending existing methods to deal with large time-calibrated phylogenies. In addition I investigate different representations of phylogenetic space through multi-dimensional scaling (MDS) or univariate distributions of distances to a focal tree and show that even for the simplest toy examples phylogenetic space remains complex and in particular not all metrics lead to desirable or useful representations. On the data integration front, Chapters 4 and 5 detail the use data from the 2013-2016 Ebola virus disease (EVD) epidemic in West Africa to show how one can combine phylogenetic and epidemiological data to tackle epidemiological questions. I explore the determinants of the Ebola epidemic in Chapter 4 through a generalised linear model framework coupled with Bayesian stochastic search variable selection (BSSVS) to assess the relative importance climatic and socio-economic variables on EVD number of cases. In Chapter 5 I tackle the question of whether a particular glycoprotein mutation could lead to increased human mortality from EVD. I show that a principled analysis of the available data that accounts for several sources of uncertainty as well as shared ancestry between samples does not allow us to ascertain the presence of such effect of a viral mutation on mortality. Chapter 6 attempts to bring the findings of the thesis together and discuss how the field of phylodynamics, in special its methodological aspect, might move forward