Abstract

Introduction to Mathematical Foundations of Molecular Phylogenetics

Tandy Warnow
University of Texas at Austin

In this introduction, I will cover some basic mathematical concepts and
techniques in molecular phylogenetics. I will explain the basic
stochastic models of molecular evolution and basic techniques used to
estimate phylogenies, including distance-based methods, maximum parsimony,
maximum likelihood, and Bayesian MCMC. I will concepts such as statistical
consistency, identifiability, and sequence length requirements of phylogeny
estimation methods. Multiple sequence alignment is an integral part of
phylogeny estimation, and so I will also describe some of the basic issues
in estimating alignments. I will provide some mathematical foundations for
analyzing phylogeny reconstruction methods and also explain how methods are
evaluated in practice (on real and simulated data). I will also briefly
describe work in advanced topics, including reticulate (non-treelike)
evolution, estimating species trees from sets of discordant gene trees,
genome-scale phylogeny estimation, supertree methods, and metagenomics.
This introduction will include material of interest to mathematicians
and statisticians, but will also seek to explain current research issues
of relevance to the practicing molecular evolutionary biologist.