Novel Mathematical Aspects of Phylogenetic Estimation (2009)
Type of ContentTheses / Dissertations
Degree NameDoctor of Philosophy
PublisherUniversity of Canterbury. Mathematics and Statistics
In evolutionary biology, genetic sequences carry with them a trace of the underlying tree that describes their evolution from a common ancestral sequence. Inferring this underlying tree is challenging. We investigate some curious cases in which different methods like Maximum Parsimony, Maximum Likelihood and distance-based methods lead to different trees. Moreover, we state that in some cases, ancestral sequences can be more reliably reconstructed when some of the leaves of the tree are ignored - even if these leaves are close to the root. While all these findings show problems inherent to either the assumed model or the applied method, sometimes an inaccurate tree reconstruction is simply due to insufficient data. This is particularly problematic when a rapid divergence event occurred in the distant past. We analyze an idealized form of this problem and determine a tight lower bound on the growth rate for the sequence length required to resolve the tree (independent of any particular branch length). Finally, we investigate the problem of intermediates in the fossil record. The extent of ‘gaps’ (missing transitional stages) has been used to argue against gradual evolution from a common ancestor. We take an analytical approach and demonstrate why, under certain sampling conditions, we may not expect intermediates to be found.
Keywordsphylogenetics; maximum parsimony; maximum likelihood; fossils
RightsCopyright Mareike Fischer
Showing items related by title, author, creator and subject.
Wang, Yuancheng (University of Canterbury. Mathematics and Statistics, 2010)Phylogenetics is the research of ancestor-descendant relationships among different groups of organisms, for example, species or populations of interest. The datasets involved are usually sequence alignments of various ...
Mossel, E.; Roch, S.; Steel, M. (University of Canterbury. Mathematics and Statistics, 2009)Ancestral maximum likelihood (AML) is a method that simultaneously reconstructs a phylogenetic tree and ancestral sequences from extant data (sequences at the leaves). The tree and ancestral sequences maximize the probability ...
Inverting random functions (II): explicit bounds for discrete maximum likelihood estimation, with applications Steel, M.A.; Szekely, L.A. (University of Canterbury. Mathematics and Statistics, 2002)In this paper we study inverting randomfunctions under the maximumlik elihood estimation (MLE) criterion in the discrete setting. In particular, we consider how many independent evaluations of the random function at a ...