Phylogeny construction and consensus methods

The study of evolutionary relationships is an important endeavour in many areas of science like molecular systematics, parasitology, biogeography, and historical linguistics, to name a few. The evolutionary relationships of a set of objects (whether genes, proteins, biological species, languages, etc.) are typically modelled using rooted trees in which the objects from the given set are at the leaves, and the internal nodes hypothesize ancestors. Such trees are called phylogenies. Phylogenies are constructed using different kinds of data, and are evaluated using various criteria. This dissertation describes various methods for phylogeny construction, and examines some of the issues involved, including computational and statistical. The contributions can be divided into three parts. Input data to phylogeny construction methods are frequently in the form of characters. Characters describe aspects (or features) of the set of objects. The first part of the dissertation describes new methods and algorithms to deal with a special kind of character data (polymorphic characters) arising in domains like historical linguistics and biology. The second part deals with the problem of obtaining a consensus phylogeny from a set of phylogenies. Optimization criteria are typically used to evaluate the fit of a phylogeny to a given data set. Searching the space of phylogenies to optimize the evaluation criterion very often results in several phylogenies which fit the data equally well. Consensus methods serve as a way of combining features that are common to these phylogenies. We introduce a new model for computing the consensus of phylogenies called Local Consensus, and show that this model has many appealing features as a consensus model. The third part of this dissertation deals with a simulation study done to assess the performance of phylogeny construction methods in the context of estimating the topology of the true phylogeny. We consider several promising methods for phylogeny construction, including standard methods like parsimony (in conjunction with several consensus methods) and neighbour joining. Based on the observations from this simulation study, we develop two approaches to obtain better topology estimates of the true phylogeny