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Seminar presented at the Maths Department, University of Portsmouth, 19th November 2014
Evolutionary biologists represent actual or hypothesised evolutionary relations between living organisms using phylogenies, directed bifurcating graphs (trees) that describe evolutionary processes in terms of speciation or splitting events (nodes) and elapsed evolutionary time or distance (edges). Molecular evolution itself is largely dominated by mutations in DNA sequences, a stochastic process. Traditionally, probabilistic models of molecular evolution and phylogenies are fitted to DNA sequence data by maximum likelihood on the assumption that a single simple phylogeny will serve to approximate the evolution of a majority of DNA positions in the dataset. However modern studies now routinely sample several orders of magnitude more DNA positions, and this assumption no longer holds. Unfortunately, our conception of ‘tree space’ - a notional multidimensional surface containing all possible phylogenies - is extremely imprecise, and similarly techniques to model phylogeny model fitting in very large datasets are limited. I will show the background to this field and present some of the challenges arising from the present limited analytical framework.