Realising evolutionary trees with local information

Realising evolutionary trees with local information

Tue, 23/10/2012
16:30 		Charles Semple (University of Canterbury) Combinatorial Theory Seminar Add to calendar SR2
Realising evolutionary trees with local information
Results that say local information is enough to guarantee global information provide the theoretical underpinnings of many reconstruction algorithms in evolutionary biology. Such results include Buneman's Splits-Equivalence Theorem and the Tree-Metric Theorem. The first result says that, for a collection $ \mathcal C $ of binary characters, pairwise compatibility is enough to guarantee compatibility for $ \mathcal C $, that is, there is a phylogenetic (evolutionary) tree that realises $ \mathcal C $. The second result says that, for a distance matrix $ D $, if every $ 4\times 4 $ distance submatrix of $ D $ is realisable by an edge-weighted phylogenetic tree, then $ D $ itself is realisable by such a tree. In this talk, we investigate these and other results of this type. Furthermore, we explore the closely-related task of determining how much information is enough to reconstruct the correct phylogenetic tree.