Phylogenetics
The accurate reconstruction of phylogenetic trees is of great importance to biologists. Although much is known about the construction of such trees there are still surprisingly many unanswered and little understood computational and mathematical problems concerning such trees. This, coupled with new kinds of data (e.g. gene order, large data sets, and whole genome data), makes it vital to unify and develop the underlying principles that are routinely used to construct phylogenetic trees and related structures.
Much of our work in phylogenetics concerns a generalization of phylogenetic trees called phylogenetic networks. It is becoming ever more apparent that phylogenetic trees do not provide a suitable model for the evolution of certain organisms. For example, recombination in viruses, lateral gene transfer in bacteria, and hybridization in plants are all processes that are not necessarily best modelled using trees. Using combinatorial and algorithmic techniques we have provided ground-breaking techniques for analysing and modelling biological data from such organisms using phylogenetic networks. This has resulted in new algorithms implemented in software packages such as SplitsTree and SpectroNet, that are regularly used by biologists to analyse their data.
In addition, we work in phylogenetic combinatorics, an emerging branch of discrete mathematics, which is concerned with the combinatorial description, analysis and structure of phylogenetic trees, phylogenetic networks, and associated mathematical structures. Recently, we ran an international conference "Phylogenetic combinatorics and its applications" that brought together several researchers working in this and related areas.
We have various international collaborators in phylogenetics, including Daniel Huson at Tuebingen University, Germany, Jack Koolen at POSTECH Mathematics, Korea, and Charles Semple and Mike Steel at the Biomathematics Research Centre, University of Canterbury, New Zealand.