Phylogenetic combinatorics is a branch of discrete applied mathematics concerned with the mathematical structures related to phylogenetic trees and networks such as graphs, split systems, metrics and tight spans. The goal is to develop the theory that forms the basis of phylogenetic reconstruction methods.
Our work includes a characterization of edge weighted phylogenetic trees in terms of conditions on a set of weighted quartets (i.e. fully resolved phylogenetic trees on just 4 leaves) , the development of closure rules for generating split systems on some set from splits on subsets of that set , and, more recently, we characterize set of partions that can be represented by a phylogenetic tree .
We have also studied phylogenetic trees in terms of their edge-product space , and made significant steps towards developing a decomposition scheme for distances using the the theory of tight spans , which allows one to e.g. express genetic distances in terms of simpler ones . The basis of this scheme is provided in part by the concept of cell-decomposability, which captures a natural way to decompose tight-spans . An introduction to phylogenetic combinatorics is provided in Basic Phylogenetic combinatorics by A. Dress, K.T. Huber, J. Koolen, V. Moulton, and A. Spillner .
- Gruenewald, S., Huber, K.T., Moulton, V., Semple, C., Encoding phylogenetic trees in terms of weighted quartets, Journal of Mathematical Biology, 56(4), 2008, 465-477.
- Gruenewald, S., Huber, K.T., Wu, Q., Two new closure rules for constructing phylogenetic super-networks. Bulletin of Mathematical Biology, 70, 2008, 1906-1924
- Huber, K.T., Moulton, V., Semple, C., Wu, T., Representing partitions on trees,SIAM Journal on Discrete Mathematics, 28(3), 2014, 1132-1172.
- Gill, J., Linusson, S., Moulton, V., Steel, M. A regular decomposition of the edge-product space of phylogenetic treesAdvances, in Applied Mathematics, 41, 2008, 158-176
- Dress, A., Moulton, V., Terhalle, W., T-Theory, The European Journal of Combinatorics, 17, 1996, 161-175.
- Dress, A., Huber, K.T., Koolen, J., Moulton, V., Compatible decompositions and block realizations of finite metrics, European Journal of Combinatorics. 29(7), 2008, 1617-1633
- Huber, K.T., Koolen, J., Moulton, V., Spillner, A., Characterizing cell-decomposable metrics,The Electronic Journal of Combinatorics 15(1), 2008.
- Dress, A., Huber, K.T., Koolen, J. Moulton, V. and Spillner, A., Basic Phylogenetic combinatorics, Cambridge University Press, 2012.