Outputs (44)

Lost in space? Generalising subtree prune and regraft to spaces of phylogenetic networks (2017)
Journal Article
Bordewich, M., Linz, S., & Semple, C. (2017). Lost in space? Generalising subtree prune and regraft to spaces of phylogenetic networks. Journal of Theoretical Biology, 423, 1-12. https://doi.org/10.1016/j.jtbi.2017.03.032

Over the last fifteen years, phylogenetic networks have become a popular tool to analyse relationships between species whose past includes reticulation events such as hybridisation or horizontal gene transfer. However, the space of phylogenetic netwo... Read More about Lost in space? Generalising subtree prune and regraft to spaces of phylogenetic networks.

An algorithm for reconstructing ultrametric tree-child networks from inter-taxa distances (2016)
Journal Article
Bordewich, M., & Tokac, N. (2016). An algorithm for reconstructing ultrametric tree-child networks from inter-taxa distances. Discrete Applied Mathematics, 213, 47-59. https://doi.org/10.1016/j.dam.2016.05.011

Traditional “distance based methods” reconstruct a phylogenetic tree from a matrix of pair-wise distances between taxa. A phylogenetic network is a generalisation of a phylogenetic tree that can describe evolutionary events such as reticulation and h... Read More about An algorithm for reconstructing ultrametric tree-child networks from inter-taxa distances.

On the Fixed Parameter Tractability of Agreement-based Phylogenetic Distances (2016)
Journal Article
Bordewich, M., Scornavacca, C., Tokac, N., & Weller, M. (2017). On the Fixed Parameter Tractability of Agreement-based Phylogenetic Distances. Journal of Mathematical Biology, 74(1), 239-257. https://doi.org/10.1007/s00285-016-1023-3

Three important and related measures for summarizing the dissimilarity in phylogenetic trees are the minimum number of hybridization events required to fit two phylogenetic trees onto a single phylogenetic network (the hybridization number), the (roo... Read More about On the Fixed Parameter Tractability of Agreement-based Phylogenetic Distances.

Reticulation-Visible Networks (2016)
Journal Article
Bordewich, M., & Semple, C. (2016). Reticulation-Visible Networks. Advances in Applied Mathematics, 78, 114-141. https://doi.org/10.1016/j.aam.2016.04.004

Let X be a finite set, N be a reticulation-visible network on X , and T be a rooted binary phylogenetic tree. We show that there is a polynomial-time algorithm for deciding whether or not N displays T. Furthermore, for all |X|≥1, we show that N has a... Read More about Reticulation-Visible Networks.

Determining phylogenetic networks from inter-taxa distances (2015)
Journal Article
Bordewich, M., & Semple, C. (2016). Determining phylogenetic networks from inter-taxa distances. Journal of Mathematical Biology, 73(2), 283-303. https://doi.org/10.1007/s00285-015-0950-8

We consider the problem of determining the topological structure of a phylogenetic network given only information about the path-length distances between taxa. In particular, one of the main results of the paper shows that binary tree-child networks... Read More about Determining phylogenetic networks from inter-taxa distances.

Defining a Phylogenetic Tree with the Minimum Number of r-State Characters (2015)
Journal Article
Bordewich, M., & Semple, C. (2015). Defining a Phylogenetic Tree with the Minimum Number of r-State Characters. SIAM Journal on Discrete Mathematics, 29(2), 835-853. https://doi.org/10.1137/130924469

Semple and Steel (2002) showed that if T is a phylogenetic X-tree and C is a collection of r-state characters that defines T , then |C| ≥ (n − 3)/(r − 1), where n = |X|. In this paper, we show that, provided n is sufficiently large, this lower bound... Read More about Defining a Phylogenetic Tree with the Minimum Number of r-State Characters.

Subset Glauber Dynamics on Graphs, Hypergraphs and Matroids of Bounded Tree-Width (2014)
Journal Article
Bordewich, M., & Kang, R. (2014). Subset Glauber Dynamics on Graphs, Hypergraphs and Matroids of Bounded Tree-Width. Electronic Journal of Combinatorics, 21(4), Article 19

Motivated by the `subgraphs world' view of the ferromagnetic Ising model, we analyse the mixing times of Glauber dynamics based on subset expansion expressions for classes of graph, hypergraph and matroid polynomials. With a canonical paths argument,... Read More about Subset Glauber Dynamics on Graphs, Hypergraphs and Matroids of Bounded Tree-Width.

Mixing of the Glauber Dynamics for the Ferromagnetic Potts Model (2014)
Journal Article
Bordewich, M., Greenhill, C., & Patel, V. (2016). Mixing of the Glauber Dynamics for the Ferromagnetic Potts Model. Random Structures and Algorithms, 48(1), 21-52. https://doi.org/10.1002/rsa.20569

We present several results on the mixing time of the Glauber dynamics for sampling from the Gibbs distribution in the ferromagnetic Potts model. At a fixed temperature and interaction strength, we study the interplay between the maximum degree (Δ) of... Read More about Mixing of the Glauber Dynamics for the Ferromagnetic Potts Model.

Accuracy Guarantees for Phylogeny Reconstruction Algorithms Based on Balanced Minimum Evolution (2013)
Journal Article
Bordewich, M., & Mihaescu, R. (2013). Accuracy Guarantees for Phylogeny Reconstruction Algorithms Based on Balanced Minimum Evolution. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 10(3), 576-583. https://doi.org/10.1109/tcbb.2013.39

Distance-based phylogenetic methods attempt to reconstruct an accurate phylogenetic tree from an estimated matrix of pairwise distances between taxa. This paper examines two distance-based algorithms (GREEDYBME and FASTME) that are based on the princ... Read More about Accuracy Guarantees for Phylogeny Reconstruction Algorithms Based on Balanced Minimum Evolution.

Budgeted Nature Reserve Selection with diversity feature loss and arbitrary split systems (2012)
Journal Article
Bordewich, M., & Semple, C. (2012). Budgeted Nature Reserve Selection with diversity feature loss and arbitrary split systems. Journal of Mathematical Biology, 64(1), 69-85. https://doi.org/10.1007/s00285-011-0405-9

Arising in the context of biodiversity conservation, the Budgeted Nature Reserve Selection (BNRS) problem is to select, subject to budgetary constraints, a set of regions to conserve so that the phylogenetic diversity (PD) of the set of species conta... Read More about Budgeted Nature Reserve Selection with diversity feature loss and arbitrary split systems.