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- J G Sumner, M A Charleston, L S Jermiin, P D Jarvis
- Journal of theoretical biology
- 2008

We explore model-based techniques of phylogenetic tree inference exercising Markov invariants. Markov invariants are group invariant polynomials and are distinct from what is known in the literature as phylogenetic invariants, although we establish a commonality in some special cases. We show that the simplest Markov invariant forms the foundation of the… (More)

- J G Sumner, J Fernández-Sánchez, P D Jarvis
- Journal of theoretical biology
- 2012

Recent work has discussed the importance of multiplicative closure for the Markov models used in phylogenetics. For continuous-time Markov chains, a sufficient condition for multiplicative closure of a model class is ensured by demanding that the set of rate-matrices belonging to the model class form a Lie algebra. It is the case that some well-known Markov… (More)

- Jeremy G Sumner, Peter D Jarvis, Jesús Fernández-Sánchez, Bodie T Kaine, Michael D Woodhams, Barbara R Holland
- Systematic biology
- 2012

The general time-reversible (GTR) model (Tavaré, 1986) has been the workhorse of molecular phylogenetics for the last decade. GTR sits at the top of the ModelTest hierarchy of models (Posada & Crandall, 1998) and, usually with the addition of invariant sites and a gamma distribution of rates across sites, is currently by far the most commonly selected model… (More)

- J G Sumner, P D Jarvis
- Journal of mathematical biology
- 2005

It is possible to consider stochastic models of sequence evolution in phylogenetics in the context of a dynamical tensor description inspired from physics. Approaching the problem in this framework allows for the well developed methods of mathematical physics to be exploited in the biological arena. We present the tensor description of the homogeneous… (More)

- J G Sumner, B R Holland, P D Jarvis
- Bulletin of mathematical biology
- 2012

It is known that the Kimura 3ST model of sequence evolution on phylogenetic trees can be extended quite naturally to arbitrary split systems. However, this extension relies heavily on mathematical peculiarities of the associated Hadamard transformation, and providing an analogous augmentation of the general Markov model has thus far been elusive. In this… (More)

- J G Sumner, P D Jarvis
- Journal of theoretical biology
- 2009

The purpose of this article is to show how the isotropy subgroup of leaf permutations on binary trees can be used to systematically identify tree-informative invariants relevant to models of phylogenetic evolution. In the quartet case, we give an explicit construction of the full set of representations and describe their properties. We apply these results… (More)

- Jesús Fernández-Sánchez, Jeremy G Sumner, Peter D Jarvis, Michael D Woodhams
- Journal of mathematical biology
- 2015

Continuous-time Markov chains are a standard tool in phylogenetic inference. If homogeneity is assumed, the chain is formulated by specifying time-independent rates of substitutions between states in the chain. In applications, there are usually extra constraints on the rates, depending on the situation. If a model is formulated in this way, it is possible… (More)

- J G Sumner, P D Jarvis
- Mathematical biosciences
- 2006

Distance based algorithms are a common technique in the construction of phylogenetic trees from taxonomic sequence data. The first step in the implementation of these algorithms is the calculation of a pairwise distance matrix to give a measure of the evolutionary change between any pair of the extant taxa. A standard technique is to use the log det formula… (More)

The purpose of this article is to show how the isotropy subgroup of leaf permutations on binary trees can be used to systematically identify tree-informative invariants relevant to models of phylogenetic evolution. In the quartet case, we give an explicit construction of the full set of representations and describe their properties. We apply these results… (More)

- J G Sumner
- 2007

This thesis develops and expands upon known techniques of mathematical physics relevant to the analysis of the popular Markov model of phylogenetic trees required in biology to reconstruct the evolutionary relationships of taxonomic units from biomolecular sequence data. The techniques of mathematical physics are plethora and have been developed for some… (More)