## Profiles

# Jeremy Sumner

# Jeremy Sumner

## Senior Research Fellow & Senior Lecturer

ARC DECRA Fellow

Room 407 , Maths-Physics Building

Dr Jeremy Sumner is a Lecturer and ARC Discovery Early Career Fellow in the School of Physical Sciences and a member of the UTAS Theoretical Phylogenetics Research Group. His research interests revolve around applications of algebraic methods to phylogenetic models. Phylogenetics is concerned with the statistical inference of the evolutionary history of present-day organisms from molecular data, such as DNA. His specialty is exploiting the symmetries inherent in the problem by applying algebraic methods such as group representation theory to analyse and improve phylogenetic methodologies.

### Biography

Between March 2007 to May 2008, Jeremy held a post-doctoral position at the University of Sydney working under the supervision of A/Prof Michael Charleston (School of IT) and Prof Lars Jermiin (School of Biological Sciences). Between June 2008 and October 2011, he was awarded an ARC Post-Doctoral Fellowship working with Reader Peter Jarvis at UTAS on the Discovery Project 'Markov invariants and phylogenetic reconstruction'. The content of this project was a direct continuation of the research he conducted during his PhD on Markov invariants, which are group invariant polynomials useful to the context of Markov models of DNA evolution. In January 2012, he was appointed on a fixed-term basis as a lecturer in statistics and a post-doctoral researcher at UTAS. In November that year, he was awarded a highly-competitive ARC Discovery Early Career Research Award (DECRA) for the project 'Group theory and Phylogenetics: Using symmetry to uncover evolutionary history'. The project focuses on the development and implementation of the so-called 'Lie-Markov' models of DNA evolution, particularly those which respect the grouping of DNA nucleotides into purines and pyrimidines. Since December 2013, Jeremy has held a permanent position as a lecturer in the School of Physical Sciences.

### Career summary

#### Qualifications

Degree | Thesis Title | University | Country | Date of Award |
---|---|---|---|---|

PhD | Entanglement, invariants, and phylogenetics | University of Tasmania | Australia | 11/09/2007 |

BSc (1^{st} Class Hons) | Polar decomposition of a Dirac spinor | University of Tasmania | Australia | 1/11/2001 |

### Memberships

#### Professional practice

- 2013-2016: UTAS representative on the Australian Mathematical Society Council

### Teaching

Statistics, Algebra, Group Theory, Representation Theory

#### Teaching responsibility

View more on Dr Jeremy Sumner in WARP

### Expertise

- Phylogenetic methods
- Group representation theory

### Research Themes

Jeremy's research in phylogenetics has primarily been based around the introduction of new mathematical methods to molecular biology; in particular algebraic methods more usually applied in theoretical physics. Taken as a whole, phylogenetics is the suite of computational and statistical techniques used by biologists to infer the past evolutionary history of organisms given present-day molecular data such as DNA. With modern DNA sequencing methods producing ever increasing amounts of data at a fraction of previous costs, over the past few decades there has been a pressing need for the development of mathematical and statistical methods to analyse this data under the evolutionary presumption of decent from a common ancestor.

By far the most difficult problem in phylogenetics is the correct inference of the evolutionary tree that relates presently observed organisms. Fundamental to this problem is the correct estimation of the rate at which DNA mutations arise under the assumption of a random process. From the mathematical point of view, this entails assuming what is known as a Markov process which in turn boils down to the estimation of a 'matrix' of nucleotide substitution rates for random changes such as *A* (adenine) goes to *C* (cytosene). For reasons of statistical efficiency and tractability, these rates are for the most part assumed to be constant in time. Of course, the historical reality is that molecular evolution is more complicated than this and one would like to ensure that the modelling simplifications made are at least *consistent *with this more complicated reality. Remarkably, the demand for consistency means that one must obtain a certain type of mathematical closure of the substitution matrices under standard algebraic operations of matrix addition and multiplication. Together with his co-authors, Jeremy has solved this problem through the development the so-called Lie-Markov models of DNA substitutions. The development of these models, together with related algebraic methods applied to phylogenetics, has formed the foundation of his research career.

### Collaboration

Jeremy is a member of the UTAS Theoretical Phylogenetic Research Group. The group organises the annual conference *Phylomania: The UTAS theoretical phylogenetics meeting*. This meeting brings together international researchers with a strong theoretical leaning, with the aim of discussing some of the more pressing problems in phylogenetics.

### Current projects

Jeremy is currently chief investigator on two ARC Discovery projects:

- 2015-2018: 'Algebraically informed models of biological sequence evolution'
- 2013-2016: 'Group theory and Phylogenetics: Using symmetry to uncover evolutionary history'

### Fields of Research

- Biological mathematics (490102)
- Other physical sciences (519999)
- Phylogeny and comparative analysis (310410)
- Molecular evolution (310510)
- Group theory and generalisations (490405)
- Stochastic analysis and modelling (490510)
- Biological physics (510501)
- Health services and systems (420399)
- Biostatistics (490502)
- Numerical analysis (490302)
- Statistical theory (490509)
- Genetic immunology (310507)
- Algebraic and differential geometry (490402)
- Gene expression (incl. microarray and other genome-wide approaches) (310505)
- Applied statistics (490501)

### Research Objectives

- Expanding knowledge in the mathematical sciences (280118)
- Expanding knowledge in the physical sciences (280120)
- Expanding knowledge in the biological sciences (280102)
- Expanding knowledge in the environmental sciences (280111)
- Information systems, technologies and services (220499)
- Terrestrial biodiversity (180606)

## Publications

Total publications

37

### Highlighted publications

(2 outputs)Year | Type | Citation | Altmetrics |
---|---|---|---|

2012 | Journal Article | Sumner JG, Fernandez-Sanchez J, Jarvis PD, 'Lie Markov models', Journal of Theoretical Biology, 298 pp. 16-31. ISSN 1095-8541 (2012) [Refereed Article] DOI: 10.1016/j.jtbi.2011.12.017 [eCite] [Details] Citations: Scopus - 40Web of Science - 39 Co-authors: Jarvis PD | |

2008 | Journal Article | Sumner JG, Charleston MA, Jermiin LS, Jarvis PD, 'Markov invariants, plethysms, and phylogenetics', Journal of Theoretical Biology, 253, (3) pp. 601-615. ISSN 0022-5193 (2008) [Refereed Article] DOI: 10.1016/j.jtbi.2008.04.001 [eCite] [Details] Citations: Scopus - 21Web of Science - 19 Co-authors: Jarvis PD |

### Journal Article

(33 outputs)Year | Citation | Altmetrics |
---|---|---|

2021 | Jarvis PD, Sumner JG, 'Correction to: Matrix group structure and Markov invariants in the strand symmetric phylogenetic substitution model (Journal of Mathematical Biology, (2016), 73, 2, (259-282), 10.1007/s00285-015-0951-7)', Journal of Mathematical Biology, 82, (7) Article 68. ISSN 0303-6812 (2021) [Contribution to Refereed Journal] DOI: 10.1007/s00285-021-01625-y [eCite] [Details] Co-authors: Jarvis PD | |

2020 | Baake M, Sumner J, 'Notes on Markov embedding', Linear Algebra and Its Applications, 594 pp. 262-299. ISSN 0024-3795 (2020) [Refereed Article] DOI: 10.1016/j.laa.2020.02.016 [eCite] [Details] Citations: Scopus - 2Web of Science - 2 | |

2020 | Shore JA, Holland BR, Sumner JG, Nieselt K, Wills PR, 'The ancient operational code is embedded in the amino acid substitution matrix and aaRS phylogenies', Journal of Molecular Evolution, 88, (2) pp. 136-150. ISSN 0022-2844 (2020) [Refereed Article] DOI: 10.1007/s00239-019-09918-z [eCite] [Details] Citations: Scopus - 3Web of Science - 4 Co-authors: Shore JA; Holland BR | |

2020 | Shore JA, Sumner JG, Holland BR, 'The impracticalities of multiplicativelyclosed codon models: a retreat to linear alternatives', Journal of Mathematical Biology pp. 1-25. ISSN 0303-6812 (2020) [Refereed Article] DOI: 10.1007/s00285-020-01519-5 [eCite] [Details] Co-authors: Shore JA; Holland BR | |

2019 | Jarvis PD, Sumner JG, 'Systematics and symmetry in molecular phylogenetic modelling: perspectives from physics', Journal of Physics A: Mathematical and Theoretical, 52, (45) Article 453001. ISSN 1751-8113 (2019) [Refereed Article] DOI: 10.1088/1751-8121/ab305b [eCite] [Details] Co-authors: Jarvis PD | |

2018 | Mitchell JD, Sumner JG, Holland BR, 'Distinguishing between convergent evolution and violation of the molecular clock for three taxa', Systematic Biology, 67, (5) pp. 905-915. ISSN 1063-5157 (2018) [Refereed Article] DOI: 10.1093/sysbio/syy038 [eCite] [Details] Citations: Scopus - 1Web of Science - 32 Co-authors: Mitchell JD; Holland BR | |

2018 | Sumner JG, Woodhams MD, 'Lie-Markov models derived from finite semigroups', Bulletin of Mathematical Biology, 81, (2) pp. 361-383. ISSN 0092-8240 (2018) [Refereed Article] DOI: 10.1007/s11538-018-0455-x [eCite] [Details] Citations: Scopus - 2Web of Science - 9 Co-authors: Woodhams MD | |

2018 | Terauds V, Sumner J, 'Maximum likelihood estimates of rearrangement distance: implementing a representation-theoretic approach', Bulletin of Mathematical Biology, 81, (2) pp. 535-567. ISSN 0092-8240 (2018) [Refereed Article] DOI: 10.1007/s11538-018-0511-6 [eCite] [Details] Citations: Scopus - 4Web of Science - 9 Co-authors: Terauds V | |

2017 | Serdoz S, Egri-Nagy A, Sumner J, Holland BR, Jarvis PD, et al., 'Maximum likelihood estimates of pairwise rearrangement distances', Journal of Theoretical Biology, 423 pp. 31-40. ISSN 0022-5193 (2017) [Refereed Article] DOI: 10.1016/j.jtbi.2017.04.015 [eCite] [Details] Citations: Scopus - 8Web of Science - 8 Co-authors: Holland BR; Jarvis PD | |

2017 | Sumner JG, 'Dimensional reduction for the General Markov Model on phylogenetic trees', Bulletin of Mathematical Biology, 79 pp. 619-634. ISSN 0092-8240 (2017) [Refereed Article] DOI: 10.1007/s11538-017-0249-6 [eCite] [Details] Citations: Scopus - 2Web of Science - 2 | |

2017 | Sumner JG, 'Multiplicatively closed Markov models must form Lie algebras', ANZIAM Journal, 59, (2) pp. 240-246. ISSN 1446-1811 (2017) [Refereed Article] DOI: 10.1017/S1446181117000359 [eCite] [Details] Citations: Scopus - 6Web of Science - 2 | |

2017 | Sumner JG, Jarvis PD, Francis AR, 'A representation-theoretic approach to the calculation of evolutionary distance in bacteria', Journal of Physics A: Mathematical and Theoretical, 50 Article 335601. ISSN 1751-8121 (2017) [Refereed Article] DOI: 10.1088/1751-8121/aa7d60 [eCite] [Details] Citations: Scopus - 7Web of Science - 6 Co-authors: Jarvis PD | |

2017 | Sumner JG, Taylor A, Holland BR, Jarvis PD, 'Developing a statistically powerful measure for quartet tree inference using phylogenetic identities and Markov invariants', Journal of Mathematical Biology, 75, (6-7) pp. 1619-1654. ISSN 0303-6812 (2017) [Refereed Article] DOI: 10.1007/s00285-017-1129-2 [eCite] [Details] Citations: Scopus - 2Web of Science - 2 Co-authors: Holland BR; Jarvis PD | |

2016 | Jarvis PD, Sumner JG, 'Matrix group structure and Markov invariants in the strand symmetric phylogenetic substitution model', Journal of Mathematical Biology, 73 pp. 259-282. ISSN 0303-6812 (2016) [Refereed Article] DOI: 10.1007/s00285-015-0951-7 [eCite] [Details] Citations: Scopus - 6Web of Science - 6 Co-authors: Jarvis PD | |

2015 | Fernandez-Sanchez J, Sumner JG, Jarvis PD, Woodhams MD, 'Lie Markov models with purine/pyrimidine symmetry', Journal of Mathematical Biology, 70, (4) pp. 855-891. ISSN 0303-6812 (2015) [Refereed Article] DOI: 10.1007/s00285-014-0773-z [eCite] [Details] Citations: Scopus - 16Web of Science - 13 Co-authors: Jarvis PD; Woodhams MD | |

2015 | Woodhams MD, Fernandez-Sanchez J, Sumner JG, 'A new hierarchy of phylogenetic models consistent with heterogeneous substitution rates', Systematic Biology, 64, (4) pp. 638-650. ISSN 1063-5157 (2015) [Refereed Article] DOI: 10.1093/sysbio/syv021 [eCite] [Details] Citations: Scopus - 19Web of Science - 18 Co-authors: Woodhams MD | |

2014 | Jarvis PD, Sumner JG, 'Adventures in invariant theory', ANZIAM Journal, 56, (2) pp. 105-115. ISSN 1446-1811 (2014) [Refereed Article] DOI: 10.1017/S1446181114000327 [eCite] [Details] Citations: Scopus - 5Web of Science - 5 Co-authors: Jarvis PD | |

2014 | Sumner JG, Jarvis PD, Holland BR, 'A tensorial approach to the inversion of group-based phylogenetic models', BMC Evolutionary Biology, 14 Article 236. ISSN 1471-2148 (2014) [Refereed Article] DOI: 10.1186/s12862-014-0236-6 [eCite] [Details] Citations: Scopus - 1Web of Science - 1 Co-authors: Jarvis PD; Holland BR | |

2013 | Allman ES, Jarvis PD, Rhodes JA, Sumner JG, 'Tensor rank, invariants, inequalities, and applications', Journal on Matrix Analysis and Applications, 34, (3) pp. 1014-1045. ISSN 0895-4798 (2013) [Refereed Article] DOI: 10.1137/120899066 [eCite] [Details] Citations: Scopus - 13Web of Science - 11 Co-authors: Jarvis PD | |

2013 | Holland BR, Jarvis PD, Sumner JG, 'Low-parameter phylogenetic inference under the general Markov model', Systematic Biology, 62, (1) pp. 78-92. ISSN 1063-5157 (2013) [Refereed Article] DOI: 10.1093/sysbio/sys072 [eCite] [Details] Citations: Scopus - 18Web of Science - 18 Co-authors: Holland BR; Jarvis PD | |

2013 | Sumner JG, 'Lie geometry of 2 x 2 Markov matrices', Journal of Theoretical Biology, 327 pp. 88-90. ISSN 0022-5193 (2013) [Refereed Article] DOI: 10.1016/j.jtbi.2013.01.026 [eCite] [Details] Citations: Scopus - 3Web of Science - 4 | |

2012 | Jarvis PD, Sumner JG, 'Markov Invariants for Phylogenetic Rate Matrices Derived from Embedded Submodels', IEEE/ACM Transactions on Computational Biology and Bioinformatics, 9, (3) pp. 828-836. ISSN 1545-5963 (2012) [Refereed Article] DOI: 10.1109/TCBB.2012.24 [eCite] [Details] Citations: Scopus - 5Web of Science - 5 Co-authors: Jarvis PD | |

2012 | Sumner JG, Fernandez-Sanchez J, Jarvis PD, 'Lie Markov models', Journal of Theoretical Biology, 298 pp. 16-31. ISSN 1095-8541 (2012) [Refereed Article] DOI: 10.1016/j.jtbi.2011.12.017 [eCite] [Details] Citations: Scopus - 40Web of Science - 39 Co-authors: Jarvis PD | |

2012 | Sumner JG, Holland BR, Jarvis PD, 'The Algebra of the General Markov Model on Phylogenetic Trees and Networks', Bulletin of Mathematical Biology, 74, (4) pp. 858-880. ISSN 1522-9602 (2012) [Refereed Article] DOI: 10.1007/s11538-011-9691-z [eCite] [Details] Citations: Scopus - 11Web of Science - 11 Co-authors: Holland BR; Jarvis PD | |

2012 | Sumner JG, Jarvis PD, Fernandez-Sanchez J, Kaine BT, Woodhams MD, et al., 'Is the general time-reversible model bad for molecular phylogenetics?', Systematic Biology, 61, (6) pp. 1069-1074. ISSN 1063-5157 (2012) [Refereed Article] DOI: 10.1093/sysbio/sys042 [eCite] [Details] Citations: Scopus - 31Web of Science - 31 Co-authors: Jarvis PD; Kaine BT; Woodhams MD; Holland BR | |

2010 | Sumner JG, Charleston M, 'Phylogenetic estimation with partial likelihood tensors', Journal of Theoretical Biology: An International Multidisciplinary Journal, 262, (3) pp. 413-424. ISSN 0022-5193 (2010) [Refereed Article] DOI: 10.1016/j.jtbi.2009.09.037 [eCite] [Details] Citations: Scopus - 6Web of Science - 6 | |

2009 | Sumner JG, Jarvis PD, 'Markov invariants and the isotropy subgroup of a quartet tree', Journal of Theoretical Biology, 258, (2) pp. 302-310. ISSN 0022-5193 (2009) [Refereed Article] DOI: 10.1016/j.jtbi.2009.01.021 [eCite] [Details] Citations: Scopus - 15Web of Science - 13 Co-authors: Jarvis PD | |

2008 | Sumner JG, Charleston MA, Jermiin LS, Jarvis PD, 'Markov invariants, plethysms, and phylogenetics', Journal of Theoretical Biology, 253, (3) pp. 601-615. ISSN 0022-5193 (2008) [Refereed Article] DOI: 10.1016/j.jtbi.2008.04.001 [eCite] [Details] Citations: Scopus - 21Web of Science - 19 Co-authors: Jarvis PD | |

2006 | Sumner JG, Jarvis PD, 'Using the tangle: A consistent construction of phylogenetic distance matrices for quartets', Mathematical Biosciences, 204, (1) pp. 49-67. ISSN 0025-5564 (2006) [Refereed Article] DOI: 10.1016/j.mbs.2006.05.008 [eCite] [Details] Citations: Scopus - 10Web of Science - 11 Co-authors: Jarvis PD | |

2006 | Sumner JG, Jarvis PD, 'Erratum-Entanglement invariants and phylogenetic branching', Journal of Mathematical Biology, 53, (3) pp. 490. ISSN 0303-6812 (2006) [Letter or Note in Journal] Co-authors: Jarvis PD | |

2005 | Jarvis PD, Bashford JD, Sumner JG, 'Path integral formulation and Feynman rules for phylogenetic branching models', Journal of Physics A: Mathematical and General, 38, (44) pp. 9621-9647. ISSN 0305-4470 (2005) [Refereed Article] DOI: 10.1088/0305-4470/38/44/002 [eCite] [Details] Citations: Scopus - 9Web of Science - 9 Co-authors: Jarvis PD; Bashford JD | |

2005 | Sumner JG, Jarvis PD, 'Entanglement invariants and phylogenetic branching', Journal of Mathematical Biology, 51, (1) pp. 18-36. ISSN 0303-6812 (2005) [Refereed Article] DOI: 10.1007/s00285-004-0309-z [eCite] [Details] Citations: Scopus - 9Web of Science - 9 Co-authors: Jarvis PD | |

2004 | Bashford JD, Jarvis PD, Sumner JG, Steel MA, 'U(1) U(1) U(1) symmetry of the Kimura 3ST model and phylogenetic branching processes', Journal of Physics A-Mathematical and General, 37, (8) pp. L81-L89. ISSN 0305-4470 (2004) [Refereed Article] DOI: 10.1088/0305-4470/37/8/L01 [eCite] [Details] Citations: Scopus - 11Web of Science - 3 Co-authors: Bashford JD; Jarvis PD |

### Chapter in Book

(2 outputs)Year | Citation | Altmetrics |
---|---|---|

2017 | Jarvis PD, Holland BR, Sumner JG, 'Phylogenetic Invariants and Markov Invariants', Reference Module in Life Sciences, Elsevier, BD Roitberg (ed), Amsterdam, Netherlands, pp. 1-3. ISBN 9780128096338 (2017) [Revised Book Chapter] DOI: 10.1016/B978-0-12-809633-8.06903-X [eCite] [Details] Co-authors: Jarvis PD; Holland BR | |

2013 | Jarvis PD, Holland BR, Sumner JG, 'Phylogenetic Invariants', Brenner's Encyclopedia of Genetics, Academic Press Ltd Elsevier Science Ltd, S Maloy, K Hughes (ed), United Kingdom, pp. 321-323. ISBN 978-0-08-096156-9 (2013) [Other Book Chapter] DOI: 10.1016/B978-0-12-374984-0.09001-X [eCite] [Details] Co-authors: Jarvis PD; Holland BR |

### Conference Publication

(1 outputs)Year | Citation | Altmetrics |
---|---|---|

2012 | Humphries MA, Holland BR, Karpievitch YV, Sumner JG, 'To gamma or not to gamma? Testing the fit of rates-across-sites models', Phylomania 2012, 8-9 November 2012, University of Tasmania, Hobart, pp. 7. (2012) [Conference Extract] Co-authors: Humphries MA; Holland BR; Karpievitch YV |

### Thesis

(1 outputs)Year | Citation | Altmetrics |
---|---|---|

2006 | Sumner JG, 'Entanglement, Invariants, and Phylogenetics' (2006) [PhD] |

## Grants & Funding

### Funding Summary

Number of grants

6

Total funding

### Projects

- Funding
- Australian Research Council ($338,178)
- Scheme
- Grant-Discovery Projects
- Administered By
- University of Tasmania
- Research Team
- Sumner JG; Francis A; Jarvis PD; Bryant D
- Period
- 2018 - 2020
- Grant Reference
- DP180102215

- Description
- To make sense of the patterns they see in the natural world, biologists across fields as diverse as genetics, epidemiology and biogeography need an accurate picture of evolutionary history. DNA sequences provide an exciting means to establish this picture of the past, but to decode it successfully requires mathematical models of how DNA evolves. Our team has identified mathematical inconsistencies with current approaches. In particular, understanding the effect of natural selection in different parts of the Tree of Life requires models that behave robustly in the face of shifting evolutionary processes. This project will use insights from algebraic methods to construct mathematically consistent models of wide biological utility.
- Funding
- Australian Research Council ($310,700)
- Scheme
- Grant-Discovery Projects
- Administered By
- University of Tasmania
- Research Team
- Holland BR; Sumner JG; Jarvis PD
- Period
- 2015 - 2017
- Grant Reference
- DP150100088

- Description
- Using advanced algebra, structural symmetries inherent in phylogenetic methods will be studied, and improved approaches will be derived. DNA sequences contain a wealth of information about evolutionary events that occurred millions of years ago, but extracting this information requires the application of robust methods.
- Funding
- Australian Research Council ($369,061)
- Scheme
- Fellowship-Discovery Early Career Researcher Award
- Administered By
- University of Tasmania
- Research Team
- Sumner JG
- Period
- 2013 - 2015
- Grant Reference
- DE130100423

- Funding
- University of Tasmania ($1,815)
- Scheme
- Grant-Conference Support Scheme
- Administered By
- University of Tasmania
- Research Team
- Sumner JG
- Year
- 2010

- Funding
- University of Tasmania ($1,500)
- Scheme
- Grant-Conference Support Scheme
- Administered By
- University of Tasmania
- Research Team
- Sumner JG
- Year
- 2009

- Funding
- Australian Research Council ($240,000)
- Scheme
- Grant-Discovery Projects
- Administered By
- University of Tasmania
- Research Team
- Jarvis PD; Sumner JG
- Period
- 2008 - 2010
- Grant Reference
- DP0877447

## Research Supervision

Current

3

Completed

3

### Current

Degree | Title | Commenced |
---|---|---|

PhD | Exploring Algebraic Coincidences in Models of Phylogenetic Convergence and Genetic Code Evolution | 2016 |

PhD | Ring Properties of Markov Invariants | 2017 |

PhD | Algebraic and Numeric Methods for Fast Computation of Evolutionary Distance Estimates in Bacteria | 2020 |

### Completed

Degree | Title | Completed |
---|---|---|

PhD | Quadratic Superalgebras in Mathematics and Physics Candidate: Luke Andrew Yates | 2019 |

PhD | Stats, Drugs and Rock and Roll: Statistical applications to temporally autocorrelated substance use data Candidate: Melissa Ann Humphries | 2017 |

PhD | Distinguishing Convergence on Phylogenetic Networks Candidate: Jonathan David Mitchell | 2016 |