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Computing Science and Mathematics

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Andy Hoyle

Dr Andy Hoyle
Senior Lecturer
Computing Sceince and Mathematics
School of Natural Sciences
University of Stirling

Tel: +44 1786 467 467
Email: Click on link at bottom of the page

NERC Advanced Training Short Course

"Introduction to mathematical modelling for the environmental and biological sciences"

Monday 20th to Friday 24th February 2017

This is a free course, open to PhD students and early career researchers in the environmental and life sciences. There is funding available which covers your travel, accommodation and food..
Click here for more details.

Education and Employment

2015-date Senior Lecturer - University of Stirling
2006-2015 Lecturer - University of Stirling
2005-2006 Research Assistant - The University of Liverpool
2002-2005 PhD - The University of Liverpool
1999-2002 BSc in Mathematics - The University of Liverpool

Research Interests

Antibiotic resistance in aquatic environments
Antibiotic resistance is one of the biggest threats the world is facing, and it affects all areas of life. We are using mathematical modelling techniques to study how resistance is spread through a bacterial population in an aquatic environment. Furthermore we use computational optimisations techniques to derive antibiotic usage strategies that will slow/prevent the build up of resistance, given various set-ups in terms of the objective function and constraints.

Modelling the long-term impact of Gyrodactylus salaris on UK Atlantic salmon population
At present the UK is free of G. salaris. We are using mathematical modelling techniques to estimate the impact of a outbreak of this macro-parasite on UK Atlantic salmon population, and subsequently how the host (Salmon) will evolve a natural resistance if the parasite is left to persist in the long-term, as demonstrated by equivelnt populations in other countries. However this resistance is not free, we therefore look at how the creation of the immune response is trade-off against costs in other life-history traits.

Evolution of host resistance, immunity and immune range
The immune response is one of the most powerful weapons hosts have evolved to fight parasitic infections, however there is still a lot we do not know. Here we use evolutionary techniques, including adaptive dynamics, to understand how the hosts immune system has developed. In particular, the host's immune range (whether immunity to one strain protects a host from similar strains), which will help understand why we have life-long immunity to some infections, but see continual outbreaks to various strains of another parasite over time.

Optimal control strategies in multi-host, shared pathogen systems in heterogeneous environments
Systems where several host species share a common pathogen is widespread (e.g. Bovine TB in cattle and badgers, Crithidia bombi in bumblebees and honeybees). However control of such pathogens can be difficult due to complex interactions and potential reservoir species. We aim to develop control strategies for such systems, via modelling and optimisation techniques, and study how we can use seasonality in our favour to reduce the amount of controls needed.

Evolution of sexual conflict

Funded Projects

2016-2017 (CoI): Introduction to mathematical modelling for the environmental and biological sciences. (NERC, £30,000)

2015-2019 (co-PI): Control of key diseases in salmonid production systems: pancreas disease, infectious pancreatic necrosis and sea lice. (SRUC/Stirling, £60,000)

2015-2016 (PI): Introduction to mathematical modelling for the environmental and biological sciences. (NERC, £27,000)

2014 (PI): Predicting the evolution of resistance in Atlantic salmon in response to a macro-parasite invasion . (IMA, £400)

2014-2015 (CoI): Introduction to mathematical modelling for the environmental and biological sciences. (NERC, £25,000)

2013-2017 (PI): Controlling antibiotic resistance in an aquatic environment: A case study based on Rainbow Trout and the fish pathogen Yersinia ruckeri. (CEFAS/Stirling, £96,000)

2013-2014 (CoI): Introduction to mathematical modelling for the environmental and biological sciences. (NERC, £30,000)

2009-2013 (CoI): Estimating the long-term impact of Gyrodactylus salaris infections in the UK. (DEFRA/CEFAS, £90,000)

2010-2011 (PI): Evolution of resistance and exclusion of pathogens/predators. (Carnegie, £400)

PhD Students

Lee Benson - Mathematical and statistical tools to quantify disease in aquaculture. (Oct 2016 - Sept 2020)

Iona Paterson - Controlling antibiotic resistance in an aquatic environment: A case study based on Rainbow Trout and the fish pathogen Yersinia ruckeri.. (Oct 2013 - Sept 2017)

Erin Scott - Multi-scale integration modelling of osmoconformers (marine invertebrates) physiology, life history and surrounding ecosystem in response to climate change. (Completed May 2016)

Jennifer McKeown - Modelling the Evolution of Mating Behaviours and Migration. (Completed May 2015)

Rachel Lintott - Mathematical modelling of population and disease control in patchy environments. (Completed Aug 2014)

Scott Denholm - Long-term impact of G. salaris on UK Atlantic salmon populations. (Completed Dec 2013)

Nicky McPherson - Model and control of Argulus spp in managed troat populations. (Completed Dec 2013)


I.K. Paterson, A.S. Hoyle G.O. Ochoa, C. Baker-Austin and N.G.H. Taylor, 2016. Optimising Antibiotic Usage to Treat Bacterial Infections. Nature Scientific Reports, 6, 37853; doi: 10.1038/srep37853

S.J. Denholm, A.S. Hoyle, A.P. Shinn, G. Paladini, N.G.H. Taylor and R.A. Norman, 2016. Predicting the potential for natural recovery of Atlantic salmon (Salmo salar L.) populations following the introduction of Gyrodactylus salaris Malmberg, 1957 (Monogenea). PlosOne (in press).

E. Scott, A. Hoyle and C. Shankland, 2016. Process Algebra with Layers: A Language for Multi-Scale Integration Modelling, Illustrated by a Cell Cycle and DNA Damage Case Study. International Conference on Computational Intelligence methods for Bioinformatics and Biostatistics (CIBB), Stirling.

J.S. Garbutt, T.J. Little and A. Hoyle, 2015. Maternal effects on offspring consumption can stabilize fluctuating predator–prey systems. Proc. Roy. Soc. B 282:20152173

S.J. Denholm, R.A. Norman, A.S. Hoyle, A.P. Shinn, G. Paladini and N.G.H. Taylor, 2013 Predicting salmon population recovery from Gyrodactylus salaris infections: A multiple-host-strain modelling approach. 7th International Symposium on Monogenea, Rio de Janeiro, Brazil.

A. Best and A. Hoyle, 2013. A limited host immune range facilitates the creation and maintenance of diversity in parasite virulence. Interface 3:6 20130024.

S.J. Denholm, R.A. Norman, A.S. Hoyle, A.P. Shinn and N.G.H. Taylor, 2013 Reproductive Trade-Offs May Moderate the Impact of Gyrodactylus salaris in Warmer Climates. PLoS ONE 8(10): e78909.

A. Best and A. Hoyle, 2013. The evolution of costly acquired immune memory. Ecology and Evolution, 3:2223-32.

R. Lintott, R. Norman and A. Hoyle, 2013. The impact of increased dispersal in reponse to disease control in patchy environments. Journal of Theoretical Biology, 323:57-68.

N.J. McPherson, R. Norman, A. Hoyle, J. Bron and N. Taylor, 2012. Stocking methods and parasite-induced reductions in capture: modelling Argulus foliaceus in trout fisheries. Journal of Theoretical Biology, 312:22-33.

E. Scott, A. Hoyle and C. Shankland. PEPA'd Oysters: Converting Dynamic Energy Budget Models to Bio-PEPA, illustrated by a Pacific oyster case study. In the proceedings of 6th International Workshop on Practical Applications of Stochastic Modelling (PASM 2012), ENTCS.

Hoyle A., A. Best and R. G. Bowers, 2012. Evolution of host resistance towards pathogen exclusion: the role of predators. Evolutionary Ecology Research, 14:125–146.

Hoyle A., R.G. Bowers and A. White, 2011. Evolutionary behaviour, trade-offs and cyclic and chaotic population dynamics. Bulletin of Mathematical Biology, 73:1154-69. PDF

Greenman J.V. and A. Hoyle, 2010. Pathogen exclusion from eco-epidemiological systems. American Naturalist, 176:149-58.

Hoyle A. and A. Gilburn, 2010. Sexually antagonistic co-evolution: a model and an empirical test. Journal of Evolutionary Biology, 23:166-174. PDF

Hoyle A. and R.G. Bowers, 2008. Can possible evolutionary outcomes be determined directly from the population dynamics? Theoretical Population Biology, 74:311-323.

Greenman J.V. and A. Hoyle, 2008. Exclusion of generalist pathogens in multi-host communities. American Naturalist, 172:576-84.

Hoyle A., R.G. Bowers, A. White and M. Boots, 2008. The influence of trade-off shape on evolutionary behaviour in classical ecological scenarios. Journal of Theoretical Biology, 250:498-511. PDF

Hoyle A. and R.G. Bowers, 2008. When is evolutionary branching in predator-prey systems possible with an explicit carrying capacity? Mathematical Biosciences, 210:1-16.

R.G. Bowers, A. Hoyle, A. White & M. Boots, 2005. The geometric theory of adaptive evolution: trade-off and invasion plots. Journal of Theoretical Biology, 233:363-377.


MATU9M1 – Mathematics 1 (Calculus) (Autumn 2015-).
MATU9JA – Optimisation in Theory and Practice (Spring 2007-).
MATU9MA – Special Topics – Mechanics and Game Theory (Autumn 2009-).
MATU9MC – Experimental Design and Mathematical Modelling (Spring 2008-).

MATU9RP – Rsearch Portfolio (Spring 2014-)
MATU9K8 – Research Project (Spring 2007-)

FINU9QA – Quantitative Methods for Business Decisions (Autumn 2007-).

Other details

I am at present responsible for the Mathematics Workshop which takes place every June at the University of Stirling. Further information on the workshop and other related events can be found here or email me.

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