Understanding the emergence, spread and evolution of infectious diseases in natural and managed populations is a major challenge. Working closely with experimental biologists, we develop mathematical models describing the interactions of hosts and their parasites using ordinary differential equations. The main focus of our research is on how population-level processes drive evolutionary dynamics.

Key questions include:

- What host characteristics select for highly virulent rather than benign parasites?
- How do other community interactions affect the evolution of host defences to disease?
- When should we expect temporal fluctuations in host and parasite strains, and when long-term coexistence?

Members working on these topics: Dr. Alex Best

Mathematical models of ecological systems are of fundamental importance for predicting and managing changes in the natural world.

At Sheffield, we are particularly interested in the following questions:

- Can we construct techniques to help predict the effects of future environmental change on the ability of animal populations to survive?
- How do complex systems of animal movements and interactions give rise to emergent population-level patterns?
- Can we predict where biological invasions are likely to occur and how can we control their spread?
- How can we infer the nature of animal interaction mechanisms, both with each other and their environment, from movement data?
- We use a range of statistical, computational, and mathematical tools to address these questions, from information criteria to statistical mechanics to partial differential equations.

Members working on these topics: Dr. Jonathan Potts

Mathematical modelling of evolution and natural selection combines the mathematical tools of dynamical systems theory, stochastic processes, combinatorics and graph theory.

At Sheffield current projects include:

- Working with Richard Southwell (Hong Kong), developing a set of models for the reproduction of networks, incorporating both removal of individuals through ageing and crowding.
- Working with Mark Broom (City University), we have been studying a population model in which individuals have preferences for the number of links to others; this has led to some original work in graph theory with respect to "graphic sequences".

Members working on these topics: Prof. Chris Cannings

Ecological models and data present many challenging statistical problems. Research on this topic in Sheffield concentrates particularly on Bayesian computer-intensive statistical methods, in collaboration with statistical colleagues, especially through the National Centre for Statistical Ecology, and with ecologists both in Sheffield and worldwide.

Examples of current interest include:

- Movement modelling and inference, using continuous-time stochastic models to interpret data from GPS and similar tracking methods, from individuals and from groups of animals.
- Statistical inference for ecosystem models, particularly size-spectrum models with marine applications through the Marine Ecosystems Research Programme.
- Statistical methods for complex systems such as individual-based models for which it is not possible to write down a likelihood function.

The left picture by Paul Blackwell.

Members working on these topics: Prof. Paul Blackwell

Understanding the role of genetics and epigenetic variation is important because it allows the possibility of personalized medicine. Approaches to studying genetic/epigenetic variation are highly statistical and probabilistic.

At Sheffield we are working on:

- Developing Bayesian statistical methods to incorporate functional genomic information into eQTL mapping.
- Novel Bayes factors for use in fine-mapping multi-factorial genetic diseases.
- Likelihood-free inference for problems involving cellular populations, particularly stem cells.
- Developing hidden Markov models to detect essential regions using bacterial transposon sequencing data.

Members working on these topics: Dr. Kevin Walters