I am a Research Associate in the Mathematics Department at the University of Bristol studying the statistics of Genetics. I am interested the inference and modelling of complex systems with a focus on stochastic models in Ecology and Evolution.
I am working with Daniel Falush, Peter Green, John (Jack) O'Brien, Xavier Didelot and Aaron Darling.
Research Interests
Applications in Evolution and Genetics
I am interested in the process of evolution, in understanding the patterns that arise from it and how we can learn about the past from it. There are two main topics:
1. How does recombination in Bacteria affect their genetics? We can learn about the evolutionary history of bacteria using the "Ancestoral Recombination Graph" model, which assumes that a population of organisms has been reproducing (and their genomes have been recombining) at random. Unfortunately, this is very unwieldy for inferring events that actually happened, so we are considering approximations that can readily find recombination events in a bacteria's history. Our model treats recombination as a relatively rare event occurring on a background of clonal reproduction, and can detect weak signals of recombination, including the origin of imported DNA.
2. How do humans relate to each other genetically? A popular program called Structure can group individuals according to how similar they are to each other, based on how they have historically recombined. The approach taken unfortunately doesn't scale to whole-genome datasets. We have developed a suite of software tools at PaintMyChromosomes.com that can take full human genomes and efficiently group individuals into populations, using the frequency of copying of segments of DNA.
Applications in Ecology
Bacteria live inside of us and are performing a range of useful activities, such as the processing of nutrients. However, not all of these bacteria are good for us. Understanding the ecological processes affecting bacteria in the gut is therefore of wide interest, for which I'm working with Grietje Holtrop of BioSS to infer actual ecological interactions of bacteria living in the gut from simple experimental data.
The birth and death processes assumed in the above genetic applications is really occurring in physical space. This has an impact on readily observable landscape scale features, such as the distribution of chemicals produced by trees in a forest. I have an ongoing project looking at this spatial distribution, and inferring ecological parameters from it.
Other applications
Why do historical states collapse? History is often viewed as a continuous progression from simple prehistoric societies to more complex societies. However, throughout history complexity has decreased locally when large organised states or empires collapse into multiple simpler entities. This is difficult to explain with verbal theories because it can involve unintuitive non-linear feedback processes; to be sure a theory can explain the observed pattern we must create a mathematical description.
Climate is the simplest explanation for state collapse. However, more dynamical possibilities exist: Turchin (2003, Historical Dynamics: Why States Rise and Fall) describes a set of mathematical theories for how states might "overshoot" their optimum size because they are more unified in their early growing period. This leads to larger states being less stable and less capable of innovation than smaller ones. This theory itself is still in its infancy, as sufficient quality quantitative data is scarce and few mathematical descriptions of history are available for comparison. However, what is clear is that it is possible to describe qualitative patterns in history with simple predictive models. This leads to the obvious question: how do we compare models?
I'm interested in exploring the many facets of quantizing the study of history in general, with the focus on asking "why?" History is clearly not just one thing after another: things change, populations grow, things get more complex (on average). This field is in its infancy, and there is no answer yet as to how much we can explain and how much of history is just chance. Ultimately, it may be possible to have an evolutionary theory for societies that has significant predictive power.
Mathematics and methods
I favour model-based research, describing as close as is possible the facts as we see them. However, the model must be as complex as possible, but no more: it should be possible to infer the parameters of a model from the data available. These two conditions are best met by stochastic modelling.
I use non-parametric Dirichlet Processes to model human genetics, as it happens that these capture the recombination process quite well. The bacterial genetics work uses Coalescent theory and the Ancestral Recombination graph, which are stochastic graph models. The other projects use fairly straightforward differential equations or simple diffusion, in an inference framework.
I am interested in model assessment and comparison, particularly for "complex" models. This has lead me to work on "Approximate Bayesian Computation", an approach that directly assesses a model by how well it can generate some observed data.