Potential research projects

I have several projects that would be suitable for Honours, Masters or PhD students. These are just some examples, and there are lots of projects available. If you are interested in studying any of these (or if you have your own idea for a project), please get in touch with me.

Scholarships are available for suitable PhD and Masters students. See also Te Pūnaha Matatini scholarships

How to combine food webs with size-based models?

Aquatic ecosystems and fishing

Multi-species communities are often described by food webs, which focus on species as the key variable determining what an individual eats. But in marine ecosystems, fish can grow by several orders of magnitude during their lives, and their diet changes as they do so. This means that body size can be more important than species identity in describing predator-prey interactions. Size-specturm models focus on body size as a key variable and keep track of how biomass flows from prey to predator through mortality and growth. In reality, size and species are both important factors and need to be considered together. This project will use size-based models to investigate the dynamics of multi-species communities. These models will also be used to investigate different fishing strategies with the twin goals of maximising yield while minimising ecosystem impact.

Random walks of building blocks

Populations of cells - sometimes called the building blocks of life - can be modelled by random walks, where cells take a sequence of steps in randomly chosen directions. If the cells all move independently, the population density follows the heat equation. But in reality, cells interact with one another via physical contacts and chemical signals. Their movement can also be impeded by obstacles in the form of extracellular material. These interactions can be included in random walk models. This project will investigate the behaviour of the cells in these models and how it affects the diffusive characteristics of the population as a whole.

To take this project, some experience with a computer programming language such as Matlab or Python is needed. Prior study of PDEs and/or random processes would be helpful but is not essential.

The wisdom and madness of crowds

Groups of people can often come up with better solutions to problems than any one individual on their own could. But groups can also get carried away by the spread of bad ideas, e.g. the global financial crisis, or the spread of fake news. These processes can be represented by social networks: people and the connections between them – see this interactive tutorial by Nicky Crase https://ncase.me/crowds/. This project is about mathematical models of the spread of an idea or behaviour through a social network. The aim is to investigate how the network structure (e.g. clustering, degree distribution, small-world) affects the speed of transmission through the network and the success or failure of the contagion to take over the network.

To take this project, some experience with computer programming is needed, e.g. Matlab or Python. Previous study of discrete maths and/or random processes would be helpful but is not essential.

Experimental image of part of a cell population

Collective cell behaviour

Collective cell behaviour is the driving force behind many physiological processes, including embryonic development, tissue repair and tumour growth. Experiments on collective cell behaviour typically collect data at the level of the population rather than the individual cell. We’d like to be able to translate data from observing populations of cells into knowledge about how individual cells work and how they interact with their neighbours. This project will approach this problem using approximate Bayesian computation (ABC). At its simplest, this involves sampling model parameters from a prior distribution and simulating cell behaviour. If the model output is “close” to the experimental data, the parameter values are accepted as part of the posterior distribution, otherwise they are rejected. This will be used to estimate quantities such as cell proliferation and movement rates and the strength of interactions with neighbouring cells.

This project will require some experience of a computer programming language, e.g. Matlab and an interest in working with biological data. Prior knowledge of Bayesian statistics is NOT required.