PhD Research Project: Spatial predator-prey dynamics in the landscape of fear

The mathematical study of predator-prey dynamics is one of the oldest subjects in mathematical biology. In a spatial setting, understanding predator-prey interactions is important for a variety of ecological issues, such as maintaining biodiversity and establishing sound conservation principles. Mathematical models have played a vital role in this understanding for many decades. However, many questions remain unanswered.

This project will examine the effect of the `landscape of fear' on spatial population dynamics. As well as affecting the number of animals in a population, the existence of predators is a spatial deterrent, meaning that prey will avoid areas of the landscape where they believe predators are likely to be present. Meanwhile, predators will be actively seeking-out areas of the landscape where they expect to find prey. Recent empirical research, from both ecology and neuroscience, suggests that animals build up a cognitive map of their environment which they use to navigate the terrain, seeking-out areas that may be beneficial to them and avoiding those that will not.

The candidate will use mathematical models to understand (a) how the landscape of fear emerges, (b) what it might look like under different ecologically-motivated scenarios, and (c) how it affects the demographic dynamics and ultimately the survival of each species. Ecologically, this will be motivated by various study systems that range from caribou-wolf interactions to orca-narwhal systems. However, we will always seek out general lessons that may be applicable across taxa.

Mathematically, we will study systems of reaction-diffusion-taxis equations, where the `reaction' term models birth and death of animals, the `diffusion' term models aspects of movement that are either unknown or not explicitly modelled, and `taxis' is movement away from undesirable areas towards more desirable ones. These will be coupled through ordinary differential equations which model the extent to which a part of space is considered desirable or undesirable by the species at any point in time. The candidate will make use of a variety of tools from spatial pattern-formation analysis, building on recent studies of cross-diffusive systems, which have many mathematical similarities to the systems studied here.

Funding Notes

This project would best suit a student with a good mathematics degree (e.g. MMath 1st, MSc distinction or equivalent) with a demonstrable interest in ecology. However, I am willing to consider excellent candidates with slightly different academic backgrounds. Students can apply for both places and funding (subject to eligibility requirements) through the Sheffield School of Maths and Stats website. Please feel free to contact Dr. Jonathan Potts for informal enquiries.