Combining game theory and the weak noise limit to understand spatio-temporal ecological models of animal movements.
This research project is in competition for funding with one or more projects available across the EPSRC Doctoral Training Partnership (DTP). Usually the projects which receive the best applicants will be awarded the funding. Find out more information about the DTP and how to apply.
Application deadline: 15 March 2019
Start date: 1 October 2019
The project seeks to bring together two different but complementary fields of mathematics in order to extract further understanding from each.
Locusts and other migrating insects can form cohesive swarms at large population densities, which subsequently travel over huge distances and can have a devastating effect on agriculture. It is therefore important to understand the mechanisms governing how the population decides collectively on the direction of migration and the population density at which this occurs.
There has been much interest recently regarding the modelling of such animal movement. Specifically, as mathematicians we try to express animal interactions mechanistically, with a view to understanding emergent group phenomena, such as swarming and directionality.
Critically, there are multiple ways of understanding such phenomena. Two such ways are through using game theoretic techniques (Vince Knight’s (VK) area of expertise), whilst another is through using agent based modelling and the weak noise limit (Thomas Woolley’s (TW) and Louise Dyson’s (LD) area of expertise). This project seeks to bridge the gap between these two complementary skill sets in order to understand the role of noise in agent based decision making and specify how individual actions can lead to global decision making.
Our initial point of interest is a recent minimal model of collective motion (developed by LD). The model describes density-dependent bistability in population-level decision making. This model demonstrates a kind of bistability that is only present when demographic noise is included. Namely, the randomness in the system does not simply cause transitions between different population states (e.g. individual left movement vs individual right movement) but instead actively constructs new possible population states (globally organised movement).
We seek to use game theoretic approaches (a specific example being the Ohtsuki-Nowak approximation) that will allow us to remove topology from this problem and, thus, lead to a dramatic simplification. This simplification will shed light on the creation of the new states that depend on randomness, thus, generalising the cases in which we would expect noise dependent dynamics to occur. In turn, this will highlight ecological cases were such complexity would be expected to arise.
Project aims and methods
In order to foster this collaboration the student will be jointly supervised by TW and VK, who will manage the majority of your time, focusing on mathematical modelling. LD will provide additional mathematical supervision, biological background and data, as needed.
You will learn multiple theoretical skills, such as: game theory, stochastic modelling, data fitting and perturbative methods. These skills will be combined to produce a theoretical framework, in which we can understand when spatial aspects of a problem can be removed from a system, with particular emphasis on ecological problems and animal motion. In turn, these theoretical insights will need to be backed up by simulation, thus, advanced numerical coding skills for simulating spatio-temporal systems will be mastered.
Due to this collaborative aspect you must learn to communicate with interdisciplinary colleagues, constantly translating ideas between biological and mathematical languages, resulting in useful predictions and explanations for field workers.
Dr Louise Dyson, University of Warwick.