Modelling Biodiversity and Pattern Formation with Evolutionary Games

Summary

Understanding the maintenance of biodiversity and the emergence of cooperation are important topics in the Life and Behavioural Sciences. Evolutionary game theory, where the success of one species depends on what the others are doing, provides a promising mathematical framework to study the dynamics of interacting populations.

As paradigmatic examples, the prisoners dilemma and the rock-paper-scissors games have emerged as a fruitful metaphor for cooperative and co-evolutionary dynamics, with applications in microbiology and ecology. While mathematical biology classically deals with deterministic, often spatially homogeneous, models; the joint effects of noise and spatial degrees of freedom are important for realistic description of population dynamics. In our research, we use stochastic processes, differential equations and computer simulations to study the dynamics of interacting populations. Our approach will be to adopt an individual-based metapopulation model formulation in which interacting sub-populations are subdivided in connected islands and can migrate from one patch to another.

In our research, we use stochastic processes, differential equations and computer simulations to study the dynamics of interacting populations broadly motivated by the problems of maintenance of biodiversity, species coexistence and evolution of cooperation. Possible lines of investigation are:

(i) It has recently been demonstrated that populations movement can have important evolutionary implications. Here, we shall consider evolutionary models with realistic forms of mobility (e.g,. inspired by chemotaxis) and different types of interactions between the species (e.g., to account for long-range interactions between bacteria, or mutations), and study the joint influence of movement and randomness on population's self-organisation, species coexistence, and on survival and extinction scenarios.

(ii) Mathematical models of population dynamics are classically formulated in terms of rate equations whose predictions are known to be altered by stochastic effects. The extinction of sub-populations and the fixation of mutants are striking examples of the influence of stochastic noise. To analyse these phenomena we will notably use suitable size expansion methods (e.g. diffusion approximation, WBK theory) that will allow us to account for random fluctuations of various intensity. It will be interesting to carry out this line of research for ecologically and biologically motivated models, first in well-mixed and then spatially-structured populations

(iii) In nature, organisms often interact with a finite number of individuals in their neighbourhood. The population is thus heterogeneously structured and cannot be described by well-mixed models. This often results in patterns observed in ecosystems and whose origin is an intense subject of research. According to Turing's deterministic theory, diffusion can yield pattern-forming instabilities in systems if some specific conditions are satisfied. However, these conditions are often too stringent, and pattern formation has been observed in many ecosystems where they would not be expected according to Turing's theory. In this context, it has recently been proposed that noise together with movement can be a mechanism responsible for the emergence of patterns. We would like to test this scenario by investigating the origin of pattern formation in paradigmatic examples like the "rock-paper-scissor" model and its variants, in the presence of both demographic and envionmental fluctuations. In our approach, we will adopt an "individual-based" metapopulation model formulation in which interacting sub-populations are subdivided in connected islands and can migrate from one patch to another.

Some aspects of this research are related to the interdisciplinary project Eco-Evolutionary Dynamics of Fluctuating Populations, an international collaboration funded by the EPSRC in the UK and the NSF in the USA.

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid. Some schools and faculties have a higher requirement.