PhD Studentship: A mathematical control theoretic approach to ecosystem composition and function

University of Bath - Mathematical Sciences

Qualification Type: PhD Bath UK Students, EU Students £14,777 annual stipend (2018/19 rate) + tuition fees + £1,000 p/a training support grant for up to 3.5 years Full Time
Placed On: 8th November 2018 16th December 2018

Co-supervisor: Dr Jane White

Project description:

This project seeks to use ideas from mathematical systems and control theory to find theoretical answers to questions of the form:

(a) how does ecosystem composition and function respond to changes, both internal and external, to the ecosystem?

(b) under what circumstances can an invasive mutant establish in a wild-type population?

Quoting [1] ``The field of mathematical control theory concerns itself with the basic theoretical principles underlying the analysis of feedback and the design of control systems. It differs from the more classical study of dynamical systems in its emphasis on inputs (or controls) and outputs (or measurements).’’ Ecosystems are complicated, multi-faceted, levels of organisation between communities of organisms, which may be organised according to, for example, biomass, functional trait, or trophic level. However, the interactions between these levels are naturally described by feedbacks, making them amenable to the proposed approach. Mathematical control theory also provides a set of tools for predicting the effects of interventions, or management actions, to ecosystems. Consequently, the current project shall adopt use the above described tools to seek answers to (a) with potential applications to: safeguarding biodiversity or food webs, or; improved food security, see [2].

The second question above is well-studied, from a variety of perspectives and in numerous contexts. It may be posed at a population level, in a community ecology context, or on the scale of within host. The present project shall originally address the question from a systems and control perspective, by posing the problem as one of (multiple) dynamical systems, coupled by feedback. We then seek to explore and understand any resulting (in)stability. We shall seek to extend recent results of from [3], and exploit the property that these models are naturally instances of so-called positive dynamical systems.

The project will suit someone with a background, and interest, in applied mathematics, or mathematical biology. Existing knowledge of mathematical control theory would be useful, but not essential. The lead supervisor, Chris Guiver, is part of the mathematical systems and control theory research group in the Department of Mathematical Sciences, but with close ties to mathematical biology research group. Please feel free to get in contact if you would like more information or to discuss the project (c.guiver@bath.ac.uk).

Applications:

Formal applications should be made via the University of Bath’s online application form:

Please quote the supervisor’s name and project title in the ‘Your research interests’ section.

http://www.bath.ac.uk/guides/how-to-apply-for-doctoral-study/

Anticipated start date: 30 September 2019.

Funding:

Candidates may be considered for a University Research Studentship covering UK/EU tuition fees, a training support fee of £1,000 p.a. and a tax-free maintenance allowance at the UKRI Doctoral Stipend rate (£14,777 in 2018-19) for a period of up to 3.5 years.

References:

[1] Stability and Stabilization of Nonlinear Systems by I. Karafyllis and Z.-P. Jiang, Springer, 2011.

[2] C. Guiver, M. Mueller, C. Edholm, R. Rebarber, Y. Jin, B. Tenhumberg, J. Powell, and S. Townley, Simple adaptive control for positive linear systems with applications to pest management, SIAM J. Appl. Math., 76 (2016), 238–275.

[3] C. Guiver, H. Dreiwi, D.-M. Filannino, D. Hodgson, S. Lloyd, and S. Townley. The role of population inertia in predicting the outcome of stage-structured biological invasions. Math. BioSci., 265 (2015), 1–11.