Modelling Biodiversity and Pattern Formation with Evolutionary Games

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. <br /> <br /> 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.

<p>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:</p> <p>(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.</p> <p>(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</p> <p>(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.</p> <p>Some aspects of this research are related to the interdisciplinary project <a href="https://eps.leeds.ac.uk/maths-research-innovation/dir-record/research-projects/4345/eco-evolutionary-dynamics-of-fluctuating-populations">Eco-Evolutionary Dynamics of Fluctuating Populations</a>, an international collaboration funded by the <a href="https://gow.epsrc.ukri.org/NGBOViewGrant.aspx?GrantRef=EP/V014439/1">EPSRC in the UK</a> and the NSF in the USA.</p>

<p>Formal applications for research degree study should be made online through the <a href="https://www.leeds.ac.uk/info/130206/applying/91/applying_for_research_degrees">University's website</a>. Please state clearly in the Planned Course of Study section that you are applying for <em><strong>PHD Applied Mathematics FT,</strong></em> in the research information section that the research degree you wish to be considered for is <em><strong>Modelling Biodiversity and Pattern Formation with Evolutionary Games </strong></em>as well as <a href="https://eps.leeds.ac.uk/maths/staff/4064/professor-mauro-mobilia">Professor Mauro Mobilia</a> as your proposed supervisor and in the finance section, please state clearly <em><strong>the funding that you are applying for, if you are self-funding or externally sponsored</strong></em>.</p> <p>If English is not your first language, you must provide evidence that you meet the University's minimum English language requirements (below).</p> <p class="MsoNoSpacing"><em>As an international research-intensive university, we welcome students from all walks of life and from across the world. We foster an inclusive environment where all can flourish and prosper, and we are proud of our strong commitment to student education. Across all Faculties we are dedicated to diversifying our community and we welcome the unique contributions that individuals can bring, and particularly encourage applications from, but not limited to Black, Asian, people who belong to a minority ethnic community, people who identify as LGBT+ and people with disabilities. Applicants will always be selected based on merit and ability.</em></p> <p class="MsoNoSpacing" style="text-align:start; margin-bottom:24px">Applications will be considered after the closing date.  Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application.  We also advise that you apply at the earliest opportunity as the application and selection process may close early, should we receive a sufficient number of applications or that a suitable candidate is appointed.</p> <p class="MsoNoSpacing"><strong>Please note that you must provide the following documents in support of your application by the closing date of Monday 6 January 2025 if applying for the China Scholarship Council-University of Leeds Scholarship, Monday 3 February 2025 if applying for Leeds Doctoral Scholarship or Tuesday 1 April 2025 for Leeds Opportunity Research Scholarship.</strong></p> <p><strong>If you are applying for the School of Mathematics Scholarship 2025/26, or with external sponsorship or you are funding your own study, please ensure you provide your supporting documents at the point you submit your application:</strong></p> <ul> <li>Full Transcripts of all degree study or if in final year of study, full transcripts to date</li> <li>Personal Statement outlining your interest in the project</li> <li>CV</li> </ul>

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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.

<p style="margin-bottom:12px"><strong>Self-Funded or externally sponsored students are welcome to apply.</strong></p> <p><strong>UK</strong> – The <a href="http://phd.leeds.ac.uk/funding/138-leeds-doctoral-scholarship-2025-faculty-of-engineering-and-physical-sciences#:~:text=Key%20facts&text=One%20Leeds%20Doctoral%20Scholarship%20is,rata%20for%20part%2Dtime%20study.">Leeds Doctoral Scholarship</a> <strong>(closing date: Monday 3 February 2025)</strong>, <a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a><strong> (closing date: Tuesday 1 April 2025)</strong> and <a href="https://phd.leeds.ac.uk/funding/55-school-of-mathematics-scholarship-2025-26">School of Mathematics Scholarship 2025/26</a> <strong>(open from October 2024) </strong>are available to UK applicants.</p> <p><strong>Non-UK</strong> – <a href="https://phd.leeds.ac.uk/funding/55-school-of-mathematics-scholarship-2025-26">School of Mathematics Scholarship 2025/26</a> <strong>(open from October 2024)</strong> are available to all International applicants.  The <a href="https://phd.leeds.ac.uk/funding/48-china-scholarship-council-university-of-leeds-scholarships-2021">China Scholarship Council - University of Leeds Scholarship</a> <strong>(closing date: Monday 6 January 2025)</strong> is available to nationals of China. The <a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a> is available to support US citizens. <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p>You will be responsible for paying the overtime fee in full in your writing up/overtime year (£320 in Session 2024/25), but the scholarship maintenance allowance will continue to be paid for up to 6 months in the final year of award.</p> <p><strong>Important:</strong> Please note that that the award does <em><strong>not</strong></em> cover the costs associated with moving to the UK.  All such costs (<a href="https://www.leeds.ac.uk/international-visas-immigration/doc/applying-student-visa">visa, Immigration Health Surcharge</a>, flights etc) would have to be met by yourself, or you will need to find an alternative funding source. </p> <p>Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals.</p>

<p>For further information about your application, please contact PGR Admissions by email to <a href="mailto:EMAIL@leeds.ac.uk">m</a><a href="mailto:maps.pgr.admissions@leeds.ac.uk">aps.pgr.admissions@leeds.ac.uk</a>, </p> <p>For further information about this project, please contact Professor Mauro Mobilia by email to <a href="mailto:M.Mobilia@leeds.ac.uk">M.Mobilia@leeds.ac.uk</a></p>