Eco-Evolutionary Dynamics of Populations in Fluctuating Environments

Understanding the origin of species diversity and the evolution of cooperation is a fundamental puzzle resonating with societal concerns, like the rise of antimicrobial resistance and the loss of biodiversity. Population dynamics traditionally ignores fluctuations and considers static or homogeneous environments. However, fluctuations from random birth and death events and changing environmental conditions play a crucial role in understanding the population eco-evolutionary dynamics, i.e. how its size and composition co-evolve. We will focus on the poorly understood situations where the population eco-evolutionary dynamics is shaped by the coupling of demographic noise and environmental variability. This is particularly relevant to understand the evolution of antimicrobial resistance, and poses interesting mathematical challenges.<br /> <br /> Two concrete objectives:<br /> - Generalization of Phys. Rev. Lett. 119, 158301 (2017) and Phys. Rev. Lett. 125, 048105 (2020) in various evolutionary scenarios.<br /> - Modelling of microbial life cycles in fluctuating environments.

<p>Understanding the origin of species diversity and the evolution of cooperation is a major scientific riddle that resonates with numerous societal concerns, like the rise of antimicrobial resistance or the loss of biodiversity, and is even relevant to epidemiology. Population dynamics traditionally ignores fluctuations and considers static and homogeneous environments. However, fluctuations arising from randomly occurring birth and death events (demographic noise) and the change of environmental conditions (environmental variability), together with the spatial dispersal of species, play a crucial role in understanding how the size and composition of a population jointly evolve in time, i.e. the population eco-evolutionary dynamics. In this project, we focus on the ubiquitous situation where the eco-evolutionary dynamics of fluctuating populations is shaped by the coupling of demographic noise and environmental variability. As an example, we can consider population consisting of a two strains of bacteria, with a “free-rider” strain having a constant selective advantage over the other (cooperators) that produces a public good. While free riders always prevail in the absence of randomness, the probability that cooperators take over is greatly enhanced when the population size is driven by a carrying capacity that randomly switches from a state of abundance in which the population size is large to a state of scarcity in which the population shrinks.</p> <p>The interdependence of environmental variability and demographic noise is poorly understood but of great importance in microbial communities, which are often subject to sudden and extreme environmental changes, and is crucial for understanding the evolution of microbial antibiotic resistance. Evolutionary game theory (EGT) describes the dynamics of populations in which the success of one type depends on the actions of the others, and provides a suitable framework to model the evolution of cooperation. While EGT models have been extensively studied in static and homogeneous environments, little is known about the joint effect of coupled environmental and demographic randomness on cooperation, and even less is known about their effects in spatial settings.</p> <p>This research is 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 class="western" style="margin-bottom: 0cm; line-height: 100%">Some concrete objectives of this project are:</p> <p class="western">- Generalization of the approaches of <a href="https://doi.org/10.1103/PhysRevLett.119.158301">Physical Review Letters <strong>119,</strong> 158301 (2017)</a>, <a href="https://royalsocietypublishing.org/doi/10.1098/rsif.2018.0343">Journal of the Royal Society Interface <strong>15</strong>, 20180343:1-12 (2018)</a>, <a href="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.048105">Physical Review Letters <strong>125</strong>, 048105 (2020)</a>, and analysis of how environmental randomness affects the evolution of EGT under various competition and cooperation scenarios. We will consider paradigmatic EGT models and public goods games in finite populations of fluctuating size with a varying carrying capacity.</p> <p class="western">- Study of the spatially-extended counterparts of EGT competition and cooperation scenarios, with the population is arranged on lattices of interconnected patches of fluctuating size between which individuals can migrate. The circumstances under which space favours/hinders the evolution of cooperation will be analysed.</p> <p>Keywords: population dynamics, stochastic processes, fluctuations, evolutionary games, complex systems, ecology, individual-based modelling, statistical mechanics, stochastic simulations, migration, structured populations.</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 Planned Course of Study section that you are applying for <em><strong>PHD Applied Mathematics FT</strong></em> and in the research information section that the research degree you wish to be considered for is <em><strong>Eco-Evolutionary Dynamics of Populations in Fluctuating Environments </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 style="margin-bottom:11px"><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">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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<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="https://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>