Eco-Evolutionary Dynamics of Populations in Fluctuating Environments

Understanding the evolution of cooperation and the origins of species diversity is central to evolutionary biology and deeply connected to societal concerns, including the rapid spread of antimicrobial resistance and global biodiversity loss. Traditional approaches to population dynamics often assume static environments and neglect fluctuations. Yet, demographic noise and environmental variability critically shape eco-evolutionary dynamics by influencing both population size and composition. This project investigates how fluctuating conditions affect biological populations, in both well-mixed communities and spatially structured metapopulations, offering insights into persistence, coexistence, and collapse. Applications include the spread of antimicrobial resistance.<br /> Concrete objectives:<br /> - Extending recent theoretical advances in fluctuating population dynamics to broader evolutionary scenarios (Phys. Rev. Lett. 119, 158301 (2017), Phys. Rev. Lett. 125, 048105 (2020));<br /> - Investigating cooperative antimicrobial resistance, building on recent work linking population growth, public-goods, and survival under fluctuating environmental conditions (J. R. Soc. Interface 20, 20230393:1-13 (2023), https://www.biorxiv.org/content/10.1101/2024.12.30.630406v3);<br /> - Analysing competition between microbial strains whose interactions unfold across time-varying, spatially structured landscapes (Phys. Rev. Research 7, 043205 (2025)); <br /> - Modelling of microbial life cycles in fluctuating environments.<br /> <br /> Together, these objectives aim to deepen our understanding of how fluctuating environments drive ecological and evolutionary outcomes, with relevance for public health and the management of microbial communities.

<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 selective advantage over the other type  that produces a public good (“cooperators”). 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 is of great importance in microbial communities. These 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 <a href="https://eedfp.com/">EEDFP project</a> on <a href="https://eps.leeds.ac.uk/faculty-engineering-physical-sciences/dir-record/research-projects/4345/eco-evolutionary-dynamics-of-fluctuating-populations">Eco-Evolutionary Dynamics of Fluctuating Population</a>s, an international collaboration that was funded by the UK Research Councils (EPSRC) and the National Science Foundation (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 populations arranged on lattices of interconnected patches of fluctuating size between which individuals can migrate, see, e.g., <a href="https://doi.org/10.1103/6w4h-8xvk">Phys. Rev. Research 7, 043205 (2025)</a> and <a href="https://www.biorxiv.org/content/10.1101/2024.12.30.630406v3">https://www.biorxiv.org/content/10.1101/2024.12.30.630406v3</a>. Inspired by <a href="https://royalsocietypublishing.org/doi/10.1098/rsif.2023.0393">J. R. Soc. Interface 20, 20230393:1-13 (2023)</a>, <a href="https://iopscience.iop.org/article/10.1088/1751-8121/ad4ad6">J. Phys. A: Math. Theor. 57, 265003:1-29 (2024)</a> and <a href="https://iopscience.iop.org/article/10.1088/1367-2630/ad0d36">New J. Phys 25, 123010:1-18 (2023)</a>, we shall be particularly interested in the influence of spatial migration and fluctuations on the fate of microbial populations, with applications to antimicrobial resistance.</p> <p>Keywords: population dynamics, stochastic processes, fluctuations, evolutionary games, complex systems, ecology, individual-based modelling, statistical physics, stochastic simulations, migration, structured populations, antimicrobial resistance.</p>

<p>To apply for this project you will need to make a formal application for research degree study through the <a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University website</a>. You will need to create a login ID with a username and PIN. </p> <p>•    For <strong>Application type</strong> please select <strong>Research Degrees – Research Postgraduate</strong>. <br /> •    The admission year for this project is <strong>2026/27</strong> Academic Year. <br /> •    You will need to select your <strong>Planned Course of Study</strong> from a drop-down menu. For this project, scroll down and select <strong>PHP Applied Mathematics Full Time.</strong> <br /> •    The project start date for this project is <strong>1 October 2026</strong>, please use this as your <strong>Proposed Start Date of Research</strong>. <br /> •    Please state clearly in the<strong> Research Information Section</strong> that the research degree you wish to be considered for is <strong>Eco-Evolutionary Dynamics of Populations in Fluctuating Environments </strong>as well as <a href="https://eps.leeds.ac.uk/maths/staff/4064/professor-mauro-mobilia">Professor Mauro Mobilia</a> as your proposed supervisor.</p> <p><strong>Please state clearly in the Finance section</strong>, <strong>the funding that you are applying for, if you are self-funding or externally sponsored</strong>.</p> <p>More information on how to apply is available on our website <a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">here</a>. You will be required to provide a personal statement which outlines your interest in the project you are applying for, why you have chosen it and how your skills map onto the requirements of the project.</p> <p>We will assess applications continuously as we receive them. We welcome and strongly encourage any potential applicants to contact the supervisor(s) for an informal discussion, prior to applying, and recommend submitting your application early.</p> <p><strong>If you are applying for University or School Scholarships for 2026/27 entry, 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 including the grading scheme</li> <li>Personal Statement outlining your interest in the project</li> <li>CV</li> </ul> <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><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>

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.

<p><strong>Self-Funded or externally sponsored students are welcome to apply.</strong></p> <p><strong>Scholarship opportunities open from October 2025</strong></p> <p><strong>UK</strong> – The <a href="https://phd.leeds.ac.uk/funding/209-leeds-doctoral-scholarships-2024">Leeds Doctoral Scholarship</a> <strong>(closing date: 1 April 2026)</strong> and <a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a> <strong>(closing date: 1 April 2026)</strong> are available to UK applicants.  <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><strong>Non-UK</strong> – 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> is available to nationals of China <strong>(Now closed for October 2026 entry)</strong>. 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>Please note that if you are successful in securing an academic offer for PhD study, this does not mean that you have been successful in securing an offer of funding.</p> <p>If you are applying for the Leeds Doctoral Scholarship or the Leeds Opportunity Research Scholarship, you will need to complete a separate application, specific to these scholarships, to be considered for funding.</p> <p>You will be responsible for paying the overtime fee in full in your writing up/overtime year (£340 in Session 2025/26), but the scholarship maintenance allowance will continue to be paid for up to 6 months in the final year of award.</p> <p><strong>Eligibility Criteria</strong></p> <ul> <li>Applications are open to either International or Home (UK) applicants.</li> </ul> <p>Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website or our <a href="https://www.leeds.ac.uk/undergraduate-fees/doc/fee-assessment">fee assessment page</a> for information regarding Fee Status for Non-UK Nationals.</p> <p><strong>Important: Please be aware that any expenses related to the relocation of international students to the UK (<a href="https://www.leeds.ac.uk/international-visas-immigration/doc/applying-student-visa">visa, Immigration Health Surcharge</a>, flights, etc) would be their responsibility and is not covered by this award</strong></p> <p><strong>Other Conditions</strong></p> <ul> <li>Candidates who have previously been awarded a PhD or are currently registered on a PhD are excluded from applying. Those who were previously studying for a PhD but did not complete may be considered. </li> <li>Awards must be taken up by 1st October 2026.</li> <li>Applicants must live within a reasonable distance of the University of Leeds whilst in receipt of this scholarship.</li> </ul>

<p>For further information about your application, please contact PGR Admissions by email to <a href="mailto:phd@engineering.leeds.ac.uk">phd@engineering.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>