Evolutionary game theory of scarce resources

The principles of Darwinian evolution were discovered long ago but their consequences for networks of randomly interacting organisms are still actively researched. Some generic features of evolution, such as speciation, convergence, cooperativity etc., can be modelled by Evolutionary Game Theory (EGT). In EGT, the complex competitive processes of life are modelled by simple agents playing a simple game. They reproduce and die according to the game’s outcome, and their offspring inherit imperfect copies of the parent’s strategy.<br /> <br /> In this project, a student will investigate the application of EGT to various paradigmatic models, in the regime where the opportunities to exploit natural resources are rare compared with the rate of birth and death. In recent work [1], it was shown that this regime can lead to the evolution of risk-aversion and can thereby explain the evolution of altruism - a phenomenon that has long been studied in the literature but is still not fully understood. That recent investigation [1] included the discovery of a generally-applicable theorem, but was applied to only one game (the ultimatum game) of the many standard paradigms in the EGT literature.<br /> <br /> (i) The student will further test the new theorem to understand whether the results are generalisable to other standard games in the non-standard regime of scarce resources. This will involve analytical calculations for simple cases and some numerical simulations involving very large numbers of agents.<br /> (ii) The student will investigate a novel hybrid model, designed to investigate how rare, high-value events influence the evolution of strategies for common, low-value interactions. This will model whether rare events in an organism's evolutionary history, such as famines and gluts, can account for day-to-day altruism.<br /> (iii) The student will have the opportunity to interact with colleagues (both theorists and experimentallists) within the UK and internationally. This will potentially allow the student to explore the relationship between the abstract mathematical models and real microbial populations.<br /> <br /> References<br /> [1] R M L Evans, 'Pay-off scarcity causes evolution of risk-aversion and extreme altruism', Sci. Rep 8:16074 (2018)<br /> See also https://physicsbloke.blogspot.com/2018/11/evolutionary-games-and-altruism-in-face.html

<p>See also<a href="https://physicsbloke.blogspot.com/2018/11/evolutionary-games-and-altruism-in-face.html"> https://physicsbloke.blogspot.com/2018/11/evolutionary-games-and-altruism-in-face.html</a></p>

<p>Formal applications for research degree study should be made online through the <a href="https://www.leeds.ac.uk/research-applying/doc/applying-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>Evolutionary game theory of scarce resources</strong></em> as well as <a href="https://www.sites.google.com/site/rmlevans">Dr R M L Evans</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> <p> </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 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 general enquiries about applications, please contact PGR Admissions by email to <a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a></p> <p>For questions about the research project, contact Dr Mike Evans by email to <a href="mailto:R.M.L.Evans@leeds.ac.uk">R.M.L.Evans@leeds.ac.uk</a></p>