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Stochastic Evolution of Populations in Fluctuating Environments

PGR-P-198

Key facts

Type of research degree
PhD
Application deadline
Ongoing deadline
Country eligibility
International (open to all nationalities, including the UK)
Funding
Competition funded
Supervisors
Dr Mauro Mobilia
Schools
School of Mathematics
Research groups/institutes
Applied Mathematics
<h2 class="heading hide-accessible">Summary</h2>

Why does cooperation abound in Nature? Why are there so many coexisting species and not just a few dominant ones? These are issues of paramount importance in biology and ecology. In fact, while there are many examples of cooperative behaviour in Nature, these challenge Darwinian evolution since, in the absence of appropriate mechanisms, cooperation is not sustained by evolution. Furthermore, how the interactions between organisms and between the environment and the species shape the biodiversity remains a fascinating puzzle: Some ecological system are composed by a very large number of coexisting species and others by much fewer, and species diversity can greatly vary within an ecosystem. It is well established that birth and death events by which the composition of a finite population changes yield demographic fluctuations that can lead to the extinction of some species. Moreover, organisms of an ecosystem generally move and form spatial arrangements that often help maintain their coexistence. In addition, natural populations face ever-changing environmental conditions that can influence their evolution. The changes in external conditions are often modelled by environmental noise whose impact has often been studied by assuming that demographic noise is independent of it. However, the dynamics of the population composition is often coupled with the evolution of its size, resulting in a coupling between demographic fluctuations and environmental noise. This is particularly relevant to microbial communities, which can experience sudden environmental changes. 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, 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. Hence, objectives of this project are: - Generalization of the approach of Physical Review Letters 119, 158301 (2017) and analysis of how environmental randomness affects the evolution of EGT cooperation scenarios. We will consider paradigmatic EGT models and public goods games in finite well-mixed populations of fluctuating size, e.g. with a randomly switching carrying capacity.

<h2 class="heading hide-accessible">Full description</h2>

<p>Why does cooperation abound in Nature? Why are there so many coexisting species and not just a few dominant ones? These are issues of paramount importance in biology and ecology.</p> <p>In fact, while there are many examples of cooperative behaviour in Nature, these challenge Darwinian evolution since, in the absence of appropriate mechanisms, cooperation is not sustained by evolution. Furthermore, how the interactions between organisms and between the environment and the species shape the biodiversity remains a fascinating puzzle: Some ecological system are composed by a very large number of coexisting species and others by much fewer, and species diversity can greatly vary within an ecosystem. It is well established that birth and death events by which the composition of a finite population changes yield demographic fluctuations that can lead to the extinction of some species.</p> <p>Moreover, organisms of an ecosystem generally move and form spatial arrangements that often help maintain their coexistence. In addition, natural populations face ever-changing environmental conditions that can influence their evolution. The changes in external conditions are often modelled by environmental noise whose impact has often been studied by assuming that demographic noise is independent of it. However, the dynamics of the population composition is often coupled with the evolution of its size, resulting in a coupling between demographic fluctuations and environmental noise. This is particularly relevant to microbial communities, which can experience sudden environmental changes.</p> <p>As an example, we can consider population consisting of a two strains of bacteria, with a &ldquo;free-rider&rdquo; 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>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, 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>Hence, objectives of this project are: -&nbsp;<a href="www1.maths.leeds.ac.uk/~amtmmo/PhysRevLett.119.158301.pdf">Generalization of the approach of Physical Review Letters 119, 158301 (2017)</a>&nbsp;and analysis of how environmental randomness affects the evolution of EGT cooperation scenarios. We will consider paradigmatic EGT models and public goods games in finite well-mixed populations of fluctuating size, e.g. with a randomly switching carrying capacity.</p> <p>The probability that cooperation prevails and the mean time for this to happen will be studied, as well as the population size distribution. - Study of the spatially-extended counterparts of EGT 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. - Study of the influence of environmental noise on species diversity in the voter model with speciation when the population size fluctuates.</p> <p>This reference neutral model (selection is neglected) will be studied on lattices of patches of fluctuating size connected by migration. We will be particularly interested in the species-area relationship measuring how the number of observed species increases upon enlarging the sampled area. The ultimate goal will be to gain a thorough understanding of the evolution of populations subject to randomness stemming from a coupling between environmental factors and demographic stochasticity. It is expected that some of the theoretical predictions could be tested experimentally, e.g. in microbial communities with engineered switching strains.</p> <p>Keywords: population dynamics, stochastic processes, fluctuations, evolutionary games, complex systems, ecology, individual-based modelling, statistical mechanics, stochastic simulations, networks.</p>

<h2 class="heading">How to apply</h2>

<p>Formal applications for research degree study should be made online through the&nbsp;<a href="https://www.leeds.ac.uk/info/130206/applying/91/applying_for_research_degrees">University&#39;s website</a>. Please state clearly in the research information section&nbsp;that the research degree you wish to be considered for is &lsquo;Stochastic Evolution of Populations in Fluctuating Environments&rsquo; as well as <a href="https://physicalsciences.leeds.ac.uk/staff/64/dr-mauro-mobilia">Dr Mauro Mobilia</a>&nbsp;as your proposed supervisor.</p> <p>If English is not your first language, you must provide evidence that you meet the University&#39;s minimum English language requirements (below).</p> <p><em>We welcome applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates. All scholarships will be awarded on the basis of merit.</em></p>

<h2 class="heading heading--sm">Entry requirements</h2>

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.

<h2 class="heading heading--sm">English language requirements</h2>

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.

<h2 class="heading">Funding on offer</h2>

<p><strong>Self-Funding Students</strong></p> <p><strong>Funding Eligibility</strong></p> <p><strong>UK/EU</strong> &ndash;&nbsp;&nbsp;Alumni Bursary is available to previous University of Leeds graduates offering 10% discount on Academic Fees.</p> <p><strong>International Students</strong> &ndash;&nbsp;Commonwealth Scholarship, Alumni Bursary is available to previous University of Leeds graduates offering 10% discount on Academic Fees.</p>

<h2 class="heading">Contact details</h2>

<p>For further information please contact Doctoral College Admissions by&nbsp;email:&nbsp;<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>, or by telephone: +44 (0)113 343 5057</p>


<h3 class="heading heading--sm">Linked funding opportunities</h3>
<h3 class="heading heading--sm">Linked research areas</h3>