How Space and Noise Influence the Coexistence of Species in Cyclic Competition

Lead Research Organisation: University of Leeds
Department Name: Applied Mathematics


In Nature, organisms interact with a finite number of individuals in their neighbourhood, they move and ecosystems are therefore not aptly described by well-mixed models. In fact, populations often self-organise by forming spatial patterns whose origin is an intense subject of research. Recently, there has been an
increasing interest in investigating how fluctuations and nonlinearity influence the formation of biological patterns. In spite of the progress made, the biological significance of emerging patterns and mobility still remains unclear. Here, these questions will be investigated within the framework of the paradigmatic spatial rock-paper-scissors game motivated by the cyclic competition in microbial experiments [B. Kerr et al., Nature *418*, 171 (2002)].
In a series of works, Mobilia and co-workers considered a spatial rock-paper-scissors model with linear diffusion and established a diffusion threshold below which all species coexist and form spiralling patterns, while above the threshold only one species survives [see, e.g., Nature *448*, 1046 (2007)]. Recently, in a PhD thesis supervised by Mobilia and Rucklidge, a metapopulation modelling approach was developed to establish a rigorous connection between the
individual-based model and its macroscopic description [EPL *102*, 28012 (2013); Phys. Rev. E *90*, 032704 (2014)]. However, as yet no systematic studies have been carried out to understand how species coexistence is affected by the joint effect of nonlinear mobility and noise, and what is the evolutionary significance of the resulting patterns.
These and related questions will be investigated for a rock-paper-scissors model in which the agents' movement is directed (driven by nutrients). Within a metapopulation approach, this model will be studied at micro-level and then up-scaled to yield partial differential equations with nonlinear diffusion terms. One goal will be to understand under which circumstances coherent patterns emerge and how noise and directed nonlinear mobility affect their properties. We will also systematically investigate how the self-organisation into patterns influences the time during which species coexist before extinction.


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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509681/1 01/10/2016 30/09/2021
1802031 Studentship EP/N509681/1 01/10/2016 31/03/2020 Robert Edward West
Description IWEE Leeds 19 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Postgraduate students
Results and Impact I was part of a team of four people that organised a two-day interdisplinary workshop exploring evolution and ecology from a mathematical, historical and philosophical perspective. It was aimed at early career researchers, with two keynote presentations by more established scientists. This was the first time that we ran it, and recieved feedback from nearly all attendees that they would like participate in future events like this one.
Year(s) Of Engagement Activity 2019