I am a second year PhD working on the mathematical modelling of microbial communities. I am developing work started by Todd Parsons (University of Toronto) who has worked with my supervisor, Chris Quince, on the dynamics of quasi-neutral species. Quasi-neutral species are defined as species whose parameters are such that they have equivalent fitness in a given environment. We are interested in a chemostat environment with a explicit resource term. When two species co-exist at a deterministic equilibrium, their dynamics will be determined by stochastic fluctuations. We suppose that co-existing species follow a Poisson process. Todd has formulated a diffusion approximation to this Poisson process in the limit of infinite volume. In this limit the substrate concentration is invariant to stochastic fluctuations. From this we can calculate a fixation probability for a given species in competition to another and further explore the dynamics of the system.

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School of Engineering,

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University of Glasgow,

Glasgow

E-mail:s.luo.1@research.gla.ac.uk

Phone: +44 (0) 141 330 6311