Stochastic models of microbial communities: stochastic dynamics of quasi-neutral species in a resource-limited chemostat environment

The most indispensable work for microbial ecologists is to develop mathematical models in order to describe microbial communities. In this aspect, a proper understanding of microorganism richness and abundance is of paramount importance. A chemostat environment is a classic open microbial community, where multiple species compete for limited nutrients, whose mathematical model has broad applications in microbiology and population biology. Generally speaking, there are four key processes that may influence the diversity: selection, speciation, drift and dispersal. The debate between niche assembly theory and neutral theory has lasted for decades about the dominant process. In term of simplicity, Hubbell's unified neutral theory of biodiversity has a distinct advantage for sampling and parameterisation. It offers a quantitative stochastic base model of island macroscopic community coupled with meta-community, where species compete in a finite environment. In this thesis, an explicit quasi-neutral chemostat model is fully devised by reconciling neutral theory and niche difference, which gives insight into how the origin, maintenance and loss of biodiversity in the local competitive community at different time scales are influenced by selection, stochastic drift and dispersal. An analysis of the deterministic dynamics is conducted to explain the niche assembly rule, and to further show that the species at the same largest fitness will be selected to coexist through life history trade-offs. These species are quasi-neutral. However, over a long period of time, stochastic drift will play a dominant role in constructing the pattern of the local communities. Without dispersal, extinction is the ultimate fate of stochastic drift. Both analytical and numerical methods established in this thesis verify that the quasi-neutral species are in fact not competitively equivalent. Their difference will drive a superior species to fix in the isolated community. When dispersal is incorporated, even with low immigration rate, it will drive the long term drift of large communities, and balance extinction to maintain the diversity of the local communities. An explicit results for the stationary abundance distribution is calculated, which helps to demonstrate a deviation from the neutral model. These results from the explicit stochastic model highlight the importance of incorporating species interaction into the basic neutral model