Analyzing individual-based models of microbial systems

There is a debate in ecology between those favoring simple aggregated mathematical models containing only a few equations expressing a small number of general principles and those preferring complex individual-based models that are more structurally realistic with a more detailed representation of the basic processes and interactions at the level of the individuals. In this thesis we attempt to bridge these two approaches by deriving deterministic moment approximation models of microbial individual-based models. We illustrate the approach on the example of bio lm growth with immotile and motile bacteria. We show that moment model can capture the main features of spatial pattern that arise in simpli ed bio lm individual-based models. Finally we assess the limitation of moment models in capturing the e ect of the local uctuation of the individual's environment. te l-0 07 12 15 3, v er si on 1 26 J un 2 01 2