Abstract : 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 thosepreferring complex individual-based models that are more structurally realistic with a more detailedrepresentation of the basic processes and interactions at the level of the individuals. In this thesis we attempt to bridge these two approaches by derivingdeterministic moment approximation models of microbial individual-based models. We illustrate the approach on the example of biofilm growth with immotile and motile bacteria. we show that moment models can capture the main features of spatial patterns that arise in simplified biofilm individual-based models. Finally we assess the limitation of the moment models in capturing the e ect of the local uctuation of the individual's environment.