Abstract
Mathematical modelling is nowadays a central tool in microbial ecology. Ecological theory and numerical modelling are essential for developing a deeper understanding of the mechanisms that shape the assembly and evolution of microbial communities. Microbes interact among themselves and with their environment in complex ways, and can display a very rich set of spatiotemporal dynamics. Modelling these processes is thus a challenging enterprise that needs to be subject to experimental validation. This article provides a review of the state-of-the-art of models in microbial ecology, ranging from the microscopic level (e.g., resource uptake) to the macroscopic level (e.g., spatial organization). Special emphasis is given to the modelling of (i) uptake kinetics, elemental stoichiometry and functional trade-offs; (ii) food web and eco-evolutionary dynamics; (iii) micro-scale variability and social behavior in microbes. The overarching point of view is the use of theoretical models to improve our understanding of how microbial communities operate and affect ecosystem functioning.