Aggregation and emergence in ecological modelling: integration of ecological levels

Modelling ecological systems implies to take into account different ecological levels: the individual, population, community and ecosystem levels. Two large families of models can be distinguished among different approaches: (i) completely detailed models involving many variables and parameters; (ii) more simple models involving only few state variables. The first class of models are usually more realistic including many details as for example the internal structure of the population. Nevertheless, the mathematical analysis is not always possible and only computer simulations can be performed. The second class of models can mathematically be analysed, but they sometimes neglect some details and remain unrealistic. We present here a review of aggregation methods, which can be seen as a compromise between these two previous modelling approaches. They are applicable for models involving two levels of organisation and the corresponding time scales. The most detailed level of description is usually associated to a fast time scale, while the coarser one rather corresponds to a slow time scale. A detailed model is thus considered at the individual level, containing many micro-variables and consisting of two parts: a fast and a slow one. Aggregation methods allow then to reduce the dimension of the initial dynamical system to an aggregated one governing few global variables evolving at the slow time scale. We focus our attention on the emerging properties of individual behaviours at the population and community levels.