Ecological modelers produce models with more and more details, leading to dynamical systems involving lots of variables. This chapter presents a set of methods which aim to extract from these complex models some submodels containing the same information but which are more tractable from the mathematical point of view. This "aggregation" of variables is based on time scales separation methods. The first part of the chapter is devoted to the presentation of mathematical aggregation methods for ODE's, discrete models, PDE's and DDE's. The second part presents several applications in population and community dynamics.

Abstract. Three indices of larval retention have been used in the literature to assess the tendency for self-maintenance of local marine populations: local retention (LR), selfrecruitment (SR), and relative local retention (RLR). Only one of these, LR, defined as the ratio of locally produced settlement to local egg production, has a clear relationship to selfpersistence of individual sites. However, SR, the ratio of locally produced settlement to settlement of all origins at a site, is generally easier to measure experimentally. We use theoretical, simulation, and empirical approaches to bridge the gap between these different indices, and demonstrate that there is a proportional relationship between SR and LR for metapopulations close to a stable state and with lifetime egg production (LEP) approximately uniform over space. Similarly, for systems where larval mortality rates are a relatively uniform function of release site, RLR (defined as the ratio of locally produced settlement to all settlement of local origin) and LR will also be proportional. Therefore, SR and RLR provide information on relative rates of LR for systems satisfying these conditions. Furthermore, the ratio between LR and SR can be used to evaluate global persistence of metapopulations, and therefore provides valuable information not necessarily available if only LR is considered.

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