Résumé
In ecology, the study of population dynamics is an important source of information for biodiversity conservation. Among the mathematical approaches used to model population dynamics, Hidden Markov Models (HMM) are well adapted in the case where the species of interest is difficult to observe. For a broader application of HMM in ecology, two limits need to be overcome. First, in most cases, HMM are used to deal with detection errors. But, another important situation is when only some life stages of the population can be observed while the others remain hidden. Second, conservation efforts actually require knowledge at the level of metapopulation more than a single population. Therefore there is a need to extend the HMM framework to the case of several couples of hidden and observed sub-populations in interaction. Depending on the species under study (plant, fungus, animal) the interaction between populations can be from and to observable or hidden stages and this structure must be explicitly modeled. In this work, we propose a conceptual guide to modeling and estimating parameters involved in metapopulation dynamics with partially observable populations, using the framework of Partially Observable Dynamic Bayesian Networks (PO-DBN). We show that only $4$ interaction structures are needed to describe the main metapopulation models. Based on biological examples, we show how to build the associated PO-DBN for each of these structures. Finally, we consider parameter estimation using the EM algorithm for these models. We establish for which structures implementing EM is straightforward and for which there are computational limits. In these cases, we discuss methods from approximate inference that can be used to overcome them. This study provides the practical foundations for modeling and estimating the dynamics of a metapopulation with partially observable populations. It points out the computational challenges that remain to be tackled for a practical use.