Résumé
In ecology, among the mathematical approaches used to model population dynamics, Hidden Markov Models (HMM) are well adapted to 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. While HMMs are often used to deal with detection errors, another important situation is when only some life stages of the population can be observed while the others remain hidden. Also, understanding ecological patterns of dispersal requires a model at the metapopulation level rather than for a single population. Therefore, there is a need to extend the HMM framework to the case of several couples of hidden and observed life stages interacting via dispersal, which depends on the studied species (plant, fungus, animal). Such interactions have to be modeled explicitly. In this work, we propose a conceptual guide to model and estimate metapopulation parameters using the framework of Partially Observable Dynamic Bayesian Networks (PO-DBN). We show that only four interaction structures are needed to describe the main metapopulation models. We illustrate the four structures with examples of species dynamics and we show how to build the associated interacting PO-DBN. Finally, we consider parameter estimation using the EM algorithm. We establish that for two structures the complexity of EM remains linear in the number of patches, which means that estimation is easily accessible for the associated metapopulations. For the two other structures, the EM complexity is exponential and we discuss methods from approximate inference to overcome this difficulty. This study provides the practical foundations for modeling and estimating the dynamics of a metapopulation with hidden life stages.