Interacting Partially Observable DBN to model the dynamics of partially observable metapopulations: Opportunities and open challenges

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 can deal with detection errors, another important situation is when only some life stages of the population can be observed while the others remain hidden. The metapopulation level, rather than a single population, makes it possible to incorporate dispersal processes, often linked to hidden life stages. 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. We propose a conceptual guide to model and estimate such dynamics using the framework of interacting Partially Observable Dynamic Bayesian Networks (PO-DBN). We show that only four interaction structures are needed to describe the main metapopulation models. We illustrate them on concrete examples. Well known computational challenges apply to inference in metapopulation models with partial observation, due to the problem dimension. We discuss parameter estimation using the EM algorithm and we establish that for two structures the complexity of EM is actually 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 for approximate inference. This study provides the practical foundations for modelling and estimating the dynamics of a metapopulation with hidden life stages.