Coupling agent-based with equation-based models to study spatially explicit megapopulation dynamics

The incorporation of the spatial heterogeneity of real landscapes into population dynamics remains extremely difficult. We propose combining equation-based modelling (EBM) and agent-based modelling (ABM) to overcome the difficulties classically encountered. ABM facilitates the description of entities that act according to specific rules evolving on various scales. However, a large number of entities may lead to computational difficulties (e.g., for populations of small mammals, such as voles, that can exceed millions of individuals). Here, EBM handles age-structured population growth, and ABM represents the spreading of voles on large scales. Simulations applied to the spreading of a montane water vole population demonstrated that our model is quite efficient in representing the pattern observed and might help to highlight some key parameters during population expansion. This method paves the way for further developments, including the introduction of density-dependent parameters (predation, diseases, etc.) capable of triggering population declines in an explicitly spatial context.