An Exact Coarse-Graining Consistent Metapopulation Model

Different levels of coarse-graining are of paramount importance to understand how conclusions drawn from local studies can be made general and extrapolated to larger regions. We here investigate how consist metapopulation model are when considering different resolutions of the landscape matrix, i.e. different levels of coarse-graining. A formulation of the metapopulation model, taking into consideration a dispersal volume depending on the grid-cell area is proposed. This first derivation from the classical model is then extended in order to account for intra-cellular colonization (called self-colonization), which permits an aggregation of cells, as typically done with coarse-graining. The consistency of the proposed model formulations is then investigated, first, in a flat homogeneous domain, where the results are independent of the landscape structure. In a second step, a complex landscape structure is introduced in the form of an elevation field, the Gran Paradiso National Park. The results suggest that the proposed formulations of the model are independent of coarse-graining in the flat domain. This appears to be the case in the park as well, up to a certain level of coarse-graining, where loss of information on the landscape matrix becomes too severe. In all considered levels of coarse-graining the proposed formulation of the model outperforms the previously proposed models in terms of convergence of the results.