Figure 1. Conceptual illustration of the Jacobian matrix in random meta-ecosystems.

The model represents the dynamics of a meta-ecosystem, pictured as a spatial network of interaction networks (top left). The Jacobian matrix representing all interactions among pairs of species and locations is highly structured. It is made of the sub-matrices A, M and D. The spatial heterogeneity among locations is implemented by varying interaction coefficients in space (different entries in each interaction sub-matrix) and the landscape is implemented by varying the spatial structure of the model (entries in each pairwise dispersal matrix).