Spatial dynamics of green corridors

Forest management aims at building ecological networks that minimize the impacts on timber production. We formalize the construction of ecological networks in forest environments as the optimal control dynamic graph-theoretic problem. The ecological network is based on a set of bioreserves and patches linked by green corridors. The network is defined as a graph, in which bioreserves, which host the species, are represented by the target nodes provided with an attraction function. The role of patches, which are represented by the unmarked nodes, is to receive the species before redirecting them to bioreserves. We consider two cases: a case of complete graph, where the ecological network is fully connected, and a case of incomplete graph, where the ecological network is partially connected. We use an ecologically and economically weighted Mahalanobis distance when dealing with the species migration through the grid. We find that the connectivity between areas depends on their ecological similarity. In both cases, at the equilibrium, the ecological network maintains its connectedness while minimizing the distances between nodes weighted by the opportunity costs of timber production. Whether the graph is complete or incomplete, the optimal control imposes specific conditions on the shadow values. Our simulations show that taking into account the opportunity costs of timber production is essential to determine the economic soundness of the ecological project, but the optimality threshold depends on the type of network that is envisaged.