Context — Land development and expansion of anthropic areas have caused the ecological fragmentation of territory, leading to the decline of species. In order to minimize the ensuing damages and to ensure the species viability, the supply of green corridors has been developed. Indeed, biologists have emphasized the need of connecting areas of biological and ecological significance. Thereby, correctly implemented green corridors provide benefits by returning the landscape to its natural connected state; they likewise facilitate the adaptation of vulnerable species to the environmental disturbances.

Objectives — The objective is to analyze the ecological networks under the spectrum of graph theory seen by the optimal control. The ecological network is defined as a connected network of bioreserves and patches linked by the green corridors. The network will be represented by a graph, in which bioreserves will be symbolized by target nodes to which the forest manager assigns some ecological objective. Patches will be symbolized by unmarked nodes which are driven to the ecological objective by means of the target nodes. The management policy aims at building the ecological network while minimizing the economic impact on timber production. 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.

Approach — When dealing with species migration through the green corridors, we shall use an ecologically and economically weighted Mahalanobis distance rather than the standard Euclidean distance. We submit the coordinates of the graph nodes to the Laplacian dynamics or the consensus differential equation. The output of the model is a matrix equation subjected to optimality constraints on the shadow values.

Key results —

• Our results show that the connectivity between ecological zones depends on their ecological similarity.

•  At the equilibrium, the ecological network maintains its connectedness while minimizing the impact on timber production on which depend the forest owner revenues.

•  Optimization and control of partially connected ecological networks are more expensive than the optimization and control of ecological networks fully connected.

•  When timber production is lowered significantly, only partially connected ecological networks should be established.

 

Main conclusions  — We applied the optimal control properties to a network topology in order to obtain the graph-theoretic characterization of controllability. By doing so, we allowed for the ecological network control. To nuance the last statement, this work has to be considered as initiatory, provided that graph theory is a schematized representation of network patterns. Thereby, case studies related to forest environments should be done. For example, one could value the levels of shadow values, through market-based mechanisms such as auctions, and assess the opportunity costs, through the inventory of forest stands, with a view to reveal the landowners’ optimality thresholds.

Future Perspectives — The future avenues of research can be classified in two categories. The first category concerns the migratory species, that is, the introduction of population dynamics and migratory flows, in order to estimate the needed sizes of bioreserves and the number of patches that would prevent from the occurrence of congestion. The second category involves the graph topology, through the implementation of probabilistic corridors on random graphs, by reason of the stochastic processes in nature. As the risk of occurrence of exogenous events, such as storms, fires, pathologies, and floods steps up, the probability of existence of the ecological network in its initial configuration is threatened. The second category also pertains to the introduction of an evolutive variance-covariance matrix, so as to seize the impacts of climate change on the biophysical properties of ecological sites.

 

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Presentations at scientific meetings and conferences —

2015

• RMA Conference, University of Bordeaux, Bordeaux, France;
• MMEE Conference, Collège de France, Paris, France

2014

• FAERE Conference, University of Montpellier, Montpellier, France;
• ISDG Symposium, University of Amsterdam, Amsterdam, Netherlands;
• WCERE Congress, Istanbul Technical University, Istanbul, Turkey.

2013

• M3d Workshop, French National Network of Complex Systems, Oléron Island, France;
• AFSE Congress, Aix-Marseille School of Economics, Aix-en-Provence, France.

 

Publications —

• Dragicevic, A., Boulanger, V., Bruciamacchie, M., Chauchard, S., Dupouey, J.-L. and Stenger, A. (2017), Network Connectivity Value, Journal of Theoretical Biology, 419: 310–322.

• Perez, M. (2015), Economic Impact of the Implementation of Green Corridors, Mémoire de fin d’études, réalisé au Laboratoire d’Economie Forestière, sous la direction d’Arnaud Dragicevic.

• Dragicevic, A. (2016), From Robustness to Resilience: A Network Price Identity Approach, Ecological Complexity, 28: 47–53.