Unifying Reserve Design Strategies with Graph Theory and Constraint Programming

The delineation of areas of high ecological or biodiversity value is a priority of any conservation program. However, the selection of optimal areas to be preserved necessarily results from a compromise between the complexity of ecological processes and managers’ constraints. Current reserve design models usually focus on few criteria, which often leads to an oversimplification of the underlying conservation issues. This paper shows that Constraint Programming (CP) can be the basis of a more unified, flexible and extensible framework. First, the reserve design problem is formalized. Secondly, the problem is modeled from two different angles by using two graph-based models. Then CP is used to aggregate those models through a unique Constraint Satisfaction Problem. Our model is finally evaluated on a real use case addressing the problem of rainforest fragmentation in New Caledonia, a biodiversity hotspot. Results are promising and highlight challenging perspectives to overtake in future work.

[1]  J. Elith,et al.  Species Distribution Models: Ecological Explanation and Prediction Across Space and Time , 2009 .

[2]  Antoine Guisan,et al.  Predictive habitat distribution models in ecology , 2000 .

[3]  Hugh P. Possingham,et al.  Marxan with Zones: Software for optimal conservation based land- and sea-use zoning , 2009, Environ. Model. Softw..

[4]  Charles S. ReVelle,et al.  Spatial attributes and reserve design models: A review , 2005 .

[5]  Peter J. Stuckey,et al.  Explaining Flow-Based Propagation , 2012, CPAIOR.

[6]  R L Pressey,et al.  Beyond opportunism: Key principles for systematic reserve selection. , 1993, Trends in ecology & evolution.

[7]  Willem Jan van Hoeve,et al.  An efficient generic network flow constraint , 2011, SAC '11.

[8]  Nicolas Beldiceanu,et al.  Global Constraint Catalog, 2nd Edition (revision a) , 2012 .

[9]  Philippe Birnbaum,et al.  Accounting for the indirect area effect in stacked species distribution models to map species richness in a montane biodiversity hotspot , 2015 .

[10]  Alain Billionnet,et al.  Solving the probabilistic reserve selection problem , 2011 .

[11]  D. Legrand,et al.  Individual dispersal, landscape connectivity and ecological networks , 2013, Biological reviews of the Cambridge Philosophical Society.

[12]  Alain Billionnet,et al.  Designing Connected and Compact Nature Reserves , 2016, Environmental Modeling & Assessment.

[13]  J. Orestes Cerdeira,et al.  Flexibility, efficiency, and accountability: adapting reserve selection algorithms to more complex conservation problems , 2000 .

[14]  Mats Carlsson,et al.  Graph Invariants as Necessary Conditions for Global Constraints , 2005, CP.

[15]  Nicolas Beldiceanu,et al.  Integration of AI and OR Techniques in Contraint Programming for Combinatorial Optimzation Problems , 2012, Lecture Notes in Computer Science.

[16]  K. Sahr,et al.  Geodesic Discrete Global Grid Systems , 2003 .

[17]  Yves Deville,et al.  CP(Graph): Introducing a Graph Computation Domain in Constraint Programming , 2005, CP.

[18]  Alexander Bockmayr,et al.  Network Flow Problems in Constraint Programming , 2001, CP.

[19]  J. Lawton,et al.  Rare species, the coincidence of diversity hotspots and conservation strategies , 1993, Nature.

[20]  Claire A. Montgomery,et al.  Trade‐offs and efficiencies in optimal budget‐constrained multispecies corridor networks , 2017, Conservation biology : the journal of the Society for Conservation Biology.

[21]  Bistra N. Dilkina,et al.  Achieving full connectivity of sites in the multiperiod reserve network design problem , 2017, Comput. Oper. Res..

[22]  F. Boissieu,et al.  ssdm: An r package to predict distribution of species richness and composition based on stacked species distribution models , 2017 .

[23]  J A Heesterbeek,et al.  On optimal size and number of reserves for metapopulation persistence. , 2000, Journal of theoretical biology.

[24]  Ellen I. Damschen,et al.  Habitat fragmentation and its lasting impact on Earth’s ecosystems , 2015, Science Advances.

[25]  Philippe Birnbaum,et al.  How does forest fragmentation affect tree communities? A critical case study in the biodiversity hotspot of New Caledonia , 2017, Landscape Ecology.

[26]  Colin P.D. Birch,et al.  Rectangular and hexagonal grids used for observation, experiment and simulation in ecology , 2007 .

[27]  Grégoire Dooms,et al.  The CP(Graph) computation domain in constraint programming , 2006 .

[28]  Paul Beier,et al.  Toward Best Practices for Developing Regional Connectivity Maps , 2011, Conservation biology : the journal of the Society for Conservation Biology.

[29]  Jared M. Diamond,et al.  THE ISLAND DILEMMA: LESSONS OF MODERN BIOGEOGRAPHIC STUDIES FOR THE DESIGN OF NATURAL RESERVES , 1975 .

[30]  Mats Carlsson,et al.  Graph Properties Based Filtering , 2006, CP.

[31]  C. Revelle,et al.  Counterpart Models in Facility Location Science and Reserve Selection Science , 2002 .