Optimal design of compact and functionally contiguous conservation management areas

Compactness and landscape connectivity are essential properties for effective functioning of conservation reserves. In this article we introduce a linear integer programming model to determine optimal configuration of a conservation reserve with such properties. Connectivity can be defined either as structural (physical) connectivity or functional connectivity; the model developed here addresses both properties. We apply the model to identify the optimal conservation management areas for protection of Gopher Tortoise (GT) in a military installation, Ft. Benning, Georgia, which serves as a safe refuge for this ‘at risk’ species. The recent expansion in the military mission of the installation increases the pressure on scarce GT habitat areas, which requires moving some of the existent populations in those areas to suitably chosen new conservation management areas within the boundaries of the installation. Using the model, we find the most suitable and spatially coherent management areas outside the heavily used training areas.

[1]  Atte Moilanen,et al.  Connectivity, Probabilities and Persistence: Comparing Reserve Selection Strategies , 2006, Biodiversity & Conservation.

[2]  Hayri Önal,et al.  Designing a connected nature reserve using a network flow theory approach , 2013 .

[3]  J. Gamarra,et al.  Metapopulation Ecology , 2007 .

[4]  Hayri Önal,et al.  Incorporating spatial criteria in optimum reserve network selection , 2002, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[5]  Hayri Önal,et al.  Selection of a minimum–boundary reserve network using integer programming , 2003, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[6]  Hayri Önal,et al.  Designing a conservation reserve network with minimal fragmentation: A linear integer programming approach , 2005 .

[7]  Erik Matthysen,et al.  The application of 'least-cost' modelling as a functional landscape model , 2003 .

[8]  Jamie B. Kirkpatrick,et al.  An iterative method for establishing priorities for the selection of nature reserves: An example from Tasmania , 1983 .

[9]  George A. McLachlan,et al.  Threatened and Endangered Species , 2002 .

[10]  John W. Hearne,et al.  A new method to solve the fully connected Reserve Network Design Problem , 2013, Eur. J. Oper. Res..

[11]  H. Possingham,et al.  Spatial conservation prioritization: Quantitative methods and computational tools , 2009 .

[12]  Kevin McGarigal,et al.  Estimating landscape resistance to movement: a review , 2012, Landscape Ecology.

[13]  Les G. Underhill,et al.  Optimal and suboptimal reserve selection algorithms , 1994 .

[14]  B. Stein,et al.  Federal Lands and Endangered Species: The Role of Military and Other Federal Lands in Sustaining Biodiversity , 2008 .

[15]  Lenore Fahrig,et al.  Connectivity Conservation: Landscape connectivity: a return to the basics , 2006 .

[16]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[17]  Hayri Önal,et al.  Designing connected nature reserve networks using a graph theory approach , 2011 .

[18]  Hugh P. Possingham,et al.  Effectiveness of alternative heuristic algorithms for identifying indicative minimum requirements for conservation reserves , 1997 .

[19]  Miguel Constantino,et al.  Imposing Connectivity Constraints in Forest Planning Models , 2013, Oper. Res..

[20]  Robert G. Haight,et al.  Integer programming methods for reserve selection and design , 2009 .

[21]  K. D. Rothley,et al.  DESIGNING BIORESERVE NETWORKS TO SATISFY MULTIPLE, CONFLICTING DEMANDS , 1999 .

[22]  Richard L. Church,et al.  Reserve selection as a maximal covering location problem , 1996 .

[23]  R. Haight,et al.  Prioritizing conservation targets in a rapidly urbanizing landscape , 2009 .

[24]  Richard L. Church,et al.  Contiguity Constraints for Single‐Region Site Search Problems , 2010 .

[25]  C. Flather,et al.  Species endangerment patterns in the United States , 1994 .

[26]  Naiara Pinto,et al.  Beyond the least-cost path: evaluating corridor redundancy using a graph-theoretic approach , 2009, Landscape Ecology.

[27]  Justin C. Williams,et al.  Optimal reserve site selection with distance requirements , 2008, Comput. Oper. Res..

[28]  Hayri Önal,et al.  A graph theory approach for designing conservation reserve networks with minimal fragmentation , 2008 .

[29]  Stephanie A. Snyder,et al.  Restoring habitat corridors in fragmented landscapes using optimization and percolation models , 2005 .

[30]  Marc E. McDill,et al.  Promoting Large, Compact Mature Forest Patches in Harvest Scheduling Models , 2008 .

[31]  R. Haight,et al.  Habitat Acquisition Strategies for Grassland Birds in an Urbanizing Landscape , 2007, Environmental management.

[32]  Michael S. Knowles,et al.  Threatened and endangered species geography: characteristics of hot spots in the conterminous United States , 1998 .

[33]  Hayri Önal,et al.  Optimal Selection of a Connected Reserve Network , 2006, Oper. Res..

[34]  Marc Bélisle,et al.  MEASURING LANDSCAPE CONNECTIVITY: THE CHALLENGE OF BEHAVIORAL LANDSCAPE ECOLOGY , 2005 .

[35]  K. D. Cocks,et al.  Using mathematical programming to address the multiple reserve selection problem: An example from the Eyre Peninsula, South Australia , 1989 .

[36]  S. Polasky,et al.  Selecting Biological Reserves Cost-Effectively: An Application to Terrestrial Vertebrate Conservation in Oregon , 2001, Land Economics.

[37]  Charles ReVelle,et al.  Binary Logic Solutions to a Class of Location Problem , 2010 .

[38]  John Sessions,et al.  Economic and Spatial Impacts of an Existing Reserve Network on Future Augmentation , 2002 .

[39]  Taku Kadoya,et al.  Assessing functional connectivity using empirical data , 2008, Population Ecology.

[40]  C. Revelle,et al.  A 0–1 Programming Approach to Delineating Protected Reserves , 1996 .

[41]  L. Fahrig,et al.  On the usage and measurement of landscape connectivity , 2000 .

[42]  Richard L. Church,et al.  The maximal covering location problem , 1974 .

[43]  R. A. Zemlin,et al.  Integer Programming Formulation of Traveling Salesman Problems , 1960, JACM.

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

[45]  Todd K. BenDor,et al.  Simulating population variation and movement within fragmented landscapes: an application to the gopher tortoise (Gopherus polyphemus). , 2009 .

[46]  David J. Tazik,et al.  US army land condition-trend analysis (LCTA) program , 1992 .

[47]  Vladimir Marianov,et al.  Selecting compact habitat reserves for species with differential habitat size needs , 2008, Comput. Oper. Res..

[48]  Timothy H. Keitt,et al.  Landscape connectivity: A conservation application of graph theory , 2000 .

[49]  A. Zoltners,et al.  Sales Territory Alignment: A Review and Model , 1983 .

[50]  Atte Moilanen,et al.  On the use of connectivity measures in spatial ecology , 2001 .

[51]  Atte Moilanen,et al.  METAPOPULATION DYNAMICS: EFFECTS OF HABITAT QUALITY AND LANDSCAPE STRUCTURE , 1998 .

[52]  Justin C. Williams,et al.  Delineating protected wildlife corridors with multi‐objective programming , 1998 .

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

[54]  Robert A. Briers,et al.  Incorporating connectivity into reserve selection procedures , 2002 .

[55]  Timothy H. Keitt,et al.  LANDSCAPE CONNECTIVITY: A GRAPH‐THEORETIC PERSPECTIVE , 2001 .

[56]  Jon M. Conrad,et al.  Wildlife corridors as a connected subgraph problem , 2012 .

[57]  H. Young Measuring the Compactness of Legislative Districts , 1988 .

[58]  Hayri Önal,et al.  Site Accessibility And Prioritization Of Nature Reserves , 2007 .

[59]  Takeshi Shirabe,et al.  A Model of Contiguity for Spatial Unit Allocation , 2005 .

[60]  Robert G. Haight,et al.  Metropolitan natural area protection to maximize public access and species representation , 2003 .

[61]  Hayri Önal,et al.  Incorporating species relocation in reserve design models: An example from Ft. Benning GA , 2012 .

[62]  Charles ReVelle,et al.  A multiobjective integer programming model for the land acquisition problem , 1983 .

[63]  Charles ReVelle,et al.  Applying mathematical programming to reserve selection , 1997 .

[64]  Justin C. Williams,et al.  Reserve assemblage of critical areas: A zero-one programming approach , 1998 .

[65]  L. Fahrig,et al.  Connectivity is a vital element of landscape structure , 1993 .

[66]  Andrew R. Solow,et al.  A note on optimal algorithms for reserve site selection , 1996 .

[67]  Shurong Zhou,et al.  One large, several medium, or many small? , 2006 .

[68]  Richard L. Church,et al.  Clustering and Compactness in Reserve Site Selection: An Extension of the Biodiversity Management Area Selection Model , 2003, Forest Science.

[69]  S. Andelman,et al.  Mathematical Methods for Identifying Representative Reserve Networks , 2000 .

[70]  J. Orestes Cerdeira,et al.  Connectivity in priority area selection for conservation , 2005 .

[71]  J. Orestes Cerdeira,et al.  Requiring Connectivity in the Set Covering Problem , 2005, J. Comb. Optim..

[72]  Justin C. Williams,et al.  A linear‐size zero—one programming model for the minimum spanning tree problem in planar graphs , 2002, Networks.

[73]  Thomas R. Etherington,et al.  Least-cost path length versus accumulated-cost as connectivity measures , 2013, Landscape Ecology.

[74]  Robert G. Haight,et al.  Reserve selection with minimum contiguous area restrictions: An application to open space protection planning in suburban Chicago , 2009 .

[75]  Richard L. Church,et al.  The p-Regions Problem. p-区域问题 , 2011 .

[76]  J. Orestes Cerdeira,et al.  Species specific connectivity in reserve-network design using graphs , 2010 .