Patch-based graphs of landscape connectivity: A guide to construction, analysis and application for conservation

Graph theory has become a popular tool for modelling the functional connectivity of landscapes. We conduct a review of studies that use graph theory to model connectivity among patches of habitat (patch-based graphs), with the intention of identifying typical research questions and their associated graph construction and analysis methods. We identify and examine nine questions of conservation importance that can be answered with these types of graph models, discussing appropriate applications of these questions and presenting a guide for using graph methods to answer them. We also investigate how the connectivity predictions of patch-based graphs have been assessed and emphasize the importance of empirical evaluation. Our findings identify commonality among diverse approaches and methodological gaps with an aim to improve application and to help the integration of graph theory and ecological analysis.

[1]  Pierre Taberlet,et al.  An evaluation of field and non-invasive genetic methods to estimate brown bear (Ursus arctos) population size , 2006 .

[2]  Atsuyuki Okabe,et al.  Spatial Tessellations: Concepts and Applications of Voronoi Diagrams , 1992, Wiley Series in Probability and Mathematical Statistics.

[3]  Jordi Bascompte,et al.  Spatial network structure and amphibian persistence in stochastic environments , 2006, Proceedings of the Royal Society B: Biological Sciences.

[4]  L. Waits,et al.  Molecular road ecology: exploring the potential of genetics for investigating transportation impacts on wildlife , 2009, Molecular ecology.

[5]  Robert S Schick,et al.  Graph models of habitat mosaics. , 2009, Ecology letters.

[6]  Dean L Urban,et al.  Graph theory as a proxy for spatially explicit population models in conservation planning. , 2007, Ecological applications : a publication of the Ecological Society of America.

[7]  Christopher P. Brooks,et al.  Quantifying population substructure: extending the graph-theoretic approach. , 2006, Ecology.

[8]  Robert S. Schick,et al.  Directed connectivity among fish populations in a riverine network , 2007 .

[9]  Andrew Fall,et al.  A domain-specific language for models of landscape dynamics , 2001 .

[10]  Todd R. Lookingbill,et al.  Combining a dispersal model with network theory to assess habitat connectivity. , 2010, Ecological applications : a publication of the Ecological Society of America.

[11]  A Coulon,et al.  Landscape connectivity influences gene flow in a roe deer population inhabiting a fragmented landscape: an individual–based approach , 2004, Molecular ecology.

[12]  Laura Finnegan,et al.  Integrating multiple analytical approaches to spatially delineate and characterize genetic population structure: an application to boreal caribou (Rangifer tarandus caribou) in central Canada , 2010, Conservation Genetics.

[13]  Santiago Saura,et al.  Impact of spatial scale on the identification of critical habitat patches for the maintenance of landscape connectivity , 2007 .

[14]  Jean Paul Metzger,et al.  Using gap‐crossing capacity to evaluate functional connectivity of two Atlantic rainforest birds and their response to fragmentation , 2008 .

[15]  Maria Tengö,et al.  The value of small size: loss of forest patches and ecological thresholds in southern Madagascar. , 2006, Ecological applications : a publication of the Ecological Society of America.

[16]  Santiago Saura,et al.  Integrating landscape connectivity in broad-scale forest planning through a new graph-based habitat availability methodology: application to capercaillie (Tetrao urogallus) in Catalonia (NE Spain) , 2006, European Journal of Forest Research.

[17]  Ernesto Estrada,et al.  Using network centrality measures to manage landscape connectivity. , 2008, Ecological applications : a publication of the Ecological Society of America.

[18]  Erik Andersson,et al.  Practical tool for landscape planning? An empirical investigation of network based models of habitat fragmentation , 2009 .

[19]  Marie-Josée Fortin,et al.  Spatial Graphs: Principles and Applications for Habitat Connectivity , 2007, Ecosystems.

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

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

[22]  Marc-André Villard,et al.  Patch-, Landscape-, and Regional-Scale Effects on Biota , 2002 .

[23]  Samuel A. Cushman,et al.  Gene Flow in Complex Landscapes: Testing Multiple Hypotheses with Causal Modeling , 2006, The American Naturalist.

[24]  Jon Norberg,et al.  A Network Approach for Analyzing Spatially Structured Populations in Fragmented Landscape , 2007, Landscape Ecology.

[25]  Kevin R. Crooks,et al.  Connectivity Conservation: Connectivity conservation: maintaining connections for nature , 2006 .

[26]  Pierre Taberlet,et al.  Landscape genetics: combining landscape ecology and population genetics , 2003 .

[27]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[28]  Scott J. Goetz,et al.  Using Widely Available Geospatial Data Sets to Assess the Influence of Roads and Buffers on Habitat Core Areas and Connectivity , 2008 .

[29]  Brendan A. Wintle,et al.  Climate change, connectivity and conservation decision making: back to basics , 2009 .

[30]  Carl Gutwin,et al.  Classes of graphs which approximate the complete euclidean graph , 1992, Discret. Comput. Geom..

[31]  Lenore Fahrig,et al.  DISPERSAL DISTANCE OF MAMMALS IS PROPORTIONAL TO HOME RANGE SIZE , 2002 .

[32]  L. Fahrig How much habitat is enough , 2001 .

[33]  M. Fortin,et al.  Use of resistance surfaces for landscape genetic studies: considerations for parameterization and analysis , 2010, Molecular ecology.

[34]  F. Jordán,et al.  Characterizing the importance of habitat patches and corridors in maintaining the landscape connectivity of a Pholidoptera transsylvanica (Orthoptera) metapopulation , 2003, Landscape Ecology.

[35]  Kevin J. Gutzwiller,et al.  Applying Landscape Ecology in Biological Conservation , 2002, Springer New York.

[36]  Jordi Bascompte,et al.  Spatial mating networks in insect-pollinated plants. , 2008, Ecology letters.

[37]  Ferenc Jordán,et al.  Carabids (Coleoptera: Carabidae) in a forest patchwork: a connectivity analysis of the Bereg Plain landscape graph , 2007, Landscape Ecology.

[38]  Andrew Fall,et al.  Testing the importance of spatial configuration of winter habitat for woodland caribou: An application of graph theory , 2006 .

[39]  Hugh P. Possingham,et al.  Graph theoretic topology of the Great but small Barrier Reef world , 2010, Theoretical Ecology.

[40]  Dean L Urban,et al.  A Graph‐Theory Framework for Evaluating Landscape Connectivity and Conservation Planning , 2008, Conservation biology : the journal of the Society for Conservation Biology.

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

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

[43]  Michael Drielsma,et al.  A raster-based technique for analysing habitat configuration : The cost-benefit approach , 2007 .

[44]  Nicola Koper,et al.  Generalized estimating equations and generalized linear mixed-effects models for modelling resource selection , 2009 .

[45]  Vladimir Batagelj,et al.  Pajek - Analysis and Visualization of Large Networks , 2004, Graph Drawing Software.

[46]  M. Boyce,et al.  Relating populations to habitats using resource selection functions. , 1999, Trends in ecology & evolution.

[47]  S. Saura,et al.  Comparison and development of new graph-based landscape connectivity indices: towards the priorization of habitat patches and corridors for conservation , 2006, Landscape Ecology.

[48]  Viral B. Shah,et al.  Using circuit theory to model connectivity in ecology, evolution, and conservation. , 2008, Ecology.

[49]  Ferenc Jordán,et al.  Graph theory in action: evaluating planned highway tracks based on connectivity measures , 2009, Landscape Ecology.

[50]  Agustín Estrada-Peña,et al.  Effects of Habitat Suitability and Landscape Patterns on Tick (Acarina) Metapopulation Processes , 2005, Landscape Ecology.

[51]  T. Lookingbill,et al.  The role of landscape connectivity in assembling exotic plant communities: a network analysis. , 2009, Ecology.

[52]  Justin M. Calabrese,et al.  A comparison-shopper's guide to connectivity metrics , 2004 .

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

[54]  Maile C. Neel,et al.  Patch connectivity and genetic diversity conservation in the federally endangered and narrowly endemic plant species Astragalus albens (Fabaceae) , 2008 .

[55]  Ping Zhu,et al.  A study of graph spectra for comparing graphs and trees , 2008, Pattern Recognit..

[56]  Santiago Saura,et al.  Conefor Sensinode 2.2: A software package for quantifying the importance of habitat patches for landscape connectivity , 2009, Environ. Model. Softw..

[57]  Lenore Fahrig,et al.  EFFECT OF HABITAT FRAGMENTATION ON THE EXTINCTION THRESHOLD: A SYNTHESIS* , 2002 .

[58]  Mariana Munguía,et al.  Incorporating connectivity into conservation planning: A multi-criteria case study from central Mexico , 2006 .

[59]  Patrick N. Halpin,et al.  Modeling population connectivity by ocean currents, a graph-theoretic approach for marine conservation , 2007, Landscape Ecology.

[60]  Santiago Saura,et al.  A new habitat availability index to integrate connectivity in landscape conservation planning : Comparison with existing indices and application to a case study , 2007 .

[61]  Santiago Saura,et al.  A common currency for the different ways in which patches and links can contribute to habitat availability and connectivity in the landscape , 2010 .

[62]  Gábor Csárdi,et al.  The igraph software package for complex network research , 2006 .

[63]  Karen A. Garrett,et al.  Connectivity of the American Agricultural Landscape: Assessing the National Risk of Crop Pest and Disease Spread , 2009 .

[64]  Andrew Fall,et al.  Comparing static versus dynamic protected areas in the Québec boreal forest , 2008 .