Landscape Ecology

, Volume 22, Issue 9, pp 1315–1323

Two measures of landscape-graph connectivity: assessment across gradients in area and configuration

  • Joseph R. Ferrari
  • Todd R. Lookingbill
  • Maile C. Neel
Research Article

Abstract

Landscape connectivity is critical to species persistence in the face of habitat loss and fragmentation. Graph theory is a well-defined method for quantifying connectivity that has tremendous potential for ecology, but its application has been limited to a small number of conservation scenarios, each with a fixed proportion of habitat. Because it is important to distinguish changes in habitat configuration from changes in habitat area in assessing the potential impacts of fragmentation, we investigated two metrics that measure these different influences on connectivity. The first metric, graph diameter, has been advocated as a useful measure of habitat configuration. We propose a second area-based metric that combines information on the amount of connected habitat and the amount of habitat in the largest patch. We calculated each metric across gradients in habitat area and configuration using multifractal neutral landscapes. The results identify critical connectivity thresholds as a function of the level of fragmentation and a parallel is drawn between the behavior of graph theory metrics and those of percolation theory. The combination of the two metrics provides a means for targeting sites most at risk of suffering low potential connectivity as a result of habitat fragmentation.

Keywords

Connectivity Fragmentation Graph theory Percolation theory Threshold 

References

  1. Bascompte J, Sole RV (1996) Habitat fragmentation and extinction thresholds in spatially explicit models. J Anim Ecol 65:465–473CrossRefGoogle Scholar
  2. Bender D, Tischendorf L, Fahrig L (2003) Using patch isolation metrics to predict animal movement in binary landscapes. Lands Ecol 18:17–39CrossRefGoogle Scholar
  3. Bunn AG, Urban DL, Keitt TH (2000) Landscape connectivity: a conservation application of graph theory. J Environ Manage 59:265–278CrossRefGoogle Scholar
  4. Calabrese JM, Fagan WF (2004) A comparison-shopper’s guide to connectivity metrics. Front Ecol Environ 2:529–536CrossRefGoogle Scholar
  5. D’Eon RS, Glenn M, Parfitt I, Fortin MJ (2002) Landscape connectivity as a function of scale and organism vagility in a real forested landscape. Conserv Ecol 6:10 (online) URL: http://www.consecol.org/vol6/iss2/art10/ Google Scholar
  6. Dijkstra EW (1959) A note on two problems in connexion with graphs. Numer Math 1:269–271CrossRefGoogle Scholar
  7. Fagan WF, Meir E, Prendergast J, Folarin A, Karieva P (2001) Characterizing population vulnerability for 758 species. Ecol Lett 4:132–138CrossRefGoogle Scholar
  8. Fahrig L (2001) How much habitat is enough? Biol Conserv 100:65–74CrossRefGoogle Scholar
  9. Fahrig L (2003) Effects of habitat fragmentation on biodiversity. Annu Rev Ecol Evol Syst 34:487–515 CrossRefGoogle Scholar
  10. Fahrig L, Merriam G (1985) Habitat patch connectivity and population survival. Ecology 66:1762–1768CrossRefGoogle Scholar
  11. Fahrig L, Paloheimo J (1988) Determinants of local population size in patchy habitats. Theor Popul Biol 34:194–213CrossRefGoogle Scholar
  12. Ferrari JR (2005) Graph theoretic connectivity analysis of the Mid-Atlantic region of the United States. MS Thesis, University of MarylandGoogle Scholar
  13. Gardner RH (1999) RULE: a program for the generation of random maps and the analysis of spatial patterns. In: Klopatek JM, Gardner RH (eds) Landscape ecological analysis: issues and applications. Springer-Verlag, New York, pp 280–303Google Scholar
  14. Gillis EA, Krebs CJ (1999) Natal dispersal of snowshoe hares during a cyclic population increase. J Mammal 80:933–939CrossRefGoogle Scholar
  15. Groffman PM, Baron JS, Blett T, Gold AJ, Goodman I, Gunderson LH, Levinson BM, Palmer MA, Paerl HW, Peterson GD, Poff N, Rejeski DW, Reynolds JF, Turner MG, Weathers KC, Wiens J (2006) Ecological thresholds: the key to successful environmental management or an important concept with no practical application. Ecosystems 9:1–13CrossRefGoogle Scholar
  16. Gross J, Yellen J (1999) Graph theory and its applications. CRC Press, Boca RatonGoogle Scholar
  17. Hargis CD, Bissonette JA, David JL (1998) The behavior of landscape metrics commonly used in the study of habitat fragmentation. Landsc Ecol 13:167–186CrossRefGoogle Scholar
  18. Hayes B (2000a) Graph theory in practice: part I. Am Sci 88:9–13CrossRefGoogle Scholar
  19. Hayes B (2000b) Graph theory in practice: part II. Am Sci 88:104–109CrossRefGoogle Scholar
  20. Keitt TH, Urban DL, Milne BT (1997) Detecting critical scales in fragmented landscapes. Conserv Ecol 1:4 (online) URL:http://www.consecol.org/Journal/vol1/iss1/art4Google Scholar
  21. Lande R (1987) Extinction thresholds in demographic models of territorial populations. Am Nat 130:624–635CrossRefGoogle Scholar
  22. Levins R (1969) Some demographic and genetic consequences of environmental heterogeneity for biological control. Bull Entom Soc Am 15:237–240Google Scholar
  23. Levins R (1970) Extinction. In: Gerstenhaber M (ed) Lectures on mathematics in the life sciences. American Mathematics Society, Providence, pp 77–107 Google Scholar
  24. Lindenmayer DB, Luck G (2005) Synthesis: thresholds in conservation and management. Biol Conserv 124:351–354CrossRefGoogle Scholar
  25. McGarigal K, Cushman SA, Neel MC, Ene E (2002) FRAGSTATS: spatial pattern analysis program for categorical maps. University of Massachusetts, AmherstGoogle Scholar
  26. Moffatt AS (1994) Theoretical ecology: winning its spurs in the real world. Science 263:1090–1092CrossRefGoogle Scholar
  27. Moilanen A, Nieminen M (2002) Simple connectivity measures in spatial ecology. Ecology 83:1131–1145Google Scholar
  28. Muradian R (2001) Ecological thresholds: a survey. Ecol Econ 38:7–24CrossRefGoogle Scholar
  29. Neel MC, McGarigal K, Cushman SA (2004) Behavior of class-level landscape metrics across gradients of class aggregation and area. Landsc Ecol 19:435–455CrossRefGoogle Scholar
  30. O’Neill RV, Milne BT, Turner MG, Gardner RH (1988) Resource utilization scales and landscape pattern. Landsc Ecol 2:63–69CrossRefGoogle Scholar
  31. Pascual-Hortal L, Saura S (2006) Comparison and development of new graph-based landscape connectivity indices: towards the prioritization of habitat patches and corridors for conservation. Landsc Ecol 21:959–967CrossRefGoogle Scholar
  32. Pimm SL, Askins RA (1995) Forest losses predict bird extinctions in eastern North-America. Proc Natl Acad Sci USA 92:9343–9347PubMedCrossRefGoogle Scholar
  33. Rapport DJ, Regier HA, Hutchinson TC (1985) Ecosystem behavior under stress. Am Nat 125:617–640CrossRefGoogle Scholar
  34. Rothley KD, Rae C (2005) Working backwards to move forwards: graph-based connectivity metrics for reserve network selection. Environ Model Assess 10:107–113CrossRefGoogle Scholar
  35. Saunders DA, Hobbs RJ, Margules CR (1991) Biological consequences of ecosystem fragmentation: a review. Conserv Biol 5:18–32CrossRefGoogle Scholar
  36. Stauffer D, Aharony A (1992) Introduction to Percolation Theory. Taylor & Francis, LondonGoogle Scholar
  37. Urban DL (2003) LANDGRAPHS: a package for graph theoretic analyses of landscapes. Landscape Ecology Laboratory, Duke University, DurhamGoogle Scholar
  38. Urban DL (2005) Modeling ecological processes across scales. Ecology 86:1996–2006CrossRefGoogle Scholar
  39. Urban DL, Keitt TH (2001) Landscape connectivity: a graph-theoretic perspective. Ecology 82:1205–1218CrossRefGoogle Scholar
  40. van Langevelde F (2000) Scale of habitat connectivity and colonization in fragmented nuthatch populations. Ecography 23:614–622CrossRefGoogle Scholar
  41. Wilcove DS, Rothstein D, Dubow J, Phillips A, Losos E (1998) Quantifying threats to imperiled species in the United States. Bioscience 48:607–615CrossRefGoogle Scholar
  42. Winfree RJ, Dushoff J, Crone EE, Schultz CB, Budny RV, Williams NM, Kremen C (2005) Testing simple indices of habitat proximity. Am Nat 165:707–717PubMedCrossRefGoogle Scholar
  43. With KA (1997) The application of neutral landscape models in conservation biology. Conserv Biol 11:1069–1080CrossRefGoogle Scholar
  44. With KA (1999) Is landscape connectivity necessary and sufficient for wildlife management? In: Rochelle JA, Lehmann LA, Wisniewski J (eds) Forest fragmentation: wildlife and management implications. Brill Academic Publishers, Leiden, pp 97–115Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  • Joseph R. Ferrari
    • 1
  • Todd R. Lookingbill
    • 1
  • Maile C. Neel
    • 2
  1. 1.Appalachian LaboratoryUniversity of Maryland Center for Environmental ScienceFrostburgUSA
  2. 2.Department of Plant Science and Landscape Architecture and Department of EntomologyUniversity of MarylandCollege ParkUSA

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