Landscape Ecology

, Volume 24, Issue 5, pp 699–709 | Cite as

Landscape patterns from mathematical morphology on maps with contagion

  • Kurt Riitters
  • Peter Vogt
  • Pierre Soille
  • Christine Estreguil
Research Article


The perceived realism of simulated maps with contagion (spatial autocorrelation) has led to their use for comparing landscape pattern metrics and as habitat maps for modeling organism movement across landscapes. The objective of this study was to conduct a neutral model analysis of pattern metrics defined by morphological spatial pattern analysis (MSPA) on maps with contagion, with comparisons to phase transitions (abrupt changes) of patterns on simple random maps. Using MSPA, each focal class pixel on a neutral map was assigned to one of six pattern classes—core, edge, perforated, connector, branch, or islet—depending on MSPA rules for connectivity and edge width. As the density of the focal class (P) was increased on simple random maps, the proportions of pixels in different pattern classes exhibited two types of phase transitions at threshold densities (0.41 ≤ P ≤ 0.99) that were predicted by percolation theory after taking into account the MSPA rules for connectivity and edge width. While there was no evidence of phase transitions on maps with contagion, the general trends of pattern metrics in relation to P were similar to simple random maps. Using an index P for comparisons, the effect of increasing contagion was opposite that of increasing edge width.


Pattern analysis Neutral model Percolation theory Phase transition Simulation Threshold 



Two anonymous reviewers are acknowledged for their assistance. Funding was provided by the Quantitative Sciences Staff, US Forest Service. Mention of trade names does not constitute endorsement or recommendation for use by the US Government.


  1. Burkett VR, Wilcox DA, Stottlemyer R, Barrow W, Fagre D, Baron J, Price J, Nielsen JL, Allen CD, Peterson DL, Ruggerone G, Doyle T (2005) Nonlinear dynamics in ecosystem response to climatic change: case studies and policy implications. Ecol Complex 2:357–394. doi: 10.1016/j.ecocom.2005.04.010 CrossRefGoogle Scholar
  2. Chaves CM, Koiller B (1995) Universality, thresholds and critical exponents in correlated percolation. Physica A 218:271–278. doi: 10.1016/0378-4371(95)00076-J CrossRefGoogle Scholar
  3. Cushman SA, McGarigal K, Neel MC (2007) Parsimony in landscape metrics: strength, universality, and consistency. Ecol Indic 8:691–703. doi: 10.1016/j.ecolind.2007.12.002 CrossRefGoogle Scholar
  4. Essam JW (1980) Percolation theory. Rep Prog Phys 43:833–912. doi: 10.1088/0034-4885/43/7/001 CrossRefGoogle Scholar
  5. Ferrari JR, Lookingbill TR, Neel MC (2007) Two measures of landscape-graph connectivity: assessment across gradients in area and configuration. Landscape Ecol 22:1315–1323. doi: 10.1007/s10980-007-9121-7 CrossRefGoogle Scholar
  6. Filho FJBdO, Metzger JP (2006) Thresholds in landscape structure for three common deforestation patterns in the Brazilian Amazon. Landscape Ecol 21:1061–1073. doi: 10.1007/s10980-006-6913-0 CrossRefGoogle Scholar
  7. Fournier A, Fussel D, Carpenter L (1982) Computer rendering of stochastic models. Commun ACM 25:371–384. doi: 10.1145/358523.358553 CrossRefGoogle Scholar
  8. Frary ME, Schuh CA (2007) Correlation-space description of the percolation transition in composite microstructures. Phys Rev E Stat Nonlin Soft Matter Phys 76:041108. doi: 10.1103/PhysRevE.76.041108
  9. 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
  10. Gardner RH, Urban DL (2007) Neutral models for testing landscape hypotheses. Landscape Ecol 22:15–29. doi: 10.1007/s10980-006-9011-4 CrossRefGoogle Scholar
  11. Gardner RH, Milne BT, Turner MG, O’Neill RV (1987) Neutral models for the analysis of broad-scale landscape pattern. Landscape Ecol 1:19–28. doi: 10.1007/BF02275262 CrossRefGoogle Scholar
  12. Gardner RH, O’Neill RV, Turner MG, Dale VH (1989) Quantifying scale-dependent effects of animal movement with simple percolation models. Landscape Ecol 3:217–227. doi: 10.1007/BF00131540 CrossRefGoogle Scholar
  13. Groffman PM, Baron JS, Blett T, Gold AJ, Goodman I, Gunderson LH, Levinson BM, Palmer MA, Paerl HW, Peterson GD, Poff NL, 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 (N Y, Print) 9:1–13. doi: 10.1007/s10021-003-0142-z CrossRefGoogle Scholar
  14. Gustafson EJ, Parker GR (1992) Relationships between landcover proportion and indices of landscape spatial pattern. Landscape Ecol 7:101–110. doi: 10.1007/BF02418941 CrossRefGoogle Scholar
  15. Keitt TH (2000) Spectral representation of neutral landscapes. Landscape Ecol 15:479–493. doi: 10.1023/A:1008193015770 CrossRefGoogle Scholar
  16. King AW, With KA (2002) Dispersal success on spatially structured landscapes: when do spatial pattern and dispersal behavior really matter? Ecol Model 147:23–39. doi: 10.1016/S0304-3800(01)00400-8 CrossRefGoogle Scholar
  17. Malanson GP (2003) Dispersal across continuous and binary representations of landscapes. Ecol Model 169:17–24. doi: 10.1016/S0304-3800(03)00204-7 CrossRefGoogle Scholar
  18. Mandelbrot BB (1983) The fractal geometry of nature. W.H Freeman and Company, New York, p 468Google Scholar
  19. Neel MC, McGarigal K, Cushman SA (2004) Behavior of class-level landscape metrics across gradients of class aggregation and area. Landscape Ecol 19:435–455. doi: 10.1023/B:LAND.0000030521.19856.cb CrossRefGoogle Scholar
  20. O’Neill RV, Milne BT, Turner MG, Gardner RH (1988) Resource utilization scales and landscape pattern. Landscape Ecol 2:39–63. doi: 10.1007/BF00138908 Google Scholar
  21. O’Neill RV, Gardner RH, Turner MG (1992) A hierarchical neutral model for landscape analysis. Landscape Ecol 7:55–61. doi: 10.1007/BF02573957 CrossRefGoogle Scholar
  22. Ostapowicz K, Vogt P, Riitters KH, Kozak J, Estreguil C (2008) Impact of scale on morphological spatial pattern of forest. Landscape Ecol 23:1107–1117. doi: 10.1007/s10980-008-9271-2 CrossRefGoogle Scholar
  23. Plotnick RE, Gardner RH (1993) Lattices and landscapes. In: Gardner RH (ed) Lectures on mathematics in the life sciences, Volume 23: predicting spatial effects in ecological systems. American Mathematical Society, Providence, RI, pp 129–157Google Scholar
  24. Riitters KH, Vogt P, Soille P, Kozak J, Estreguil C (2007) Neutral model analysis of landscape patterns from mathematical morphology. Landscape Ecol 22:1033–1043. doi: 10.1007/s10980-007-9089-3 CrossRefGoogle Scholar
  25. Saupe D (1988) Algorithms for random fractals. In: Peitgen HO, Saupe D (eds) The science of fractal images. Springer-Verlag, New York, pp 71–136Google Scholar
  26. Serra J (1982) Image analysis and mathematical morphology. Academic Press, LondonGoogle Scholar
  27. Soille P (2003) Morphological image analysis: principles and applications, 2nd edn. Springer-Verlag, BerlinGoogle Scholar
  28. Soille P, Vogt P (2009) Morphological segmentation of binary patterns. Pat Recog Let 30:456–459. doi: 10.1016/j.patrec.2008.10.015 CrossRefGoogle Scholar
  29. Stauffer D (1985) Introduction to percolation theory. Taylor & Francis, LondonGoogle Scholar
  30. Vogt P (2009) GUIDOS installation. European Commission, Joint Research Centre, Ispra, Italy, 4 pp. (online) URL: (accessed 29 January 2009)
  31. Vogt P, Riitters KH, Estreguil C, Kozak J, Wade TG, Wickham JD (2007a) Mapping spatial patterns with morphological image processing. Landscape Ecol 22:171–177. doi: 10.1007/s10980-006-9013-2 CrossRefGoogle Scholar
  32. Vogt P, Riitters KH, Iwanowski M, Estreguil C, Kozak J, Soille P (2007b) Mapping landscape corridors. Ecol Indic 7:481–488. doi: 10.1016/j.ecolind.2006.11.001 CrossRefGoogle Scholar
  33. With KA (2002) Using percolation theory to assess landscape connectivity and effects of habitat fragmentation. In: Gutzwiller KJ (ed) Applying landscape ecology in biological conservation. Springer-Verlag, New York, pp 105–130Google Scholar
  34. With KA (2004) Assessing the risk of invasive spread in fragmented landscapes. Risk Anal 24:803–815. doi: 10.1111/j.0272-4332.2004.00480.x PubMedCrossRefGoogle Scholar
  35. With KA, King AW (1997) The use and misuse of neutral landscape models in ecology. Oikos 79:219–229. doi: 10.2307/3546007 CrossRefGoogle Scholar
  36. With KA, King AW (2001) Analysis of landscape sources and sinks: the effect of spatial pattern on avian demography. Biol Conserv 100:75–88. doi: 10.1016/S0006-3207(00)00209-3 CrossRefGoogle Scholar

Copyright information

© US Government 2009

Authors and Affiliations

  • Kurt Riitters
    • 1
  • Peter Vogt
    • 2
  • Pierre Soille
    • 3
  • Christine Estreguil
    • 2
  1. 1.US Department of Agriculture, Forest Service, Southern Research StationResearch Triangle ParkUSA
  2. 2.European Commission, Joint Research CentreInstitute for Environment and SustainabilityIspra (VA)Italy
  3. 3.European Commission, Joint Research CentreInstitute for the Protection and Security of the CitizenIspra (VA)Italy

Personalised recommendations