Skip to main content
SpringerLink
Log in

Landscape graphs: Ecological modeling with graph theory to detect configurations common to diverse landscapes

  • Published:
Landscape Ecology Aims and scope Submit manuscript

Abstract

In view of the bewildering diversity of landscapes and possible patterns therein, our objectives were to see if a useful modeling method for directly comparing land mosaics could be developed based on graph theory, and whether basic spatial patterns could be identified that are common to diverse landscapes. The models developed were based on the spatial configuration of and interactions between landscape elements (ecosystems, land uses or ecotopes). Nodes represented landscape elements and linkages represented common boundaries between elements. Corridors, corridor intersections, and the matrix were successfully incorporated in the models. Twenty-five landscape graphs were constructed from aerial photographs chosen solely to represent a breadth of climates, land uses and human population densities. Seven distinctive clusters of nodes and linkages were identified and common, three of which, in the forms of a ‘spider’, ‘necklace’ and ‘graph cell,’ were in >90% of the graphs. These represented respectively the following ‘configurations’ of patches, corridors and matrix: (1) a matrix area surrounding or adjoining many patches; (2) a corridor bisecting a heterogeneous area; and (3) a unit in a network of intersecting corridors. The models also indicated that the connectivity or number of linkages for several common elements, such as fields and house clearings, was relatively constant across diverse landscapes, and that linear shaped elements such as roads and rivers were the most connected. Several additional uses of this graph modeling, including compatibility with systems dynamics models, are pinpointed. Thus the method is useful in allowing simple direct comparisons of any scale and any landscape to help identify patterns and principles. A focus on the common and uncommon configurations should enhance our understanding of fluxes across landscapes, and consequently the quality of land planning and management.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Allen, T.F.H., O'Neill, R.V. and Hoekstra, T.W. 1984. Interlevel Relations in Ecological Research and Management: Some Working Principles from Hierarchy Theory, USDA Forest Service: General Technical Report RM-110.

  • Andow, D.A., Kareiva, P.M., Levin, S.A. and Okubo, A. 1990. Spread of invading organisms. Landscape Ecology 4: 177–188.

    Google Scholar 

  • Baker, W.L. 1989. A review of models of landscape change. Landscape Ecology 2: 111–133.

    Google Scholar 

  • Burke, I.C., Schimel, D.S., Yonker, C.M., Parton, W.J., Joyce, L.A. and Lauenroth, W.K. 1990. Regional modeling of grassland biogeochemistry using GIS. Landscape Ecology 4: 45–54.

    Google Scholar 

  • Burrough, P.A. 1981. Fractal dimensions of landscapes and other environmental data. Nature 294: 240–242.

    Google Scholar 

  • Burrough, P.A. 1986. Principles of Geographic Information Systems for Land Resources Assessment. Oxford: Oxford University Press.

    Google Scholar 

  • Caswell, H. 1976. Community structure: A neutral model analysis. Ecological Monographs 46: 327–354.

    Google Scholar 

  • Christaller, W. 1933. Die Zentralen Orte in Suddentschland. Jena: Fischer.

    Google Scholar 

  • Cohen, J.E. 1978. Food Webs and Niche Space. Princeton, New Jersey: Princeton University Press.

    Google Scholar 

  • Cohen, J.E., Briand, F. and Newman, C.M. 1990. Community Food Webs: Data and Theory. New York: Springer-Verlag.

    Google Scholar 

  • Couclelis, H. 1985. Cellular worlds: A framework for modeling micro-macro dynamics. Environment and Planning A17: 585–596.

    Google Scholar 

  • Dale, M. 1985. Graph theoretical methods for comparing phytosociological structures. Vegetatio 63: 79–88.

    Google Scholar 

  • DeAngelis, D.L., Waterhouse, J.C., Post, W.M. and O'Neill, R.V. 1985. Ecological modelling and disturbance evaluation. Ecological Modeling 29: 399–419.

    Google Scholar 

  • Dykstra, D.P. 1981. Spatial integrity in forest planning models. In Proceedings of the Forest Industry Workshop — 7–11. Edited by P. Uronen. International Institute for Applied Systems Analysis. A-2361 Laxenburg, Austria. CP-81–3.

    Google Scholar 

  • Fahrig, L. and Merriam, G. 1985. Habitat patch connectivity and population survival. Ecology 66: 1762–1768.

    Google Scholar 

  • Forman, R.T.T. 1979. The New Jersey Pine Barrens, an ecological mosaic. In Pine Barrens: Ecosystem and Landscape. Edited by R.T.T. Forman. New York: Academic Press, pp. 569–585.

    Google Scholar 

  • Forman, R.T.T. 1991. Landscape Corridors: From Theoretical Foundations to Public Policy. In Nature Conservation: The Role of Corridors. Edited by D.A. Saunders and R.J. Hobbs. Chipping Norton, Australia: Surrey Beatty. pp. 71–84.

    Google Scholar 

  • Forman, R.T.T. and Godron, M. 1984. Landscape ecology principles and landscape function. In Proceedings of the First International Seminar on Methodology in Landscape Ecological Research and Planning. Edited by J. Brandt and P. Agger. Roskilde, Denmark: Roskilde Universitetsforlag GeoRuc. Vol. 5, pp. 4–14.

    Google Scholar 

  • Forman, R.T.T. and Godron, M. 1986. Landscape Ecology. New York: John Wiley.

    Google Scholar 

  • Franklin, J.F. and Forman, R.T.T. 1987. Creating landscape patterns by forest cutting: ecological consequences and principles. Landscape Ecology 1: 5–18.

    Google Scholar 

  • Gardner, R.H., Milne, B.T., Turner, M.G. and O'Neill, R.V. 1987. Neutral models for the analysis of broad-scale landscape pattern. Landscape Ecology 1: 19–28.

    Google Scholar 

  • Gardner, R.H., O'Neill, R.V., Turner, M.G. and Dale, V.H. 1989. Quantifying scale-dependent effects of animal movement with simple percolation models. Landscape Ecology 3: 217–227.

    Google Scholar 

  • Godron, M. 1966. Application de la theorie de l'information a l'etude de l'homogeneite et de la structure de la vegetation. Oecologia Plantarum 1: 187–197.

    Google Scholar 

  • Gross, T.E. and Dykstra, D.P. 1989. Scheduling Timber Harvests for Wildlife, Allowing Well-defined Violations to Age Class Nonadjacency Constraints. In Multiresource Management of Ponderosa Pine Forests. USDA Forest Service General Technical Report RM-185.

  • Haggett, P., Cliff, A.D. and Frey, A. 1977. Locational Analysis in Human Geography. New York: Wiley.

    Google Scholar 

  • Hansen, A.J., Urban, D.L. and Marks, B. 1992. Avian community dynamics: The interplay of landscape trajectories and species life histories. In Landscape Boundaries: consequences for Biotic Diversity and Ecological Flows. Hansen, A.J. and DiCastri, F. eds. New York, Springer-Verlag. pp. 170–195.

    Google Scholar 

  • Harary, F. 1972. Graph Theory. Reading, Massachusetts: Addison Wesley.

    Google Scholar 

  • Harms, W.B. and Opdam, P. 1990. Woods as habitat patches for birds: Application in landscape planning in the Netherlands. In Changing Landscapes: An Ecological Perspective. Edited by I.S. Zonneveld and R.T.T. Forman. Springer-Verlag: New York. pp. 73–97.

    Google Scholar 

  • Hastings, A. 1990. Spatial heterogeneity and ecological models. Ecology 71: 426–428.

    Google Scholar 

  • Henein, K. and Merriam, G. 1990. The elements of connectivity where corridor quality is variable. Landscape Ecology 4: 157–170.

    Google Scholar 

  • High Performance Systems, Inc. 1990. STELLA II®.

  • Johnson, L. 1990. Analyzing spatial and temporal phenomena using geographical information systems: A review of ecological applications. Landscape Ecology 4: 31–43.

    Google Scholar 

  • Kozova, M., Smitalova, K. and Vizyova, A. 1986. Use of measures of network connectivity in the evaluation of ecological landscape stability. Ekologia (Czechoslovakia) 5: 187–202.

    Google Scholar 

  • Levin, S.A. 1976. Population dynamic models in heterogeneous environments. Annual Review of Ecology and Systematics 7: 287–310.

    Google Scholar 

  • Levins, R. 1975. Evolution in communities near equilibrium. In: Ecology and Evolution of Communities. Edited by M.L. Cody and J.M. Diamond. Cambridge, Massachusetts: Belknap Press. pp. 16–50.

    Google Scholar 

  • Lowe, J.C. and Moryadas, S. 1975. The Geography of Movement. Boston: Houghton Mifflin.

    Google Scholar 

  • Lyon, J. 1983. Road density models describing habitat effectiveness for elk. Journal of Forestry 81: 592–595.

    Google Scholar 

  • Merriam, G. 1990. Ecological processes in the time and space of farmland mosaics. In Changing Landscapes: An Ecological Perspective. Edited by I.S. Zonneveld and R.T.T. Forman. New York: Springer-Verlag. pp. 121–133.

    Google Scholar 

  • Milne, B.T. 1988. Measuring the fractal geometry of landscapes. Applied Mathematics and Computation 27: 67–79.

    Google Scholar 

  • Milne, B.T., Johnston, K.M. and Forman, R.T.T. 1989. Scale-dependent proximity of wildlife habitat in a spatially neutral Bayesian model. Landscape Ecology 2: 101–110.

    Google Scholar 

  • O'Neill, R.V., Johnson, A.R. and King, A.W. 1989. A hierarchical framework for the analysis of scale. Landscape Ecology 3: 193–205.

    Google Scholar 

  • O'Neill, R.V., Milne, B.T., Turner, M.G. and Gardner, R.H. 1988. Resource utilization scales and landscape pattern. Landscape Ecology 2: 63–69.

    Google Scholar 

  • O'Neill, R.V., DeAngelis, D.L., Waide, J.B. and Allen, T.F.H. 1986. A Hierarchical Concept of Ecosystems. Princeton, N.J.: Princeton University Press.

    Google Scholar 

  • Odum, E.P. and Turner, M.G. 1990. The Georgia landscape: a changing resource. In Changing Landscapes: An Ecological Perspective. Edited by I.S. Zonneveld and R.T.T. Forman. New York: Springer-Verlag. pp. 137–164.

    Google Scholar 

  • Odum, H.T. 1983. Systems Ecology: An Introduction. New York: John Wiley.

    Google Scholar 

  • Ore, O. 1963. Graphs and Their Uses. New York: Random House.

    Google Scholar 

  • Pastor, J. and Broschart, M. 1990. The spatial pattern of a northern conifer-hardwood landscape. Landscape Ecology 4: 55–68.

    Google Scholar 

  • Pickett, S.T.A. and White, P.S. eds., 1985. The Ecology of Natural Disturbance and Patch Dynamics. New York: Academic Press.

    Google Scholar 

  • Risser, P.G., Karr, J.R. and Forman, R.T.T. 1984. Landscape Ecology: Directions and Approaches. Illinois Natural History Survey, Champaign, Illinois. Special Publ. 2.

    Google Scholar 

  • Roberts, D.W. 1989. Analysis of forest succession with fuzzy graph theory. Ecological Modelling 45: 261–274.

    Google Scholar 

  • Robertson, D., Bundy, A., Muetzelfeldt, R, Haggith, M. and Uschold, M. 1991. Eco-Logic: Logic-Based Approaches to Ecological Modeling. Cambridge, MA: The MIT Press.

    Google Scholar 

  • Rouvray, D.H. 1973. The search for useful topological indices in chemistry. American Scientist 61: 729–735.

    Google Scholar 

  • Rugg, D.S. 1979. Spatial Foundations of Urbanism. Dubuque, Iowa: Wm. C. Brown Company.

    Google Scholar 

  • Shugart, H.H., Jr. and Seagle, S.W. 1985. Modeling forest landscapes and the role of disturbance in ecosystems and communities. In The Ecology of Natural Disturbance and Patch Dynamics. Edited by S.T.A. Pickett and P.S. White. New York: Academic Press. pp. 353–368.

    Google Scholar 

  • Sklar, F.H., Costanza, R. and Day, J.W., Jr. 1985. Dynamic spatial simulation modeling of coastal wetland habitat succession. Ecological Modeling 29: 261–281.

    Google Scholar 

  • Stanley, H.E. 1977. Cluster shapes at the percolation threshold: an effective cluster dimensionality and its connection with critical-point exponents. Journal of Physics A — Mathematical and General 10: L211-L215.

    Google Scholar 

  • Stauffer, D. 1985. Introduction to percolation theory. London: Taylor and Francis.

    Google Scholar 

  • Sugihara, G. 1983. Holes in niche space: A derived assembly rule and its relation to intervality. In Current Trends in Food Web Theory: Report on a Food Web Workshop. Edited by DeHuxlis, Post and G. Sugihara. Oak Ridge, Tennessee: Oak Ridge National Lab, Publ.-5983, pp. 25–35.

    Google Scholar 

  • Sugihara, G. 1984. Graph Theory, Homology and Food Webs. In Proceedings of Symposia in Applied Mathematics. American Mathematical Society 30: 83–101.

    Google Scholar 

  • Taaffe, E.J. and Gauthier, H.L., Jr. 1973. Geography of Transportation. Englewood Cliffs, New Jersey: Prentice-Hall.

    Google Scholar 

  • Turner, M.G. 1987a. Spatial simulation of landscape changes in Georgia: A comparison of three transition models. Landscape Ecology 1: 29–36.

    Google Scholar 

  • Turner, M.G. 1987b. Landscape Heterogeneity and Disturbance. New York: Springer-Verlag.

    Google Scholar 

  • Turner, M.G. 1988. A spatial simulation model of land use changes in Georgia. Applied Mathematics and Computation 27: 39–51.

    Google Scholar 

  • Turner, M.G. and Gardner, R.H. eds. 1991. Quantitative Methods for Analyzing Landscape Pattern. New York: Springer-Verlag.

    Google Scholar 

  • Wegner, J.F. and Merriam, G. 1979. Movements by birds and small mammals between a wood and adjoining farmland habitats. Journal of Applied Ecology 16: 349–358.

    Google Scholar 

  • Wiens, J.A. and Milne, B.T. 1989. Scaling of ‘landscapes’ in landscape ecology, or, landscape ecology from a beetle's perspective. Landscape Ecology 2: 87–96.

    Google Scholar 

  • Wilson, R.J. 1979. Introduction to Graph Theory. New York: Academic Press.

    Google Scholar 

  • Zeigler, B.P. 1976. Theory of Modeling and Simulation. New York: John Wiley.

    Google Scholar 

Download references

Author information

Author notes

  1. Margot D. Cantwell

    Present address: Environmental Design and Management, P.O. Box 34110, B3J 3S1, Halifax, Nova Scotia, Canada

Authors and Affiliations

  1. Harvard University, Graduate School of Design, 02138, Cambridge, Massachusetts, USA

    Margot D. Cantwell & Richard T. T. Forman

Authors
  1. Margot D. Cantwell
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Richard T. T. Forman
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cantwell, M.D., Forman, R.T.T. Landscape graphs: Ecological modeling with graph theory to detect configurations common to diverse landscapes. Landscape Ecol 8, 239–255 (1993). https://doi.org/10.1007/BF00125131

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00125131

Keywords

Search

Navigation