Percolation Theory and its Applications in Landscape Ecology

Document Type : Original Article

Authors

Gorgan University

Abstract

 
Successful dispersal of species in a landscape depends on the degree of landscape connectivity. The obvious effect of landscape connectivity on the conservation of key species has led to a proliferation of connectivity measures. To correctly apply these measures we should consider a species perception of landscape connectivity as a fundamental approach. In this regard, percolation theory as one of the fundamental theories in understanding landscape connectivity has many abilities in determining thresholds of connectivity for animal species under study. The theory is based on random distributions of habitat patches and deals with determination of landscape connectivity. According to the theory if a landscape is occupied at 0.5928 of habitat patches, then we can say the landscape is connected for the species in question. This theory is used in neutral landscape models as the main concept and has many applications in determining the effects of habitat fragmentation, extinction thresholds, estimation of landscape connectivity and identification of critical habitat patches. Because of the important role of this theory in landscape ecology, this study aims to introduce percolation theory and its applications in landscape ecology. Some of these applications are neutral landscape models, critical patches of the landscape for owl, determining of critical habitat patches and forest fire.

Keywords

Main Subjects


Bascompte, J. & Sole, R.V. 1996. Habitat fragmentation and extinction thresholds in spatially explicit models. 1. Anim. Eco. 65: 465 - 473.
Bennett, A..F. 1999. Linkages in the landscape: the role of corridors and connectivity in wildlife conservation. Iucn. p.
Dale, Y.H.; Pearson, S.M.; Offerman, H.L, & O'Neill, R.V. 1994. Relating patterns ofland-use change to faunal biodiversity in the central Amazon. Conserv. BioI. 8:1027-1036.
Doak, D.P.; Marino, P.C. & Kareiva, P.M. 1992. Spatial scale mediates the influence of habitat fragmentation on dispersal success: implications for conservation. Theor. Pop. BioI. 41:315-336.
Forman, R. T & Godron, M. 1986. Landscape ecology. 619 pp. Jhon Wiley & Sons, New York.
Forman, R. T. 1995. Land mosaics: the ecology of landscapes and regions. Cambridge university press.‌ p.
Gardner, R.H.; Turner, M.G.; Dale, V.H. &‌ O’Neill, R.V. 1992. A percolation model of ecological flows. In: Hansen, A.J. & di Castri, F. (eds.), Landscape boundaries. Consequences for biotic diversity and ecological flows. Springer-Verlag, New York. Pp 259–269.
Gardner, R.H.; Milne, B.T.; Turner, M.G. &‌ O’Neill, R.V. 1987. Neutral models for the analysis of a broad-scale landscape patterns. Landscape Ecology 1: 19–28.
Gardner, RH. & O'Neill, R.V. 1991. Pattern, process, and predictability: the use of neutral models for landscape analysis. In Quantitative Methods in Landscape Ecology, eds.
Gustafson, E.J. & Gardner, R.H. 1996. The effect of landscape heterogeneity on the probability of patch colonization. Ecology 77:94-107.
Keitt, T.H.; Franklin, A. & Urban, D.L. 1995. Landscape analysis and metapopulation structure. In Recovery Plan for the Mexican Spotted Owl, Volume II, Technical and Supporting Information. Albuquerque, New Mexico: U.S. Department of the Interior, Fish and Wildlife Service.
Keitt, T.H.; Urban, D.L. & Milne, B.T. 1997. Detecting critical scales in fragmented landscapes. Conserv. Eco!. [Online] 1:4. Available from the Internet: www.consecol.org /voll/issl/art4.
Lavorel, S.; Gardner, R.H. & O'Neill, R.V. 1993. Analysis of patterns in hierarchically structured landscapes. Oikos 67:521-528.
Naveh, Z. 1994. Biodiversity and landscape management. In Biodiversity and landscapes: A paradox to humanity, eds. K.C. Kim and R.D. Weaver. 187 – 207. Cambridge: Cambridge University Press.
Noss, R.E. 1991. Landscape connectivity: different functions at different scales. In landscape Linkages and Biodiversity, ed. W. Hudson, pp. 23-39. Washington, DC:Island Press.
O'Neill, RY.; Gardner, R.H. & Turner, M.G. 1992. A hierarchical neutral model for landscape analysis. Landsc. Ecol. 7:55-61.
O'Neill, RY.; Milne, B.T.; Turner, M.G. & Gardner, R.H. 1988. Resource utilization scales and landscape pattern. Landsc. Ecol. 2:63-69.
O’Neill, R.V.; Krummel, J.R.; Gardner, R.H.; Sugihara, G.; Jackson, B.; De Angelis, D.L.; Milne, B.T.; Turner, M.G.; Zygmunt, B.; Christensen, S.W.; Dale, V.H. &‌ Graham, R.L. 1988.
Opdam, P. 1991. Metapopulation theory and habitat fragmentation: a review of holarctic breeding bird studies. Landscape ecology. 5:93-106.
Opdam, P.; van Apeldoorn, R.; Schotman, A. & Kalkhoven, J. 1993. Population responses to landscape fragmentation. Springer. p: 147-171.
Palmer, M.W. 1992. The coexistence of species in fractal landscapes. Am. Nat. 139:375-397.
Pearson, S.M.; Turner, M.G.; Gardner, R.H. & O'Neill, RY. 1996. An organism-based perspective of habitat fragmentation. In Biodiversity in Managed Landscapes, eds. RC. Szaro and D.W. Johnston, pp. 77-95. Oxford, United Kingdom: Oxford University Press.
Plotnick, R.E. & Gardner, R.H. 1993. Lattices and landscapes. Lect. Math. Life Sci. 23:129-157.
Pulliam, H.R.; Dunning, lB. Jr. & Liu, J. 1992. Population dynamics in complex landscapes: a case study. Ecol. Appl. 2:165-177.
Salwasser, H. 1991. New perspectives for sustaining diversity in U.S. national forest ecosystems. Conserv. Bioi. 5:567-569.
Saupe, D. 1988. Algorithms for random fractals. In The Science of Fractal Images, eds. H.-O. Petigen and D. Saupe, pp. 71-113. New York: Springer.
Selman, P. & Doar, N. 1992. An investigation of the potential for landscape ecology to act as a basis for rural land use plans. Journal of Environmental Management. 35:281-299.
Stauffer, D. 1985. Introduction of percolation theory. Taylor & Francis, London.
Stauffer, D. & Aharony, A. 2003. Introduction to Percolation Theory, Second Edition. London, United Kingdom: Taylor and Francis.
Taylor, P.D.; Fahrig, L.; Henein, K. & Merriam, G. 1993. Connectivity is a vital element of landscape structure. Oikos 68:571-573.
Turner, M.G. 1987. Spatial simulation of landscape changes in Georgia: A comparison of3 transition models. Landscape Ecology 1: 29 –36.
With, K.A. & Crist, T.O. 1995. Critical thresholds in species' responses to landscape structure. Ecology 76:2446-2459.
With, K.A. 1997. The application of neutral landscape models in conservation biology. Conserv. Bioi. 11: 1069-1080.
With, K.A. & King, AW. 1997. The use and misuse of neutral landscape models in ecology. Oikos 79:219-229.
With, K.A.; Gardner, R.H. & Turner, M.G. 1997. Landscape connectivity and population distributions in heterogeneous environments. Oikos 78:151-169.
With, K.A 1999. Is landscape connectivity necessary and sufficient for wildlife management?
With, K.A. & King, AW. 1999a. Dispersal success on fractal landscapes: a consequence of lacunarity thresholds. Landsc. Ecol. 14:73-82.
With, K.A. & King, AW. 1999b. Extinction thresholds for species in fractal landscapes. Conserv. BioI. 13:314-326.
With, K.A. Cadaret, S.J. & Davis, C. 1999. Movement responses to patch structure in experimental fractal landscapes. Ecology 80:1340-1353.
With K.A. 2002. Using percolation theory to asses landscape connectivity and effects of habitat fragmentation. In Applying Landscape Ecology in Biological Conservation. Springer Science Business Media New York. P 535.
Zallen, R. 1983. The Physics of Amorphous Solids. New York: John Wiley and Sons. In Forest Fragmentation: Wildlife and Management Implications, eds. J.A
Ziff, R. 1986. Test of scaling exponents for percolation-cluster perimeters. Phys. Rev. Lett. 56: 545–548.