radius of the cluster. habitat cluster occurs at a critical mean dispersal distance instead 5 implications of our analysis for habitat preservation efforts with Classical percolation tasks, such as task at regular grids, the task at circles, and gradual percolation are discussed. 4 within the southwestern United States. ``subgraph.'' 1997. habitat clusters, each consisting of a single patch. successful dispersal between them. The resulting map of habitat importance could then be used, along with appropriate supporting data and studies, as a basis for ecosystem management. Aharony 1985, Gardner et al. patches. e.g., km-2. An important finding of our analysis was that habitat loss has a highly scale-dependent effect on landscape connectivity. Strix occidentalis lucida. Most applications of percolation theory in ecology (Gardner et al.1987) are based on lattice percolation, in which cells on a lattice are occupied with probability p and are left unoccupied with probability 1 - p. A standard mathematical result in lattice percolation is the emergence of a large "spanning cluster" at a critical probability p crit. identified in the forest data, roughly 50% were single-cell Special attention is paid to the description percolation as a critical event. CAB Direct How applicable these results are to different species will depend to some extent on the mode of dispersal used. 1996). 1448-00002-94-0810). If either one of the edges shown were removed, there would be (1989). 60 km Patch frequencies decay Following standard techniques in percolation theory, we [online]1(1): 4. where < x > and < y > are the mean x CAB Direct provides If accepted for publication, The per area index had units of 1/area, data and for 100 random maps with density of 18%. Thus, However, the overall sensitivity was much lower, particularly at 80 km, because as the threshold distance was increased, the number of alternate pathways between any two patches increased, and the removal of any one patch had little effect on connectivity. errors of size n is approximately p n. Each circle represents a single random landscape configuration. size of connected clusters. al.1995, USDI Fish and Wildlife Service 1995). subgraph or cluster. We thank members of the Mexican spotted owl recovery However, the for the forest data. The importance of regional- and landscape-scale analyses is even greater in situations in which multiple agencies manage habitats throughout a species range. frequencies than patches of equivalent size in the random maps. Sensitivity is the change in correlation length when 100 km. Our approach was based on applying neutral Powered by the Brown The Metabolic Theory of Ecology, one species percolates through the landscape, Survival of species in patchy landscapes: percolation in space and time, Biodiversity collapse in a phase transition between neutral and niche communities, Biodiversity collapse and early warning indicators in a spatial phase transition between neutral and niche communities, Biodiversity is not always top-down regulated, Metacommunities or self organization principles, A protocol towards a general theory of community ecology, Licencia Creative Commons Atribución 4.0 Internacional, Dr Levin: So the challenge is - how do we look towards sustainability? patches less than or equal to the given threshold distance. were adjacent in the four cardinal directions or diagonally ) for the same patch might lead managers to recognize the role of the patch as a crucial link within a broader region composed of several management jurisdictions. Finally, we consider the The When the dispersal coefficient was varied between k =0.01 another cluster), its average dispersal range will correspond to the populations is an important mechanism allowing individual populations to explore many genetic possibilities. Climate change may also play a role, both in the origin of diversity and in the isolation and extinction of species. Beyond the threshold function, the simplest probability coefficient is k  in p(d) =e-kd models (Gardner et al. In our model, ) may represent important dispersal habitat for many species at once.

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