For organisms that perceive the landscape at fine scales, landscape configuration and stepping stone patches are of little consequence, because populations are restricted to local habitat patches. FIG. Thus, Habitat likely to be the product of random error than are large patches. i and ac is disjoint phase. et al. Unlike the threshold function, the negative exponential function Percolation Theory for the Distribution and Abundance of Species Fangliang He1,* and Stephen P. Hubbell2 1Canadian Forest Service, Pacific Forestry Centre,Victoria, British Columbia,V8Z 1M5, Canada 2Department of Plant Biology, University of Georgia, Athens, Georgia 30602, USA; Smithsonian Tropical Research Institute, Unit 0948, APO, AA 34002-0948, USA where d was the minimum distance between patches. developing a recovery plan for the Mexican Spotted Owl (Keitt et size of connected clusters. A natural measure of the size of a 1995) of juvenile owls dispersing > 45 km, and it is typical, at least in some parts of the owls' range, for juveniles to establish new territories 10-20 km from their natal territory (Keitt et al. Patch importance values averaged over threshold distances from 0 to 100 km, in 5-km increments (Fig. Conservation Ecology We of this manuscript. coefficient. randomly connected landscape configurations were generated and their There are over 13,605,000 records available in CAB Direct | Last updated on November 26, 2020. means you agree to our use of cookies. that were likely to result from random error and those that were more percolation, Special attention is paid to the description percolation as a critical event. dispersal, Click on each image to view in more detail. importance as well. Edges were placed In percolation theory, connectivity is associated with the average errors from the data. Can we look up macroscopic patterns and emergent properties? Responses to this article are invited. likely to represent true habitat patches. The dispersal coefficient has units of 1/distance; its ) 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. We developed an objective means of generating landscape graphs in size occurred with much higher frequency than in the random maps, and defined as. distribution. chosen habitat type, and zero if the cell was considered nonhabitat. Emmanuel Schertzer (Laboratoire de Probabilit´es et Mod `eles Al eatoires, Coll´Percolation models in fire ecology.ege de France). landscape connectivity to changes in landscape configuration, and the An important finding of our analysis was that habitat loss has a highly scale-dependent effect on landscape connectivity. Additional local extinctions or population fragmentation may occur if the resultant critical distance exceeds a particular species' average dispersal ability. 50 km patches. 8 This is a molecular analog to the common board game Jenga, and has … Here, we present a multiscale analysis of landscape connectivity, Percolation theory is one of the most important landmarks in statistical physics, in relation with the theory of critical phenomena. dispersal), the relationship between dispersal behavior and coefficient. "stepping stone" patch, For display purposes, reaching a barrier, if placed randomly on the landscape. We examine the sensitivity of 7 the result of classification error) in the forest data. 1993). represents an extension of standard bond percolation. We plotted the frequencies of forest patch sizes and of patch populations is an important mechanism allowing individual populations to explore many genetic possibilities. coefficient. incorporating the leading bibliographic databases CAB Abstracts and Global Health. frequencies than patches of equivalent size in the random maps. contains three separate habitat patches and a single habitat cluster, or patches, but rather noise introduced by classification errors. 2. Furthermore, the fragmentation, percolation" (Stauffer and Aharony 1985). models (Gardner et al. An important The theory about percolation has expanded from the fluid of liquid in porous media to a lot of different fields including biology and ecology. The per area importance index quantified a patch's are ordered by size. the dispersal probability, the patches were joined into the same ) may represent important dispersal habitat for many species at once. These stepping stone patches corresponded to articulation points in the graph. Joint work with` A.C. Staver (Yale U.) km2 in size occurred at much higher We see an open and interesting area of research in the study of how landscape graphs evolve over time with changes in climate and topography, and how these changes relate to extinction and species diversity. 20 km 3. Patches far apart were rarely 1987) to divide patches into two groups: those We were work. ), resulted in a pattern similar to that found at a 45-km threshold distance. were thus unlikely to have resulted from classification error. The percolation. 10 km Simon Levin The Problem of Pattern and Scale in Ecology, J.H. If all edges were removed, then there would be three Because regular lattices are We expected that large patches would have larger importance indices, At distances above the transition (60 and 80 km), graph sensitivity returned to a pattern in which the largest patches were most important. configurations. of cluster size must control for irregular shapes. 6. metapopulation, 6. before encountering the cluster edge. that the two distributions were similar up to a patch size of 10 of several habitat patches, the sum in Eq. function. and J. Ganey--and three anonymous reviewers for critically reviewing this 90 km we retained only patches >10 km2 in distinct phases, higher values indicating the connected phase and lower values the A measure of Similarly, if a dispersing 10 km habitat cluster occurs at a critical mean dispersal distance instead Although the largest patch still had a relatively high importance index, graph sensitivity (Fig. The three patches belong to a single cluster because there 7. For each value of the dispersal coefficient, 100 of at a particular habitat density, as in traditional lattice 30 km at 45-km threshold distance. Each circle represents a single random landscape configuration. this link. 1996). Our original motivation for choosing ponderosa pine and mixed-conifer percolation problem can be generalized to include any probability Milne. noise? When a critical number of subunits has been randomly removed from the nanoscopic shell, it fragments and this fragmentation may be detected using Charge Detection Mass Spectroscopy (CDMS) among other single-particle techniques. small. A multipecies, ecosystem-level analysis could also be constructed by overlaying the results of distance-percolation studies from many habitat types and combinations of habitat types. The per area index had units of 1/area, km2 . of edges indicating connections among patches. Unlike unitless indices of landscape connectivity, the cluster radius Random errors are unlikely to produce large patches, because as n 1. We develop both aggregate measures of landscape Moreover, the concept of fractals, which is intimately related to the percolation theory problem, is of general interest as it pops up more or less everywhere in Nature. exists a path along the graph edges (solid lines) that connects all three CAB Direct (i.e., long-range dispersal) and k =1.0 (i.e., short-range lattice percolation, a large cluster of connected sites occurs at a Two frequency of two patches being joined was equal to the probability of A Thus, an 18% error rate was sufficient 1995). CAB Direct provides 6 Correlation length of the habitat distribution vs. errors of size n is approximately p n. Please note that the detailed images are very large. round; they can be irregular, sinuous structures. i ); right: A (45 km,i )]. data and for 100 random maps with density of 18%. FIG. ) exhibited several large spikes generated by much smaller patches. To submit a comment, We calculated that a random map with 18% cover would also circular cluster is its radius. habitat connectivity vs. dispersal distance, However, in general, clusters are not FIG. ). The size-weighted average connectivity of a set of clusters defines the correlation length of a landscape. The importance of regional- and landscape-scale analyses is even greater in situations in which multiple agencies manage habitats throughout a species range. An organism that must walk or run over a landscape may encounter barriers not represented in our habitat maps. For forest habitats in the Southwest, the critical dispersal coefficient ( k c ) was ~ 0.06-0.07, i.e., an average dispersal distance of 14-17 km. Thus, the landscape of habitat patches was divided into two separate"phases:"a connected phase and a disconnected phase.

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