#### Transcript Causes and Consequences of Spatial Heterogeneity

Causes and Consequences of Spatial Heterogeneity Ecolog(ists) use(s) the concept of a landscape in two ways. The first, which considers a landscape as a specific area based on human scales, is intuitive: Landscapes are ecological systems that exist at the scale of kilometers and comprise recognizable elements such as forest patches, fields, and hedgerows, human settlements, and natural ecosystems. The second use of landscape is as an abstraction representing spatial heterogeneity at any scale. (Pickett and Cadenasso 1995, Science) In this guise, the landscape is an ecological criterion for a spatial approach to any ecological system. From Webster’s Dictionary (10th edition), 2001 Heterogeneity: The quality or state of being heterogeneous. Heterogeneous: consisting of dissimilar or diverse ingredients or constituents. Relative term (i.e., similar?) Measured by ecological characteristics Emphasis on changes across the space Depending on interests, objectives Function of time. Again, “ephemeral” is a relative concept. Mosaic: a surface decoration made by inlaying pieces of variously colored (attentions here!) materials to form pictures or patterns. Coherent structure or relationship Examples of mosaics and heterogeneity Examples of mosaics and heterogeneity Causes Spatial Heterogeneity Natural disturbances: fires, tornados, hurricanes, flooding, volcanoes, outbreaks of diseases and insects, … Human disturbances: harvesting, urbanization, conversion (to agricultural lands, fragmentation, wars, … Climatic Differences: continental vs marine climate, global climate change, … Landform: elevation, slope, aspect, … Differentiations in ecosystem dynamics: Other unpredictable events: introductions of invasive species, migration of keystone species, … Consequences of Spatial Heterogeneity (ecological) Pros Cons Choices of habitats Loss of key habitat Encouraging metapopulation Loss of large, continuous patch High species richness Increases in AEI Effects on disturbances Invasive species Effects on landscape processes Effects on disturbances Effects on landscape processes Quantifying Spatial Heterogeneity: Evenness, Contagion, Fractal dimension, Patchiness (Li & Reynolds 1995) Evenness: n 2 ln pi i 1 E 100 ln n Pi = the probability that a random chosen pixel belong to type i N = the total number of patch types E, ranges between 0 and 1, responds to the number of patch types and their proportions in a landscape. Higher values indicate a more homogeneous landscape. Quantifying Spatial Heterogeneity: Evenness, Contagion, Fractal dimension, Patchiness (Li & Reynolds 1995) P ln P s 1 Contagion: C s i 1 j 1 ij ij 2 ln s Pij = the probability that two randomly chosen adjacent pixels belong to cover type I and j; S= number of cover types C ranges from 0 to 1, with a high value indicating a landscape with a generally clumped patterns of cover across the landscape and a low value indicating a landscape with a dispersed pattern of cover types. Quantifying Spatial Heterogeneity: Evenness, Contagion, Fractal dimension, Patchiness (Li & Reynolds 1995) Fractal Dimension: A fractal will look the same whatever the level of resolution used to observe the object, i.e. a shape made of parts similar to the whole in some way. (Mandelrot 1985) ln( N ) D ln(r ) Where N is number of steps used to measure a pattern unit length, and r is the scale ratio. What is the fractal of (a), (b), ©, and (d)? Quantifying Spatial Heterogeneity: Evenness, Contagion, Fractal dimension, Patchiness (Li & Reynolds 1995) E Patchiness: P 100 ij Dij Nb N= the total number of patches Eij = the number of edges between patch type i and j Dij = the dissimilarity value between patch type i and j Nb = the total number of edges of pixels (i.e., each pixel has 4 edges) P, ranges between 0 and 1, measures the contrast of neighboring patch types in a landscape mosaic and may indirectly reflect the spatial arrangement. Higher P values indicate more diverse land mosaic. Handout: Exercise during the class