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Spatial Pattern Analysis Exploring the relationship between ecological pattern, ecological function and ecological processes. Spatial Structure -> Ecological Function -> Change …. pressure, state, response Spatial Structure Composition Configuration www.mosaicr.com Assess Pattern Input = classified input Output = spreadsheet of selected metrics Spatial Structure • Composition = The presence and amount of each element type without spatially explicit measures. – Proportion, richness, evenness, diversity • Configuration = The physical distribution in space and spatial character of elements. – Isolation, placement, adjacency Rugosity Jeff Jenness and Pat Iampietro Histogram Classification 1 band, Red wavelength Multi original continuous data 3 band “true color” Red, Green, Blue; 5 class, “isodata” R,G,B,IR Various histogram classification results 5 class Natural breaks 5 class Equal Interval 11 class (1/2 equal Interval) Defined Interval 5 class Quantile 5 class Quantile Jenk’s classifier equal-sized sub-ranges An interval which equally Divides a range Each class has equal Number of features 1 standard deviation Clustering Multivariate Spatial Data Clusters ISODATA clusters Inner radius Outer radius Classification Ridge Upper Slope Middle Slope Flat Lower Slope Valley 1 “landscape” 3 “patches” Same “class” 1 “patches” differ “class” Types of Metrics • • • • • • • • Area, Density, Diversity Shape Core area Isolation/proximity, Nearest-Neighbor Contrast metrics Contagion / Interspersion Connectivity Diversity Area, Density, Diversity Metrics Shannon Diversity Index Patch Density Shape Metrics perimeter-area relationships Fractal: a pattern composed of identical parts • Shape Index (SHAPE) -- complexity Fractal Dimension (D), or of patch compared to standard (FRACT) shape - log P = 1/2D*log A; P = – vector uses circular; raster uses perimeter, A = area square – Mean Shape Index (MSI) = perimeter-to-area ratio fractal dimension indicates the extent – Area-Weighted Mean Shape to which the fractal object fills the Euclidean dimension Index (AWMSI) – Landscape Shape Index (LSI) E = total edge A = total area Contagion, Interspersion and Juxtaposition • • • When first proposed (O’Neill 1988) proved incorrect, Li & Reynolds (1993) alternative Based upon the product of two (2) probabilities – Randomly chosen cell belongs to patch “i” – Conditional probability of given type “i” neighboring cells belongs to “j” Interspersion (the intermixing of units of different patch types) and Juxtaposition (the mix of different types being adjacent) index (IJI) M = number of classes Eik = length of edge between classes Landscape Metrics Number of Patches 1 4 5 19 32 13 Largest Patch 100 89 Area-weighted mean shape 1 1.45 1.85 ? 1.10 ? 40 ? Shannon’s Diversity 0 .69 Interspersion 0 30.2 Class Metrics Percent of Landscape | Patch Density | Patch Size CV | Area-weighted Mean Shape 10 27 ? 2 3 ? 0 4? 1.30 1 4 1 2 0 .25 1 1.12 89 69 1 5 0 4 1.60 1.87 1.5 ? Landscape Ecology • Structure = the spatial relationships among the distinctive ecosystems or “elements” • Function = the interactions among the spatial elements • Change = the alteration in the structure and function of the ecological mosaic over time Landscape Structure Physiognomy / Pattern • Composition = The presence and amount of each element type without spatially explicit measures. – Proportion, richness, evenness, diversity • Configuration = The physical distribution in space and spatial character of elements. – Isolation, placement, adjacency • ** some metrics do both ** Types of Metics • • • • • • • • Area Metrics Patch Density, Size and Variability Edge Metrics Shape Metrics Core Area Metrics Nearest-Neighbor Metrics Diversity Metrics Contagion and Interspersion Metrics Shape Metrics perimeter-area relationships • Shape Index (SHAPE) -- complexity of patch compared to standard shape – – – – vector uses circular; raster uses square Mean Shape Index (MSI) = perimeter-to-area ratio Area-Weighted Mean Shape Index (AWMSI) Landscape Shape Index (LSI) • Fractal Dimension (D), or (FRACT) – – – – log P = 1/2D*log A; P = perimeter, A = area P = sq.rt. A raised to D, and D = 1 (a line) as polygons move to complexity P = A, and D -> 2 A few fractal metrics • Double log fractal dimension (DLFD) • Mean patch fractal (MPFD) • Area-weighted mean patch fractal dimension (AWMPFD) Contagion, Interspersion and Juxtaposition • When first proposed (O’Neill 1988) proved incorrect, Li & Reynolds (1993) alternative • Based upon the product of two (2) probabilities – Randomly chosen cell belongs to patch “i” – Conditional probability of given type “i” neighboring cells belongs to “j” • Interspersion (the intermixing of units of different patch types) and Juxtaposition (the mix of different types being adjacent) index (IJI)