Spatial Pattern Analysis Exploring the relationship between ecological pattern, ecological function and ecological processes. Spatial Structure -> Ecological Function -> Change …. pressure, state, response Composition Configuration Spatial Structure

Assess Pattern Input = classified inputOutput = spreadsheet of selected metrics

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 Spatial Structure

Rugosity Jeff Jenness and Pat Iampietro

3 band “true color” Red, Green, Blue; 1 band, Red wavelength 5 class Natural breaks Jenk’s classifier 5 class Equal Interval equal-sized sub-ranges 11 class (1/2 equal Interval) Defined Interval An interval which equally Divides a range 5 class Quantile Each class has equal Number of features 5 class Quantile 1 standard deviation 5 class, “isodata” R,G,B,IR Histogram Classification original continuous data Various histogram classification results Multi

Clustering Multivariate Spatial Data

Clusters

ISODATA clusters

Inner radius Outer radius

Classification Ridge Upper Slope Middle Slope Flat Lower Slope Valley

3 “patches” Same “class” 1 “patches” differ “class” 1 “landscape”

Types of Metrics Area, Density, Diversity Shape Core area Isolation/proximity, Nearest-Neighbor Contrast metrics Contagion / Interspersion Connectivity Diversity

Area, Density, Diversity Metrics Patch Density Shannon Diversity Index

Fractal: a pattern composed of identical parts 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 indicates the extent to which the fractal object fills the Euclidean dimension Fractal Dimension (D), or (FRACT) - log P = 1/2D*log A; P = perimeter, A = area 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 E ik = length of edge between classes

Landscape Metrics Class Metrics Number of Patches Largest Patch Area-weighted mean shape Shannon’s Diversity Interspersion Percent of Landscape | Patch Density | Patch Size CV | Area-weighted Mean Shape ? ? ? ? ? ? ?

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)