Spatial Pattern AnalysisSpatial Pattern Analysis

Exploring the relationship between ecological pattern, ecological function and ecological processes.

Spatial Structure -> Ecological Function -> Change …. pressure, state, response

CompositionComposition ConfigurationConfiguration

Spatial StructureSpatial Structure

www.mosaicr.com

Assess PatternAssess Pattern

Input = classified input Output = 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 StructureSpatial Structure

Rugosity

Jeff Jenness and Pat Iampietro

3 band “true color”Red, Green, Blue;

1 band, Red wavelength

5 class Natural breaksJenk’s classifier

5 class Equal Intervalequal-sized sub-ranges

11 class (1/2 equal Interval)

Defined IntervalAn interval which equallyDivides a range

5 class QuantileEach class has equal Number of features

5 class Quantile1 standarddeviation

5 class, “isodata”R,G,B,IR

Histogram ClassificationHistogram Classification

original continuous data

Various histogram classification results

Multi

Clustering MultivariateSpatial DataClustering MultivariateSpatial Data

Clusters

ISODATA clusters

Inner radiusOuter 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 Metricsperimeter-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 edgeA = 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 classesEik = 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

4

89

1.45

.69

30.2

10 2 0 1.30

1 1 0 1 89 1 0 1.60

5

32

1.85

1.10

40

27 3 4 1.5

4 2 .25 1.12

69 5 4 1.87

19

13

?

?

?

? ? ? ?

1

100

1

0

0

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 Metricsperimeter-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)