Transcript Introduce Pattern Metrics

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
•
•
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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)