Quantifying Landscape Pattern

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Quantifying Landscape Pattern

• ESM 215
• Feb 3, 2003

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Changes in forest cover, Cadiz Township,
Wisconsin (Curtis 1956)
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Landscapes over time
1972 1984 1991
1972
1984
1991
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Analysis of Model Outputs
1 ha clearings
30 ha clearings
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Western boundary, Yellowstone National Park
(Turner et al. Fig 5-2)
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Why quantify pattern?

• Investigate pattern ltgt process
• Landscape monitoring
• Comparison across landscapes
• Compare and contrast management strategies
• Sampling and experimental design

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Classification and Pattern
Turner et al. 5-5
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Gustafson (1998)
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Metrics of landscape composition categorical maps

• Number of classes (richness, S)
• Proportion of area occupied by class i (pi)
• Diversity (evenness)
• SHEI (-?pi ln (pi) ) / ln (S)
• Dominance
• D (ln(S) ?pi ln(pi)) / ln(S)

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Measures of spatial configuration

• Adjacency (cell-based)
• Contagion and Interspersion (cell-based)
• Perimeter-area (patch)
• Connectivity (patch)
• Proximity (patch)
• Patch size distribution (e.g., area-weighted
  patch size)

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Contagion

• C 1 ??? Pij ln (Pij)
• 2 ln (S)
• P probability that 2 randomly chosen adjacent
  cells are the same cover type
• S of cover types

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Connectivity/Fragmentation

• Patch cohesion (Schumaker 96)

• A four-part measure by Bogaert et al. 2000.
  Wildlife Society Bulletin 28875-881.
• habitat loss, isolation, increased perimeter
  length,increase in patch number

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Fractals

• Fractals objects or patterns that have
  non-integer dimensions
• self-similarity pattern at coarse scales is
  repeated at finer and finer scales
• scale-dependence

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Fractal curves
N steps r scale ratio D log N/log r
D ln 4/ln 3 1.2618
D ln 5/ln 3 1.4650
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Fractal Patches
A (kP)d d ln(A) / (ln(P) ln(k)) kP AD D
1/d
A area P perimeter D fractal dimension K
constant
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Fractal dimensions of (D) of forest patches near
Natchez Mississippi as a function of patch
size. ( Turner fig 5.11)
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Box analysis of fractal dimension of lattices
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Procedure for box analysis

• map is superimposed with a grid gt the grain
  size. Boxes which contain class of interest (in
  any small amount) are counted.
• The process is repeated with different box sizes
  until 1-2 orders of magnitude in box size has
  been explored (say boxes of size 1 to 100).
• the logarithm of the number of occupied boxes of
  each length is regressed against the logarithm of
  box length.
• The slope of the regression is the exponent in
  the power law
• N(L) kL-Db

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1000
2,262
x
boxes
100
x
10
x
x
1
x 32,1
100
1
10
Box size
The slope of the line is the fractal dimension of
the lattice as estimated by the box counting
method
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Converting box counts to areas

• A(L) kL2-Db
• assuming self-similarity at scales below the
  grain size, the scaling relation for area could
  be used to estimate the area of a feature at
  sub-grain scales
• k lacunarity used to estimate N(L) for box
  size L

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Multiple metrics
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Which metrics?

• types, contagion, fractal dimension, mean patch
  perimeter-area ratio, relative patch area
  (Riiters et al. 1995)
• Patch shape and edge contrast, patch density,
  patch size (McGarigal and Marks (1995)
• types, proportion of each type, spatial
  arrangement of patches, patch shape, contrast
  between neighboring patches (Li and Reynolds 1994)

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Pattern in continuous variables and point
processes

• Trend surface analysis
• Spatial autocorrelation
• Semivariance
• 1-d and 2-d spectral analysis
• wavelets

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Morans I, Gearys CTwo general measures of
spatial autocorrelation

• wij - weight at distance d, that is, wij1 if
  point j is within distance class d from point i,
  else wij0
• z's are deviations (i.e., ziyi-ymean for
  variable y),
• W is the sum of all the weights.
• The summation is done for all i not equal to j

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Random landscape
Continuous gradient
Repeating pattern
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Semivariograms

• N point (location) pairs
• f1i value of variable at location 1
• f2i value of variable at location 2

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Gustafson (1998)
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Variograms and correlograms
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Example application of landscape pattern metrics

• G. Darrel Jenerette 2001. Analysis and simulation
  of land-use change in the central Arizona
  Phoenix region, USA. Landscape Ecology 16(7)
  611-626.

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