Quantifying Scale and Pattern Lecture 7 February 15, 2005

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Quantifying Scale and PatternLecture 7February
15, 2005
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Why Quantify Landscape Pattern and Scale?

• In order to relate landscape pattern to process,
  we need to quantify the pattern.
• Often have hypotheses relating pattern to
  ecological processes.
• Describe change over time.
• Compare different landscapes.

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Quantifying Scale
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Three Classes of Spatial Data 1. Spatial point
patterns 2. Geostatistical 3. Lattice Data
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Ash tree locations
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Quantifying Scale Geostatistical Data

• What is autocorrelation?
• Why do we use autocorrelation?
• Provides an estimate of mean patch size / minimum
  mapping unit.
• Can be measured for time, space, multivariate -
  particularly communities.
• Has important statistical implications -
  observations are NOT independent.

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Quantifying Scale Geostatistical Data
Semivariogram
Correlogram
Measuring Spatial Autocorrelation
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Quantifying Scale Grid (Lattice) Data
Blocking Techniques (aka Block-size ANOVA)
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Quantifying Scale Grid (Lattice) Data
Blocking Techniques (aka Block-size ANOVA,
Blocked Quadrat Variance)
out-of-phase
in-phase
Dale 1999
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Quantifying Scale Grid (Lattice) Data
Moving Window Techniques
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Quantifying Scale Grid (Lattice) Data
Moving Window Techniques
Bradshaw and Spies 1992 Wavelet Analysis
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Quantifying Landscape Pattern
Quantified Landscape Structure
The Modeled Landscape (patches and mosaics)
The Actual Landscape
Composition
Richness, Diversity, Evenness
Configuration
Size, Density, Shape, Edge, Isolation,
Dispersion, Contrast, Contagion, Interspersion,
Connectivity
Pattern Measurement
Scale detection Patch detection.
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Why compute indices of landscape pattern?
For comparative purposes To summarize differences
between study areas or landscapes.
To infer drivers of pattern As an explanatory
analysis as a precursor to more strategic
hypothesis testing.
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Critical caveats about landscape metrics

• A clear, a priori statement of objectives
• is critical to avoiding misleading comparisons
• between metrics

YES
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Critical caveats about landscape metrics

• A clear, a priori statement of objectives
• is critical to avoiding misleading comparisons
• between metrics.
• The classification scheme must be
• relevant and consistent for proper
• interpretation of landscape metrics.

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Critical caveats about landscape metrics

• A clear, a priori statement of objectives
• is critical to avoiding misleading comparisons
• between metrics.
• The classification scheme must be
• relevant and consistent for proper
• interpretation of landscape metrics.
• Both grain and extent will affect how
• landscape metrics are interpreted, and must be
• consistent across landscapes to be compared.

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Critical caveats about landscape metrics

• A clear, a priori statement of objectives is
  critical to avoiding misleading comparisons
  between metrics.
• The classification scheme must be relevant and
  consistent for proper interpretation of
  landscape metrics.
• Both grain and extent will affect how landscape
  metrics are interpreted, and must consistent
  across landscapes to be compared.
• Neighbor rules are critical in defining landscape
  metrics.

4-neighbor rule
8-neighbor rule
6 patches
2 patches
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Components of landscape structure
Landscape composition The variety and relative
abundance of landscape elements (diversity
indices). Landscape configuration The
spatial characteristics and distribution of
landscape elements.
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Landscape Composition
Number of patch types Patch richness Proportion
of each patch type of landscape Evenness Shann
ons Evenness Index Simpsons Evenness
Index Diversity Shannons Diversity
Index Simpsons Evenness Index
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Landscape Configuration
Patch level metrics Patch data at the level of
the individual patch type. Between patch
metrics The importance of the surrounding
neighborhood is acknowledged. Spatially
explicit. Landscape level metrics The relative
location of all patches on the landscape are
included in calculations. The importance of
spatial arrangement is acknowledged. Spatially
explicit.
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Metrics of Landscape Configuration
Patch size distribution and density Mean patch
size Largest patch area Variation in patch
size Patch density
Patch size
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Metrics of Landscape Configuration
Shape complexity Edge-to-area ratio Shape index
Low edge/area Low complexity
Higher edge/area Higher complexity
Complex geometry
Simple geometry
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Metrics of Landscape Configuration
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Metrics of Landscape Configuration
Contagion Contagion index Lacunarity
Low contagion
High contagion
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Metrics of Landscape Configuration
Connectivity Metrics Connectance Patch cohesion
index Percolating cluster Correlation
length Traversability index

• Refers to functional connections
• between patches.
• The functional connection depends on
• the object of interest
• May be based on
• Strict adjacency or a threshold distance
• A decreasing function of distance
• A distance function weighted for resistance the
  least-cost path between patches

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Landscape metrics Important limitations
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Landscape metrics Important limitations
Data format/Grain size
Data Format
Grain
Vector Data
Coarse- grained
Edge 1000
Edge 100
Raster Data
Fine- grained
Edge 1500
Edge 130
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Landscape metrics Important limitations
Boundary Effects
Nearest Neighbor?
Boundary effects
Landscape boundary
Landscape extent/heterogeneity
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Landscape metrics Important limitations
Measured vs. functional heterogeneity
Example Two distinct ecological neighborhoods
within one landscape
Example Relevant buffer size and core area.
Which core area is relevant? Is either?
Landscape with edge effects that limit core size
core
Landscape without any edge effect
core
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Landscape metrics Important limitations
Redundancy/correlation of landscape metrics
Redundant/correlated by definition
Statistically redundant/correlated
Edge density
Core area index
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Landscape metrics Conclusions

• Primary measures of landscape pattern
• Patch type
• Area
• Edge
• Neighbor or surrounding types
• All metrics are derived from these!

• Looking at a large sample of classified
  landscapes, Riitters et al. (1995) found that
  only five metrics were needed to explain most of
  the variability in their samples
• Number of patch types
• Mean edge/area ratio
• Contagion
• Average patch shape
• Fractal measurements

Main point The most important aspect of pattern
depends on the application which depends on
the original hypothesis!