Why Quantify Landscape Pattern?
• Comparison
(space & time)
– Study areas
– Landscapes
• Inference
– Agents of pattern
formation
– Link to ecological
processes
Programs for Quantifying Landscape
Pattern
• FRAGSTATS
– http://www.umass.edu/lan
deco/research/fragstats/do
cuments/Metrics/Metrics
%20TOC.htm
• Patch Analyst
– http://flash.lakeheadu.ca/~
rrempel/patch/
Quantifying Landscape Pattern
• Just because one can measure it, doesn’t
mean one should
– Does the metric make sense?...biologically
relevant?
– Avoid correlated metrics
– Cover the bases (comp., config., conn.)
Landscape Metrics - Considerations
• Selecting Metrics……
– Subset of metrics needed that:
• i) explain (capture) variability in pattern
• ii) minimize redundancy (i.e., correlation among
metrics = multicollinearity)
– O’Neill et al. (1988) Indices of landscape
pattern. Landscape Ecology 1:153-162
• i) eastern U.S. landscapes differentiated using
– dominance
– contagion
– fractal dimension
Landscape Metrics - Considerations
• Selecting Metrics……
– Use species-based metrics
– Use Principal Components Analysis (PCA)?
– Use Ecologically Scaled Landscape Indices
(ESLI; landscape indices, scale of species, and
relationship to process)
Quantifying Pattern: Corridors
• Internal:
– Width
– Contrast
– Env. Gradient
• External:
–
–
–
–
–
Length
Curvilinearity
Alignment
Env. Gradient
Connectivity (gaps)
Quantifying Pattern: Patches
• Levels:
– Patch-level
• Metrics for indiv.
patches
– Class-level
• Metrics for all patches
of given type or class
– Zonal or Regional
• Metrics pooled over 1
or more classes within
subregion of landscape
– Landscape-level
• Metrics pooled over all
patch classes over entire
extent
Quantifying Pattern: Patches
• Composition:
– Variety & abundance
of elements
• Configuration:
– Spatial characteristics
& dist’n of elements
Quantifying Pattern: Patches
• Composition:
– Mean (or mode,
median, min, max)
– Internal heterogeneity
(var, range)
• Spatial Characters:
– Area (incl. core areas)
– Perimeter
– Shape
Quantifying Pattern: Landscapes
(patch based)
• Composition:
– Number of patch type
• Patch richness
– Proportion of each type
• Proportion of landscape
– Diversity
• Shannon’s Diversity
Index
• Simpson’s Divesity Index
– Evenness
• Shannon’s Evenness
Index
• Simpson’s Index
Quantifying Pattern: Patches
• Configuration:
– Patch Size & Density
• Mean patch size
• Patch density
• Patch size variation
• Largest patch index
Patch-Centric
vs.
Landscape-Centric
• Mean – avg patch
attribute; for
randomly selected
patch
• Area-weighted
mean- avg patch
attribute; for a cell
selected at random
Patch-Centric
vs.
Landscape-Centric
• Consider relevant
perspective…landscape
more relevant?...use areaweighted
• Look at patch dist’ns…rightskewed = large differences
Quantifying Pattern: Patches
• Configuration:
– Shape Complexity
• Shape Index
• Fractal Dimension
• Fractals = measure of
shape complexity (also
amount of edge)
• Fractal dimension (d)
ranges from 1.0 (simple
shapes) to 2.0 (more
complex shapes)
• ln(A)/ln(P), where A =
area, P = perimeter
Quantifying Pattern: Patches
• Configuration:
– Core Area (interior
habitat)
• # core areas
• Core area density
• Core area variation
• Mean core area
• Core area index
Quantifying Pattern: Patches, Zonal
• Configuration:
– Isolation / Proximity
• Proximity index
• Mean nearest
neighbor distance
Proximity
s
k
PX  
i
n
k
where, within a user-specified search distance:
sk = area of patch k within the search buffer
nk = nearest-neighbor distance between the focal patch
cell and the nearest cell of patch k
•
Proximity Index (PXi) = measure of relative
isolation of patches; high (absolute) values
indicate relative connectedness of patches
Quantifying Pattern
• Overlay hexagon grid onto landcover map
• Compare bobcat habitat attributes to population of hexagon
core areas
Quantifying Pattern
• Landscape metrics include:
• Composition
(e.g., proportion cover type)
• Configuration
(e.g., patch isolation, shape,
adjacency)
• Connectivity
(e.g., landscape permeability)
Quantifying Pattern & Modeling
Pij   ki  kj  / pVk
p
2
k 1
• Calculate and use Penrose distance to measure similarity
between more bobcat & non-bobcat hexagons
• Where:
• population i represent core areas of radio-collared bobcats
• population j represents NLP hexagons
• p is the number of landscape variables evaluated
• μ is the landscape variable value
• k is each observation
• V is variance for each landscape variable
after Manly (2005)
Penrose Model for Michigan Bobcats
Variable
Mean Vector bobcat
hexagons
NLP hexagons
% ag-openland
15.8
32.4
% low forest
51.4
10.4
% up forest
17.6
43.7
% non-for wetland
8.6
2.3
% stream
3.4
0.9
% transportation
3.0
5.2
Low for core
27.6
3.6
Mean A per disjunct
core
0.7
2.6
Dist ag
50.0
44.9
Dist up for
55.0
43.6
CV nonfor wet A
208.3
120.1
Quantifying Pattern & Modeling
• Each hexagon in NLP
then receives a
Penrose Distance
(PD) value
• Remap NLP using these
hexagons
• Determine mean PD for
bobcat-occupied
hexagons
Preuss 2005