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/

landeco/research/fragstats/documents/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 area-weighted

• Look at patch dist’ns…right-skewed = 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

k

nk

s

iPX

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

p

kkkjkiij pVP

1

2 /

• 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 BobcatsVariable Mean Vector bobcat

hexagonsNLP 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