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 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

PX i

 

s k n k

where, within a user-specified search distance:

s k

= area of patch

k

within the search buffer

n k

= 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 ij



k p

  1  

ki

 

kj

 2 /

pV k

• 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 μ k V

is the number of landscape variables evaluated is the landscape variable value is each observation is variance for each landscape variable after Manly (2005)

Variable Penrose Model for Michigan Bobcats % ag-openland Mean Vector bobcat hexagons 15.8

NLP hexagons 32.4

% low forest % up forest 51.4

17.6

10.4

43.7

% non-for wetland % stream % transportation Low for core Mean A per disjunct core Dist ag Dist up for CV nonfor wet A 8.6

3.4

3.0

27.6

0.7

50.0

55.0

208.3

2.3

0.9

5.2

3.6

2.6

44.9

43.6

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