Metric Behavior

1
Metric Behavior

• Objectives
• Investigate behavior of individual metrics across
  gradients of landscape composition and
  configuration
• Use principle components analysis to
• examine covariance among metrics and
• disentangle the proportion of variance in metrics
  explained by composition versus configuration

2
Step 1 Generate binary neutral landscapes using
RULE
256 x 256 cell grids
Factorial Design H (n 21) x P (n 19) 100
replicates of each of 399 H x P combinations
3
Fragstats Specifications
Step 2 Calculate applicable Fragstats metrics on
all 39,900 neutral landscapes

• 30 m cell size
• 90 m edge depth
• 500 m search radius
• 0.5 similarity between the two classes
• 8 cell neighbor rule
• No border
• No background

4
Evaluating Class Metric Behavior

• Examine metrics in relation to P and H
• Compare behavior of conceptually similar metrics
• Compare conceptual classification of metrics with
  similar behavior
• Demonstrate examples of non-linear behavior
• Compare sensitivity of different metrics to
  changes in landscape structure

5
Conceptual Metric Classification
Isolation/ Proximity PROX SIMI ENN

• Area/Edge/
• Density
• CA
• PLAND
• PD
• ED
• LSI
• LPI
• AREA
• GYRATE

Shape PAFRAC PARA SHAPE FRAC
Core Area TCA CPLAND NDCA DCAD CORE DCORE CAI
Contagion/ Interspersion PLADJ CLUMPY AI IJI MFRAC
DIVISION SPLIT MESH
Connectivity COHESION
Contrast CWED TECI ECON
6
Metric Behavior
H
P
7
Metrics Related to P

• PLAND
• LPI
• GYRATE_AM
• PROX_SD
• SIMI_MN
• SIMI_AM
• SIMI_SD
• DIVISION
• MESH

AREA_AM
H
P
8
Metrics Related to H
CLUMPY

• PAFRAC
• PARA_CV
• PARA_SD
• CORE_CV
• CAI_CV
• CAI_SD

H
P
9
Metrics that Confound PH
Edge Density
AREA_CV LSI PD FRAC_AM SHAPE_AM PROX_AM NDCA DCAD
H
P
10
More Metrics that Confound PH
DCORE_CV
GYRATE_CV SHAPE_MN SHAPE_CV SHAPE_SD PARA_AM PLADJ
AI ECON_AM TECI
H
P
11
Still More Metrics that Confound PH
Core Percent Landscape
AREA_SD GYRATE_SD FRAC_MN FRAC_CV FRAC_SD TCA CORE
_AM CORE_SD DCORE_AM DCORE_SD CAI_AM PROX_MN PROX_
CV ENN_CV SIMI_CV
H
P
12
But Confounded in Different Ways
CAI
ENN_CV
H
H
P
P
FRAC_CV
AREA_SD
H
H
P
P
13
Explosion at Extreme Values
SPLIT
Cohesion
H
P
14
Explosion at Extreme Values
ENN_MN
ENN_AM
H
P
15
Explosion at Extreme Values
AREA_MN
GYRATE_MN CORE_MN DCORE_MN CAI_MN ECON_MN ECON_CV
ECON_SD TECI
H
P
16
Differential Metric Sensitivity
AREA_MN
AREA_AM
P
H
H
P
17
Main Points

• Results are based on only one configuration
  gradient (H). Varying contrast, shape, etc.
  would yield different behavior
• Need to know expected behavior to correctly
  interpret your results
• Identified gt7 behavioral groups including varying
  relationships with P and H, some depicting linear
  behavior, others with non-linear behavior, and
  lack of sensitivity in at least part of the HxP
  space
• Conceptual similarity ? behavioral similarity

18
Behavior of Conceptually Similar Metrics
H
H
P
P
H
H
P
P
19
Main Points

• Results are based on only one configuration
  gradient (H). Varying contrast, shape, etc.
  would yield different behavior
• Need to know expected behavior to correctly
  interpret your results
• Identified gt7 behavioral groups including varying
  relationships with P and H, some depicting linear
  behavior, others with non-linear behavior, and
  lack of sensitivity in at least part of the HxP
  space
• Conceptual similarity ? behavioral similarity
• Very few metrics measure configuration
  independent of area most confound P H

20
Step 3 Analyze metrics using partial principal
components analysis
Factor 1
21
Step 3 Analyze metrics using partial principal
components analysis
Factor 2
Factor 1
22
Step 3 Analyze metrics using partial principal
components analysis

• Objectives
• To examine how metrics covary in relation to P
  and H
• To quantify the amount of variance in metrics
  accounted for by composition and configuration

PCA Models

• Full Model (43 metrics)
• No contrast or similarity metrics
• With P as a covariate
• With H as a covariate
• With both P and H as covariates

23
Factor Loading Pattern Full Model PCA
27
9
7
46
Factor 4 PARA_AM PLADJ COHESION SPLIT AI
Factor 1 H PD ED LSI AREA_CV SHAPE_AM SHAPE_CV FR
AC_CV FRAC_AM PAFRAC CORE_CV CAI_MN CAI_CV DCAD PR
OX_AM ENN_CV CLUMPY
Factor 2 P PLAND LPI AREA_AM GYRATE_AM GYRATE_C
V FRAC_MN CORE_AM CPLAND PROX_MN PROX_CV ENN_CV ME
SH
Factor 3 AREA_MN GYRATE_MN CORE_MN DCORE_MN CAI_
MN
24
Variance Partitioning
31
Configuration matters!
25
Factor Loading Pattern PCA PH Partialed Out
10
7
5
3
Factor 2 PD SHAPE_CV PARA_AM DCORE_CV PROX_CV PL
ADJ AI
Factor 1 PD ED LSI GYRATE_AM AREA_CV SHAPE_AM FR
AC_AM DCAD CORE_AM CORE_CV CAI_CV CPLAND PROX_AM M
ESH
Factor 3 AREA_MN GYRATE_MN GYRATE_CV FRAC_CV PAR
A_MN CORE_MN DCORE_MN CAI_MN
Factor 4 ENN_MN ENN_AM
26
Summary and Conclusions

• Interpretation of results is limited to one
  configuration gradient (H).
• Configuration matters
• No easily interpretable principal components
• Conceptually similar metrics do not necessarily
  load similarly
• Have strongly linear behavior in some metrics and
  non-linear behavior in others
• Non-linear behavior makes metric interpretation
  difficult
• No one analytical technique will likely account
  for or adequately describe varied metric behaviors