Scale
• What’s the big deal?
• Seminal pubs
– Allen & Starr (1982) – Hierarchy: perspectives
for ecological complexity
– Delcourt et al. (1983) – Quaternary Science
Review 1:153-175
– O’Neill et al. (1986) – A hierarchical concept of
ecosystems
Long
Ecological Scaling: Scale & Pattern
Speciation
Extinction
Short
Temporal Scale
Species
Migrations
Secondary
Succession
Windthrow
Fire
Treefalls
Recruitment
Fine
Spatial Scale
Coarse
• Acts in the “ecological
theatre (Hutchinson
1965) are played out
across various scales
of space & time
• To understand these
dramas, one must
select the appropriate
scale
Ecological Scaling: Scale & Pattern
• Different patterns emerge,
depending on the scale of
investigation
Regional Scale
(thousands of ha)
American Redstart
American Redstart
Local Scale
(4 ha plots)
Least Flycatcher
Least Flycatcher
Ecological Scaling: Components of Scale
• Grain: minimum
resolution of the data
– Cell size (raster data)
– Min. polygon size
(vector data)
• Extent: scope or
domain of the data
– Size of landscape or
study area
Ecological Scale
• Scale characterized
by:
– grain: smallest
spatial resolution of
data
e.g., grid cell size,
pixel size,
quadrat size
(resolution)
Fine
Coarse
Ecological Scale
• Scale
characterized by:
– extent: size of
overall study area
(scope or domain
of the data)
Small
Large
Ecological Scaling: Components of Scale
• Minimum Patch Size:
min. size considered >
resolution of data
(defined by grain)
Ecological Scaling: Definitions
• Ecological scale & cartographic scale are exactly opposite
– Ecological scale = size (extent) of landscape
– Cartographic scale = ratio of map to real distance
Scale in
Ecology & Geography
• ecological vs. cartographic scale
Small
(Fine)
Large
(Broad)
Ecology
Geography
Fine resolution
Small Extent
Coarse resolution
Large extent
Coarse resolution
Large Extent
Fine resolution
Small extent
Scale in
Ecology & Geography
• ecological vs. cartographic scale
– e.g., map scale
1:200,000 vs. 1:24,000
fine vs. coarse
large vs. small extent
1:24,000
1:200,000
Ecological Scaling: Components of Scale
• From an organismcentered perspective,
grain and extent may
be defined as the
degree of acuity of a
stationary organism
with respect to shortand long-range
perceptual ability
What ecological concept
is important here?
Ecological Scaling: Components of Scale
• Grain = finest
component of
environment that can be
differentiated up close
• Extent = range at which
a relevant object can be
distinguished from a
fixed vantage point
Extent
Grain
Fine
Scale
Coarse
Ecological Scaling: Components of Scale
• From an anthropocentric
perspective, grain and
extent may be defined on
the basis of management
objectives
• Grain = finest unit of mgt
(e.g., stand)
• Extent = total area under
management (e.g., forest)
Ecological Scaling: Components of Scale
• In practice, grain and extent often dictated by scale of
available spatial data (e.g., imagery), logistics, or
technical capabilities
Ecological Scaling: Components of Scale
• Critical that grain and extent be defined for a study and
represent ecological phenomenon or organism studied.
• Otherwise, patterns detected have little meaning and/or
conclusions could be wrong
Scale: Jargon
• scale vs. level of organization
Individual
Space - Time
Population
Space - Time
Community
Space - Time
Ecological Scaling: Implications of Scale
• As one changes scale, statistical relationships may
change:
– Magnitude or sign of correlations
– Importance of variables
– Variance relationships
Implications of Changes in Scale
• Processes and/or patterns may change
• Hierarchy theory = structural
understanding of scale-dependent
phenomena
Example
Abundance of forest insects sampled at different distance
intervals in leaf litter,
Implications of Changes in Scale
Insects sampled at 10-m intervals for 100 m
45
40
35
30
25
Predator
Prey
20
15
10
5
0
P
r
to
da
e
r
Pr
ey
What’s the pattern?
Implications of Changes in Scale
Insects sampled at 2000-m intervals for 20,000 m
45
40
35
30
25
Predator
Prey
ey
Pr
Pr
ed
at
or
20
15
10
5
0
What’s the pattern?
Identifying the “Right” Scale(s)
•
•
•
•
No clear algorithm for defining
Autocorrelation & Independence
Life history correlates
Dependent on objectives and organisms
• Multiscale analysis!
• e.g., Australian leadbeater’s possum
Large Scale:
Scale: old
proportion
& connectivity
Local
growth with
den cavitiesof old
growth forest
Multiscale Analysis
• Species-specific perception of
landscape features : scale-dependent
– e.g., mesopredators in Indiana
• Modeling species distributions in
fragmented landscapes
Matrix
Patches
Corridors
Underlying Mechanisms
Use of Spatial
Elements
Body
Size
Niche
Breadth
Distribution
Patterns
Body Size
• Mobility
• Predation Risk
• Landscape Perception
Niche Breadth
• Food Habits
• Habitat Use
Body Size & Niche Breadth
Species
Coyote
Mean
Mass (kg)
12.78
Food
Habits
11/15
Habitat
Use
11/12
Raccoon
5.94
11/15
7/12
Longtailed
Weasel
0.15
4/15
8/12
PREDICTIONS
• Species should view the landscape at
different spatial scales. Presence of larger
species predicted by element and landscape
attributes, whereas smaller species
correlated with site characteristics.
Variables
Local Habitat:
• Ground Cover
• Canopy Cover
• Vertical Structure (4 levels from 0-3 m)
Variables
Element-level:
• Area, Fractal Dimension, Distance Nearest
Edge
Landscape-level (1-km & 3-km buffers):
• NN Distance, Proportion Area, Shannon
Diversity Index
Coyote Logistic Model
3-km2 Landscape:
Landscape-Element Model
wi = 0.77; Relative Likelihood = 3.5
•
•
•
•
Lower proportion of forest
Absence of forest patches & corridors
Closer proximity to edge
Greater fractal dimension
Raccoon Logistic Model
3-km2 Landscape:
Full Model
wi >0.999; Relative Likelihood = 999
• Lower proportion herb corridors & greater
proportion of wooded corridors
• Greater proportion of forest and forest patches
in closer proximity
• Greater fractal dimension
• Greater canopy closure & greater vertical
structure
Long-tailed Weasel
Logistic Model
3-km2 Landscape:
Full Model
wi >0.999; Relative Likelihood = 999
•
•
•
•
•
Greater proportion herb & wooded corridor
Presence of forest patches & corridors
Closer proximity to edge
Presence of small & medium prey
Increased ground cover
Swihart et al. 2003.
Diversity and
Distributions 9:1-8.
Hierarchy Theory
• Lower levels
provide mechanistic
explanations
• Higher levels
provide constraints
Scale & Hierarchy Theory
• Hierarchical structure of systems =
helps us explain phenomena
–Why?
: next lower level
–So What? : next higher level
• minimum 3 hierarchical levels needed
Constraints
(significance)
Level of Focus
(level of interest)
Components
(explanation)
Community
Population
Individual
Constraints
Why are long-tailed
weasel populations declining
in fragmented landscapes?
Components
Community
Population
Individual
Constraints
Why are long-tailed
weasel populations declining
in fragmented landscapes?
Small body size
mobility
Community
Population
Individual
Predators
Competitors
Prey dist’n
Why are long-tailed
weasel populations declining
in fragmented landscapes?
Components
Ecological Scaling: Components of Scale
• Grain and extent are
correlated
• Information content
often correlated with
grain
• Grain and extent set
lower and upper limits
of resolution in the
data, respectively
1st order – innate?
2nd order –decisions
3rd &4th order
–decisions
Scale Dependence
of Habitat Selection
1st Order
2nd Order
3rd Order
4th Order
Macrohabitat
vs.
Microhabitat