The Concept of Scale
Outline
► Introduction
► Scale
terminology
► Scale problems
► Scale concepts and hierarchy theory
► Identifying the “right” scale(s)
► Scaling up
► Summary
Key Scaling Questions
► Finding
the characteristic scale of spatial
heterogeneity or pattern (so-called "scaling
techniques");
► Defining what a "patch" is, and devising aggregate
descriptions of collections of patches (their sizes,
diversity, and such), to more complex summaries ► Connectedness, fractal geometry, and percolating
networks;
► How these aspects of pattern are interrelated in
landscapes, and how they vary according to
physiography and landscape history.
What factors drive pattern?
► The
physical template of environmental
constraints -- soils, topography, climate;
► Biotic processes -- establishment and
growth, dispersal, and mortality;
► Disturbance regimes -- fires, floods, storms,
and human land use.
Scale - Environmental Imperative
►
1980s & 1990s – importance of
scale in ecology widely
published and discussed
►
Pressing environmental issues
over large areas brought role of
scale to forefront:
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Acid rain
Global climate change
Habitat fragmentation
Conservation biology
Disturbance regimes
Fire and bugs!
Scale – Lessons Learned
►
“Lessons learned” from scale
studies (esp. last 20 years):
 No single scale is appropriate
for study of all ecological
problems
 A challenge to understand how
data collected at finer scales
(e.g., small plots) relates to
larger areas.
 Can these results be
extrapolated? CAUTION the
scaling up/down problem
Scale – Lessons Learned
►
“Lessons learned”…con’t:
 Changing the quadrat size
(grain) or the extent of the area
often yields a different
numerical result or pattern
 Disparate results from different
studies of the same
variable/organism might be due
to differences in scale
Scale – Lessons Learned
►
“Lessons learned” …con’t:
 Spatial and temporal scales
important to humans are not
necessarily the scales relevant to
other organisms or processes
 Biological interactions most likely
occur at multiple scales
(biocomplexity idea)
Scale Terminology (see Table 2.1)
►
Scale terminology – is not used
consistently; leads to confusion
►
Scale – refers to spatial or
temporal dimension of an object or
area
- vs ►
Level of organization – place
within a biotic (or other
organizational) hierarchy
(e.g.,
organism, population, community, etc.)
Scale Terminology
con’t.:
► Scale
characterized by:
 grain
 extent
►
Grain – finest spatial
resolution within a given data
set (cell size or pixel size; or
minimum mapping unit – MMU)
►
Extent – the size of the overall
study area
► Grain
Size:
 The minimum resolution
of the data
 defined by scale
► grid
data = the cell size
► in field sample data, the
quadrat (or plot) size
► in imagery, the pixel size
► in map-type (vector)data,
the minimum mapping unit.
Spatial scale is characterized by...
► Grain
- size of the smallest feature that can be
resolved from the observations
 “resolution” is used synonymously
 e.g., the length or area represented by 1 pixel in a
digital image
► Extent
- size of the largest feature that can be
captured in the observations
 e.g., the length or area represented by the entire image
Temporal scale is characterized by...
► Grain
- duration or frequency the shortest
(highest frequency) feature that can be
resolved from the time series
 e.g., the sampling rate
► Extent
- duration or frequency of the
longest (lowest frequency) feature that can
be captured in the time series
 e.g., the length of the time series
Scale Terminology – con’t.
►
A scale-dependent pattern,
process, or phenomenon =
changes with grain or extent
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Species-area (e.g., biodiversity)
Insect feeding
Disease patterns
Fire behavior
Plant or animal dispersal
Scale Terminology – con’t.
►
Absolute vs. relative scale:
►
Absolute scale = actual distance,
time, or area, etc.
►
Relative scale = two points might
be relatively closer in terms of
energy expended vs. actual
distance
(e.g., barriers; mountains,
canyons, water, etc.)
Scale Problems
►
Three basic scale
problems (Haggett
1963):
 Scale coverage problem
(large
areas difficult to map and understand)
 Scale linkage problem
(fine to
broad-scale)
 Scale standardization
problem (compare locations,
extrapolate from one place to another)
Scale concepts and hierarchy theory
►
Hierarchy
 identified with levels
organization
(e.g., cell, organism,
population, etc.)
 higher levels constrain the
lower levels to various degrees
Scale concepts and hierarchy theory
►
Three important points:
1.
Any analysis should consider at
least three hierarchical levels:
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Focal level – level of interest;
question or objective
Level above – constrains and controls
the lower levels
Level below – provides the details
needed to explain the behavior of the
focal level
Scale concepts
and hierarchy theory
2. “list” of variables may not change with
scale, but see a shift in the relative
importance or direction

Extending the spatial domain:
Rate of organic matter dynamics
example (Sollins et al. 1983. Soil OM
accretion on mudflow series)
(local = detail charac. litter, microclimate;
global = P & T)

Extending the time frame of observation:
magnitude and overall direction of
change often more apparent over longterm
Scale concepts and hierarchy theory
3. Multiple scales of pattern will exist
in landscapes
Coarse-grained: geomorphology
(substrate & soils); large disturbances
(large fires, large insect epidemics)
► Fine-grained: local disturbances
(individual tree blow down; canopy
gaps, etc.)
► Collectively, spatial pattern of an
ecosystem at any given time may reflect
these processes operating over different
scales in space & time
►
Identifying the “right” scale
►
All of these ideas are
provocative and interesting –
this still leaves us with the
burden of identifying the
“relevant scale”
►
There is no single correct scale
or level to describe a system
►
However, “(this)…does not
mean that all scales serve
equally well or that there are
not scaling laws” (Levin 1992)
Scaling Up/Scaling Down
Simplest approach - multiply a
measurement made at one scale
(e.g., unit of area) to predict at a
broad or coarser level; or its
reverse
► Example: standing biomass for a
10,000 ha forest – estimated by
multiplying the amount of biomass
measured in 1-ha stands by 10,000
► Approach assumes:
►
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that the properties of the system do not
change with scale
that the broader system behaves like the
averaged finer one
that the relationships are linear
We must think and act at a scale and pace
appropriate to the forest health crisis.
Forest Ecosystem Restoration
Analysis (FORESTERA)
► Uses
remote sensing data, on site data
(e.g., FIA data), GIS, and computer models
to synthesize past, present, and future
scenario data
► Forest health restoration is the major
impetus for greater ecosystem scale
adaptive management activities
Delcourts’ – Scale Paradigm
► Micro
► Meso
► Macro
► Mega
Delcourts’ Paradigm
Scale Paradigms – Resource Planning
Summary
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Scale is a prominent topic in restoration and adaptive management
Influences conclusions and extrapolations
Scale related to hierarchy; hierarchy theory provides a framework
(consider focal level; level above constrains; level below explains
[mechanisms])
Extrapolation from fine to broad scale is straightforward if areas are
homogeneous and relationship linear; spatial heterogeneity present,
but need to know random vs. structured pattern; fractals and other
methods possible if processes and constraints do not change across
scales
Extrapolation a very difficult problem with spatial heterogeneity and
nonlinear relationships (no general solution at present)
Just because you may not be able to scale up with great
accuracy is no excuse for ignoring restoration and adaptive
management problems at the landscape level !