2.2 Ecosystems as Hierarchies
glean from the data. Do not expect the measurement of microbes to capture the dynamics of a
whale.
Costanza and Maxwell (1994) used information
theory to investigate the effect of spatial resolution
(grain) on aspects of predictability. They use a
raster-based representation of a landscape (e.g., a
classified satellite image or a GIS layer) in which
each pixel is assigned a unique state (e.g., land
cover class). Raster pixels are equal-sized grid units
of the image. Costanza and Maxwell (1994) used
several images from the same time period with different resolutions so that the pixels in different images each represented a different amount of area on
the ground. They also used images with constant
resolution, but from different times. Two types of
prediction are presented, which we will restate. The
first is a type of spatial prediction within a scene
(autopredictability): how well can we predict the
state of a pixel given the states of its neighboring pixels? This prediction can be based on the images with
different spatial resolutions. The second is a temporal prediction across scenes (cross-predictability):
how well can we predict the state of a pixel in the
current scene given its state in another scene with
the same resolution? The general result is that, as
resolution is increased or spatial grain in the data
set is decreased (pixels represent less land surface),
the ability to predict a pixel's state based on its
neighbors increases. However, the ability to predict
a pixel's state over time from one scene to the next
decreases. This is intuitively reasonable. Landscapes usually display positive spatial autocorrelation, which decays with distance. Thus, as grain
size decreases, each pixel represents a smaller area,
and the states of neighboring pixels should be more
strongly correlated, allowing greater spatial predictability. On the other hand, because pixels represent smaller areas, smaller-scale changes in state
become evident, making prediction of changes
from scene to scene more difficult (Le., decreasing
temporal predictability). Spatial resolution of the
data should be chosen to yield an appropriate balance between spatial and temporal predictability.
Just where that balance occurs will depend on the
properties of the landscape and on the assessment
objectives.
2.2.3 Continuous versus
Discontinuous Change
Ecosystems, communities, popUlations, and organisms all change over time. Our measurements and
our expectations determine whether we perceive
31
change as continuous or discontinuous. A change
is regarded as discontinuous if there is a sudden
switch between distinct (qualitatively different)
states. A bulldozer clears an area; a graph of vegetative cover versus time has a stair-step form.
However, if a string of intermediate states is observed, the change is regarded as continuous. Measured year to year, livestock grazing may lead to a
change in composition of the plant community; the
graph is a curve. Continuity and discontinuity in
ecological systems are both idealizations. The important issue is not whether a given change is really continuous or discontinuous, but how it can
best be described, given our observations. The
grain and extent of our observation set will determine whether a given change is regarded as continuous or discontinuous. A fine-grained observation set will be more likely to resolve intermediate
states and therefore be described more naturally in
terms of a continuous change. A coarser-grained
observation set will more likely fit a description
based on discontinuous transitions between discrete
states. Observation sets with large extent will tend
to yield evidence of discontinuous change, both because the larger spatial coverage or longer temporal duration is more likely to encompass changes
of large magnitude and because observation sets
with large extent usually will be relatively coarse
grained (Ahl and Allen, 1996).
This can be illustrated by the altitudinal zonation of vegetation on a mountain. Standing back
and looking at the mountain from afar, we can see
distinct zones of vegetation, with discontinuous
change from deciduous to coniferous forest, for example. Walking up the mountain, on the other hand,
the transitions appear much more gradual, much
more continuous, as purely deciduous stands give
rise to mixed deciduous---coniferous stands and finally to purely coniferous stands. The difference in
our perception stems from the scale of our observations. Viewing the mountain from a distance, we
see a large extent (the entire altitudinal range from
foot to peak), but our eye does not resolve finegrained detail. Walking within the forest, our vision is limited in extent, but we see the fine-grained
detail of individual trees in our local environment.
Both perspectives can be useful. Thus, Whitaker
(1956), in his classic study of the vegetation of the
Great Smoky Mountains (Figure 2.2), showed cove
hardwood forests and spruce-fir forests as distinct
units on a mountain in one figure, while using gradient analysis to show a continuous gradation in
another figure. The issue of continuous versus discontinuous change is a nonissue as we choose the
appropriate description for the data set at hand.
glean from the data. Do not expect the measurement of microbes to capture the dynamics of a
whale.
Costanza and Maxwell (1994) used information
theory to investigate the effect of spatial resolution
(grain) on aspects of predictability. They use a
raster-based representation of a landscape (e.g., a
classified satellite image or a GIS layer) in which
each pixel is assigned a unique state (e.g., land
cover class). Raster pixels are equal-sized grid units
of the image. Costanza and Maxwell (1994) used
several images from the same time period with different resolutions so that the pixels in different images each represented a different amount of area on
the ground. They also used images with constant
resolution, but from different times. Two types of
prediction are presented, which we will restate. The
first is a type of spatial prediction within a scene
(autopredictability): how well can we predict the
state of a pixel given the states of its neighboring pixels? This prediction can be based on the images with
different spatial resolutions. The second is a temporal prediction across scenes (cross-predictability):
how well can we predict the state of a pixel in the
current scene given its state in another scene with
the same resolution? The general result is that, as
resolution is increased or spatial grain in the data
set is decreased (pixels represent less land surface),
the ability to predict a pixel's state based on its
neighbors increases. However, the ability to predict
a pixel's state over time from one scene to the next
decreases. This is intuitively reasonable. Landscapes usually display positive spatial autocorrelation, which decays with distance. Thus, as grain
size decreases, each pixel represents a smaller area,
and the states of neighboring pixels should be more
strongly correlated, allowing greater spatial predictability. On the other hand, because pixels represent smaller areas, smaller-scale changes in state
become evident, making prediction of changes
from scene to scene more difficult (Le., decreasing
temporal predictability). Spatial resolution of the
data should be chosen to yield an appropriate balance between spatial and temporal predictability.
Just where that balance occurs will depend on the
properties of the landscape and on the assessment
objectives.
2.2.3 Continuous versus
Discontinuous Change
Ecosystems, communities, popUlations, and organisms all change over time. Our measurements and
our expectations determine whether we perceive
31
change as continuous or discontinuous. A change
is regarded as discontinuous if there is a sudden
switch between distinct (qualitatively different)
states. A bulldozer clears an area; a graph of vegetative cover versus time has a stair-step form.
However, if a string of intermediate states is observed, the change is regarded as continuous. Measured year to year, livestock grazing may lead to a
change in composition of the plant community; the
graph is a curve. Continuity and discontinuity in
ecological systems are both idealizations. The important issue is not whether a given change is really continuous or discontinuous, but how it can
best be described, given our observations. The
grain and extent of our observation set will determine whether a given change is regarded as continuous or discontinuous. A fine-grained observation set will be more likely to resolve intermediate
states and therefore be described more naturally in
terms of a continuous change. A coarser-grained
observation set will more likely fit a description
based on discontinuous transitions between discrete
states. Observation sets with large extent will tend
to yield evidence of discontinuous change, both because the larger spatial coverage or longer temporal duration is more likely to encompass changes
of large magnitude and because observation sets
with large extent usually will be relatively coarse
grained (Ahl and Allen, 1996).
This can be illustrated by the altitudinal zonation of vegetation on a mountain. Standing back
and looking at the mountain from afar, we can see
distinct zones of vegetation, with discontinuous
change from deciduous to coniferous forest, for example. Walking up the mountain, on the other hand,
the transitions appear much more gradual, much
more continuous, as purely deciduous stands give
rise to mixed deciduous---coniferous stands and finally to purely coniferous stands. The difference in
our perception stems from the scale of our observations. Viewing the mountain from a distance, we
see a large extent (the entire altitudinal range from
foot to peak), but our eye does not resolve finegrained detail. Walking within the forest, our vision is limited in extent, but we see the fine-grained
detail of individual trees in our local environment.
Both perspectives can be useful. Thus, Whitaker
(1956), in his classic study of the vegetation of the
Great Smoky Mountains (Figure 2.2), showed cove
hardwood forests and spruce-fir forests as distinct
units on a mountain in one figure, while using gradient analysis to show a continuous gradation in
another figure. The issue of continuous versus discontinuous change is a nonissue as we choose the
appropriate description for the data set at hand.