Functional
Ecology 1989,
3, 385-397
385
ESSAY REVIEW
Spatial scaling in ecology1
J. A. WIENS
Department of Biology and Natural Resource
Ecology Laboratory, Colorado State University,
Fort Collins, Colorado 80523, USA
'The only things that can be universal, in a sense,
are scaling things'
(Mitchell Feigenbaum2)
Introduction
Acts in what Hutchinson (1965) has called the
'ecological theatre' are played out on various
scales of space and time. To understand the drama,
we must view it on the appropriate scale. Plant
ecologists long ago recognized the importance of
sampling scale in their descriptions of the dispersion
or distribution of species (e.g. Greig-Smith,
1952). However, many ecologists have behaved as
if patterns and the processes that produce them are
insensitive to differences in scale and have
designed their studies with little explicit attention
to scale. Kareiva & Andersen (1988) surveyed
nearly 100 field experiments in community
ecology and found that half were conducted on
plots no larger than 1 m in diameter, despite
considerable differences in the sizes and types of
organisms studied.
Investigators addressing the same questions
have often conducted their studies on quite
different scales. Not surprisingly, their findings
have not always matched, and arguments have
ensued. The disagreements among conservation
biologists over the optimal design of nature
reserves (see Simberloff, 1988) are at least partly
due to a failure to appreciate scaling differences
among organisms. Controversies about the role of
competition in structuring animal communities
(Schoener, 1982; Wiens, 1983, 1989) or about
the degree of coevolution in communities (Connell,
1980; Roughgarden, 1983) may reflect the
1 Adapted from the first Katharine P. Douglass Distinguished
Lecutre at the Rocky Mountain Biological
Laboratory, Gothic, Colorado, 23 July 1987.
2 Quoted in Gleick, 1987, p. 186.
imposition of a single scale on all of the species in
the community. Current ecological theories do
little to resolve such debates, because most of these
theories are mute on scale - they can be applied at
any scale on which the relevant parameters can be
measured.
Recently, however, ecologist studying a wide
range of topics have expressed concern about
scaling effects (see Dayton & Tegner, 1984; Wiens
et al., 1986a; Giller & Gee, 1987; Meetenmeyer &
Box, 1987; Frost et al., 1988; Rosswall, Woodmansee
& Risser, 1988). 'Scale' is rapidly becoming a
new ecological buzzword.
Scientists in other disciplines have recognized
scaling issues for some time. The very foundation
of geography is scaling. In the atmospheric and
earth sciences, the physical processes that
determine local and global patterns are clearly
linked (e.g. Schumm & Lichty, 1965; Clark, 1985;
Dagan, 1986; Ahnert, 1987) and their importance
is acknowledged in hierarchies of scale that guide
research and define subdisciplines within these
sciences. Physical and biological oceanographers
often relate their findings to the spectrum of
physical processes from circulation patterns in
oceanic basins or large gyres to fine-scale eddies or
rips (e.g. Haury, McGowan & Wiebe, 1978; Steele,
1978; Legrende & Demers, 1984; Hunt &
Schneider, 1987; Platt & Sathyendranath, 1988).
Physicists and mathematicians studying fractal
geometry, strange attractors, percolation theory,
and chaos address scaling as a primary focus of
their investigations (Nittman, Daccord & Stanley,
1985; Orbach, 1986; Grebogi, Ott & Yorke, 1987;
Gleick, 1987).
Why have ecologists been so slow to recognize
scaling? Ecologists deal with phenomena that are
intuitively familiar, and we are therefore more
likely to perceive and study such phenomena on
anthropocentric scales that accord with our own
experiences. We have also been somewhat tradition-bound,
using quadrats or study plots of a
particular size simply because previous workers
did. Unlike the physical and earth sciences (and
many laboratory disciplines of biology), where our
perceptual range has been extended by technology,
few tools have been available to expand
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386 our view of ecological phenomena (but see Platt &
J. A. Wiens Sathyendranath, 1988; Gosz, Dahm & Risser,
1988).
My thesis in this paper is that scaling issues are
fundamental to all ecological investigations, as
they are in other sciences. My comments are
focused on spatial scaling, but similar arguments
may be made about scaling in time.
The effects of scale
Some examples
The scale of an investigation may have profound
effects on the patterns one finds. Consider some
examples:
* In hardwood forests of the north-eastern
United States, Least Flycatchers (Empidonax
minimus Baird & Baird) negatively influence the
distribution of American Redstart (Setophaga ruticilla
L.) territories at the scale of 4-ha plots.
Regionally, however, these species are positively
associated (Sherry & Holmes, 1988). Apparently
the broad-scale influences of habitat selection
override the local effects of interspecific competition.
Similar scale-dependency has been found
in the habitat relationships of shrubsteppe birds
(Wiens, Rotenberry & Van Horne, 1986b), interspecific
associations among plant species (e.g.
Beals, 1973) or phytoplankton and zooplankton
(Carpenter & Kitchell, 1987), and the patterns of
coexistence of mosses colonizing moose dung
(Marino, 1988) or of ants on mangrove islands
(Cole, 1983).
* In the Great Barrier Reef of Australia, the
distribution of fish species among coral heads at
the scale of patch reefs or a single atoll may be
strongly influenced by chance events during
recruitment and the species composition of local
communities of fish may be unpredictable (Sale,
1988; Clarke, 1988). At the broader scales of atolls
or reef systems, community composition is more
predictable, perhaps because of habitat selection,
niche diversification, or spatial replacement of
species within trophic guilds (Ogden & Ebersole,
1981; Anderson et al., 1981; Green, Bradbury &
Reichelt, 1987; Galzin, 1987).
* On the basis of experiments conducted at the
scale of individual leaf surfaces, plant physiologists
have concluded that stomatal mechanisms
regulate transpiration, whereas meterologists
working at the broader scale of vegetation have
concluded that climate is the principal control
(Jarvis & McNaughton, 1986; Woodward, 1987). In
a similar manner, most of the variation in litter
decomposition rates among different species at a
local scale is explained by properties of the litter
and the decomposers, but at broader regional
scales climatic variables account for most of the
variation in decomposition rates (Meentemeyer,
1984).
* Domestic cattle grazing in shortgrass prairie
use elements of local plant communities quite
nonrandomly on the basis of short-term foraging
decisions, but use of vegetation types is proportional
to their coverage at the broader scale of
landscape mosaics (Senft et al., 1987).
* The distribution of phytoplankton in marine
systems is dominated by horizontal turbulent
diffusion at scales up to roughly 1 km (Platt, 1972;
Denman & Platt, 1975). At somewhat broader
scales, phytoplankton growth, zooplankton grazing,
and vertical mixing override these local effects
(Denman & Platt, 1975; Lekan & Wilson, 1978;
Therriault & Platt, 1981). At scales of >5km,
phytoplankton patchiness is controlled largely by
advection, eddies, and local upwelling occurring
over areas of 1-100 km (Gower, Denman & Holyer,
1980; Legrende & Demers, 1984). The same controls
operate in lakes, although the transitions
occur at finer scales (Powell et al., 1975).
These examples could easily be extended. The
salient point is that different patterns emerge at
different scales of investigation of virtually any
aspect of any ecological system.
Linkages between physical and biological scales
In the marine phytoplankton and other aquatic
systems, physical features may be primary
determinants of adaptations of organisms, and
physical and biological phenomena may scale in
much the same way. However, in many terrestrial
environments, atmospheric and geological influences
may often be obscured by biological interactions
(Clark, 1985). The relationships between
climate and vegetation that are evident at broad
scales, for example, may disappear at finer scales,
overridden by the effects of competition and
other biological processes (Greig-Smith, 1979;
Woodward, 1987). Local biological interactions
have the effect of decoupling systems from direct
physical determination of patterns by introducing
temporal or spatial lags in system dynamics or
creating webs of indirect effects. However, at
broader scales, physical processes may dominate
or dissipate these biological effects (Levin, 1989).
There are exceptions: plant distributions on fine
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387 scales may be controlled by edaphic or microtopoScale
in graphic factors, and vegetation may influence
ecology climate at regional scales.
System openness and the scale of constraints
Ecological systems become closed when transfer
rates among adjacent systems approach zero or
when the differences in process rates between
adjacent elements are so large that the dynamics of
the elements are effectively decoupled from one
another. In open systems, transfer rates among
elements are relatively high, and the dynamics of
patterns at a given scale are influenced by factors at
broader scales. However, 'openness' is a matter of
scale and of the phenomena considered. At the
scale of individual habitat patches in a landscape
mosaic, for example, population dynamics may be
influenced by between-patch dispersal, but at the
broader scale of an island containing that landscape,
emigration may be nil and the populations
closed. The same island, however, may be open
with regard to atmospheric flows or broad-scale
climatic influences.
The likelihood that measurements made on a
system at a particular scale will reveal something
about ecological mechanisms is a function of the
openness of the system. The species diversity of a
local community, for example, is influenced by
speciation and extinction, and by range dynamics
at regional or biogeographic scales (Ricklefs,
1987). Changes in population size at a location
may reflect regional habitat alterations, events
elsewhere in a species' range, or regional abundance
and distribution rather than local conditions
(May, 1981; Vdisdnen, Jarvinen & Rauhala,
1986; Roughgarden, Gaines & Pacala, 1987; Wiens,
1989). Habitat selection by individuals may be
determined not only by characteristics of a given
site but by the densities of populations in other
habitats over a larger area (O'Connor & Fuller,
1985). den Boer (1981) suggested that small local
populations may frequently suffer extinction, only
to be reconstituted by emigrants from other areas.
The fine-scale demographic instability translates
into long-term persistence and stability at the scale
of the larger metapopulation (Morrison & Barbosa,
1987; DeAngelis & Waterhouse, 1987; Taylor,
1988).
Ecologists generally consider system openness
in the context of how broad-scale processes constrain
finer-scale phenomena. This is one of the
primary messages of hierarchy theory (Allen &
Starr, 1982) and of 'supply-side' ecology
(Roughgarden et al., 1987) and it is supported by
studies of the temporal dynamics of food webs as
well (Carpenter, 1988). However, the ways in
which fine-scale patterns propagate to larger scales
may impose constraints on the broad-scale patterns
as well (Huston, DeAngelis & Post, 1988;
Milne, 1988). Ecologists dealing with the temporal
development of systems (e.g. forest insect epidemics:
Barbosa & Schultz, 1987; Rykiel et al., 1988)
recognize this sensitivity to small differences in
fine-scale initial conditions as the effects of historical
events on the subsequent state of the
system.
Extent and grain
Our ability to detect patterns is a function of both
the extent and the grain' of an investigation
(O'Neill et al., 1986). Extent is the overall area
encompassed by a study, what we often think of
(imprecisely) as its scale2 or the population we
wish. to describe by sampling. Grain is the size of
the individual units of observation, the quadrats of
a field ecologist or the sample units of a statistician
(Fig. 1). Extent and grain define the upper and
lower limits of resolution of a study; they are
analogous to the overall size of a sieve and its mesh
size, respectively. Any inferences about scaledependency
in a system are constrained by the
extent and grain of investigation - we cannot
generalize beyond the extent without accepting
the assumption of scale-independent uniformitarianism
of patterns and processes (which we know
to be false), and we cannot detect any elements of
patterns below the grain. For logistical reasons,
expanding the extent of a study usually also entails
enlarging the grain. The enhanced ability to detect
broad-scale patterns carries the cost of a loss of
resolution of fine-scale details.
Variance, equilibrium and predictability
When the scale of measurement of a variable is
changed, the variance of that variable changes.
How this happens depends on whether grain or
extent is altered. Holding extent constant, an
increase in the grain of measurement generally
decreases spatial variance. In a perfectly homogeneous
area (i.e. no spatial autocorrelation among
1 This use of 'grain differs from that of MacArthur &
Levins (1964), who considered grain to be a function of
how animals exploit resource patchiness in
environments.
2 Note that what is a fine scale to an ecologist is a large
scale to a geographer or cartographer, who express scale
as a ratio (e.g. 1:250 000 is a smaller scale than 1:50 000).
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388 s- - -- --- - - - J.
A. Wiens _
X / 0 - - - ;
0~~~~
Fig. 1. The effects of changing the grain and extent of a study in a patchy landscape. As the extent of the study is
increased (large squares), landscape elements that were not present in the original study area are encountered. As the
grain of samples is correspondingly increased (small squares), small patches that initially could be differentiated are
now included within samples and the differences among them are averaged out.
sample locations), the log-log plot of variance
versus grain (or N) has a slope of -1 (Fig. 2a). In a
heterogeneous area, this slope will generally be
between -1 and 0 (O'Neill et al., unpublished),
although the relationship may be curvilinear (Fig.
2a; Levin, 1989). As grain increases, a greater
proportion of the spatial heterogeneity of the
system is contained within a sample or grain and is
lost to our resolution, while between-grain heterogeneity
(= variance) decreases (Fig. 2b). If the
occurrence of species in quadrats is recorded
based on a minimal coverage criterion, rare species
will be less likely to be recorded as grain size
increases; this effect is more pronounced if the
species are widely scattered in small patches than
if they are highly aggregated (Turner et a]., unpublished).
If the measurement criterion is simply
the presence or absence of species in quadrats,
however, more rare species will be recorded as
grain increases, and diversity will increase rather
than decrease with increasing grain. Exactly how
variance changes with graiii scale thus deputids on
the magnitude and form of the heterogeneity of an
area (Milne, 1988, unpublished; Palmer, 1988) and
on the type of measurement taken.
Spatial variance is also dependent on the extent
of an investigation. Holding grain constant, an
increase in extent will incorporate greater spatial
heterogeneity, as a greater variety of patch types or
landscape elements is included in the area being
studied (Fig. 1). Between-grain variance increases
with a broadening of scale (extent) (Fig. 2b).
These considerations also relate to the patterns
of temporal variation or equilibrium of ecological
systems. Ecologists have often disagreed about
whether or not ecological systems are equilibrial
(e.g. Wiens, 1984, in press; Chesson & Case, 1986;
DeAngelis & Waterhouse, 1987; Sale, 1988).
Whether apparent 'equilibrium' or 'nonequilibrium'
is perceived in a system clearly depends on
the scale of observation. Unfortunately, current
theories provide little guidance as to what we
might expect: models in population biology (e.g.
May & Oster, 1976; Schaffer, 1984; May, 1989)
and physics (Gleick, 1987) show that order and
stability may be derived at broad scales from
finer-scale chaos or that fine-scale determinism
may produce broad-scale chaos, depending on
circumstances. Perhaps ecological systems follow
principles of universality, their final states at
broad scales depending on general system
properties rather than fine-scale details (cf.
Feigenbaum, 1979). Brown (1984) has championed
this view, but we still know far too little
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389 a
Scale in
ecology
homogeneous
0
heterogeneous
Q~~~~ri scl (lg)an
Fig. 2. (a) As the grain of samples becomes larger, spatial
variance in the study system as a whole decreases, albeit
differently for homogeneous and heterogeneous areas.
This is related to the within- and between-grain (sample)
components of variation. (b) With increasing grain scale,
less of the variance is due to differences between samples
and more of the overall variation is included within
samples (and therefore averaged away). An increase in
the extent of the investigation may increase the beweengrain
component of variance by adding new patch types
to the landscape surveyed (Fig. 1), but within-grain
variance is not noticeably affected.
about the scaling behaviour of ecological systems
to consider universality as anything other than an
intriguing hypothesis.
Predictability and space-time scaling
Because the effects of local heterogeneity are
averaged out at broader scales, ecological patterns
often appear to be more predictable there. Whether
or not the predictions are mechanistically sound
depends on the importance of the fine-scale
details. The Lotka-Volterra competition equations
may predict competitive exclusion of species that
in fact are able to coexist because of fine-scale
spatial heterogeneity that is averaged away (e.g.
Moloney, 1988). These predictions are not really
scale-independent but are instead insensitive to
important scale-dependent changes.
Our ability to predict ecological phenomena
depends on the relationships between spatial and
temporal scales of variation (Fig. 3). With
increased spatial scale, the time scale of important
processes also increases because processes operate
at slower rates, time lags increase, and indirect
effects become increasingly important (Delcourt,
Delcourt & Webb, 1983; Clark, 1985). The dynamics
of different ecological phenomena in
different systems, however, follow different traj
tories in space and time. An area of a few square
metres of grassland may be exposed to ungulate
grazing for only a few seconds or minutes, whereas
the temporal scale of microtines in the same area
may be minutes to hours and that of soil arthropods
days to months or years. There are no
standard functions that define the appropriate
units for such space-time comparisons in ecology.
Moreover, the continuous linear scales we use to
measure space and time may not be appropriate for
organisms or processes whose dynamics or rates
vary discontinuously (e.g. 'physiological time'
associated with diapause in insects; Taylor, 1981).
Any predictions of the dynamics of spatially
broad-scale systems that do not expand the temporal
scale are pseudopredictions. The predictions
may seem to be quite robust because they are made
on a fine time scale relative to the actual dynamics
of the system (Fig. 3), but the mechanistic linkages
will not be seen because the temporal extent of the
study is too short. It is as if we were to take two
space-time
scaling
of system
low
predictability A"
0
/ high apparent
predictability
-- -- -----~ -~-~~-----
of interest
Spatial scale
Fig. 3. As the spatial scaling of a system increases, so also
does its temporal scaling, although these space-time
scalings differ for different systems. Studies conducted
over a long time at fine spatial scales have low predictive
capacity. Investigations located near to the space-time
scaling functions have high predictive power. Shortterm
studies conducted at broad spatial scales generally
have high apparent predictability (pseudopredictability)
because the natural dynamics of the system are so much
longer than the period of study. Often, ecologists and
resource managers have been most interested in making
and testing predictions on relatively short time scales,
regardless of the spatial scale of the investigation.
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390 snapshots of a forest a few moments apart and use
J. A. Wiens the first to predict the second. This problem may
be particularly severe in resource management
disciplines, where the application of policies to
large areas is often based on very short-term
studies.
Detecting patterns and inferring processes
The characteristics of ecological systems at relatively
fine scales differ from those at relatively
broad scales (Table 1), and these differences
influence the ways ecologists can study the
systems. The possibilities for conducting replicated
experiments vary inversely with the scale
of investigation. The potential for sampling errors
of several kinds are greater at finer scales, although
the intensity of sampling is generally lower at
broader scales. Fine-scale studies may reveal
greater detail about the biological mechanisms
underlying patterns, but generalizations are more
likely to emerge at broader scales. Because the
time-frame of ecological processes tends to be
longer at broader scales (Fig. 3), long-term investigations
are more often necessary to reveal the
dynamics of the system. The scale of investigation
thus determines the range of patterns and processes
that can be detected. If we study a system at
an inappropriate scale, we may not detect its
actual dynamics and patterns but may instead
identify patterns that are artifacts of scale. Because
we are clever at devising explanations of what we
see, we may think we understand the system when
we have not even observed it correctly.
Dealing with scale
Scale arbitrariness
The most common approach to dealing with scale
is to compare patterns among several arbitrarily
selected points on a scale spectrum. In his analysis
Table 1. General characteristics of various attributes of ecological systems and investigations at fine and broad scales of
study. 'Fine' and 'broad' are defined relative to the focus of a particular investigation, and will vary between studies.
Scale
Attribute Fine Broad
Number of variables important in correlations many few
Rate of processes or system change fast slow
Capacity of system to track short-term environmental variations high low
Potential for system openness high low
Effects of individual movements on patterns large small
Type of heterogeneity patch landscape
mosaic
Factors influencing species' distribution resource/habitat barriers,
distribution, dispersal
physiological
tolerances
Resolution of detail high low
Sampling adequacy (intensity) good poor
Effects of sampling error large small
Experimental manipulations possible difficult
Replication possible difficult
Empirical rigor high low
Potential for deriving generalizations low high
Form of models mechanistic correlative
Testability of hypotheses high low
Surveys quantitative qualitative
Appropriate duration of study short long
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391 of reef-fish communities, for example, Galzin
Scale in (1987) compared distributions within a single
ecology transect, among several transects on the same
island, and among five islands. Roughgarden et al.
(1987) compared the dynamics of rocky intertidal
barnacle communities and assemblages of Anolis
lizards on islands at 'small', 'medium', and 'large'
spatial scales. Senft et al. (1987) examined herbivore
foraging in relation to vegetation patterns at
the scales of the local plant community, the
landscape, and the region. Multiscale studies of
birds have considered patterns at three to five
scales, and Wiens et al. (1986a) recognized four
scales of general utility in ecological investi-
gations.
In these examples, the definition of the different
scales makes intuitive sense and the analyses
reveal the scale-dependency of patterns. Casting
the relationships in the context of hierarchy theory
(Allen & Starr, 1982; O'Neill et al., 1986) may
further sharpen our focus on scaling by emphasizing
logical and functional linkages among scales.
The scales chosen for analysis are still arbitrary,
however: they tend to reflect hierarchies of spatial
scales that are based on our own perceptions of
nature. Just because these particular scales seem
'right' to us is no assurance that they are appropriate
to reef fish, barnacles, anoles, cattle, or
birds. We need nonarbitrary, operational ways of
defining and detecting scales.
Dependence on objectives and organisms
What is an 'appropriate' scale depends in part on
the questions one asks. Behavioural ecologists,
population ecologists, and ecosystem ecologists,
for example, all probe the relationship between
resources and consumers, but differences in their
objectives lead them to focus their investigations
at different scales (Pulliam & Dunning, 1987).
Conservation of key species or habitats may target
particular patches or landscape fragments for
management, whereas programmes emphasizing
species richness or complexes of communities
may concentrate on preserving broader-scale landscape
mosaics (Noss, 1987; Scott et al., 1987).
Differences among organisms also affect the
scale of investigation. A staphylinid beetle does
not relate to its environment on the same scales as
a vulture, even though they are both scavengers.
What is a resource patch to one is not to the other.
The scale on which an oak tree 'perceives' its
environment differs from that of an understorey
bluebell or a seedling oak (Harper, 1977). Local
populations of vagile organisms may be linked
together into larger metapopulations and their
dynamics may be less sensitive to the spatial
configuration of local habitat patches than more
sedentary species (Morrison & Barbosa, 1987;
Fahrig & Paloheimo, 1988; Taylor, 1988). Chronically
rare species may follow different dispersal
and scaling functions than persistently common
species. Consumers that use sparse or clumped
resources are likely to operate at larger spatial
scales than those using abundant or uniformly
distributed resources, especially if the resources
are critical rather than substitutable (Tilman,
1982; O'Neill et al., 1988).
Such scaling differences among organisms may
be viewed in terms of 'ecological neighbourhoods'
(Addicott et al., 1987) or 'ambits' (Hutchinson,
1953; Haury et al., 1978); areas that are scaled to a
particular ecological process, a time period, and an
organism's mobility or activity. The ecological
neighbourhood of an individual's daily foraging
may be quite different from that of its annual
reproductive activities. The ecological neighbourhood
of the lifetime movements of a tit in a British
woodland may comprise an area of a few square
kilometres whereas a raptor may move over an area
of hundreds or thousands of square kilometres; a
nomadic teal of ephemeral desert ponds in
Australia may range over the entire continent.
Incidence functions (Diamond, 1975) or fragmentation
response curves (Opdam, Rijsdijk &
Hustings, 1985) depict the ecological neighbourhoods
of species with respect to colonization and
persistence of populations in areas of different
sizes (scales).
To some extent, differences in ecological neighbourhoods
among taxa parallel differences in body
mass. This raises the possibility of using allometric
relationships (e.g. Calder, 1984) to predict
scaling functions for organisms of different sizes.
On this basis, for example, one might expect the
scale of the home range of a 20-g lizard to be
approximately 0 3 ha, whereas that of a 20-g bird
would be in the order of 4 ha; the parallel scale for
a 200-g bird would be 92ha. Although such an
approach ignores variation in allometric relationships
associated with diet, age, season, phylogeny,
and a host of other factors, it may still provide an
approximation of organism-dependent scaling
that is less arbitrary than those we usually use.
Because species differ in the scales of their
ecological neighbourhoods, studies of interactions
among species may be particularly sensitive to
scaling. The population dynamics of predators
and of their prey, for example, may be influenced
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392 A
J. A. Wiens important elements of components of patterns
pattern or controls or mechanisms
omitted averaged out
transition |< domain transition I
A A A 4A. A A A
B c study scale
<,~~~~~ i /
bug
P,~~~a
fine S broad
Scale
Fig. 4. (A) The domain of scale of a particular ecological phenomenon (i.e. a combination of elements of a natural
system, the questions we ask of it, and the way we gather observations) defines a portion of the scale spectrum within
which process-pattern relationships are consistent regardless of scale. Adjacent domains are separated by transitions in
which system dynamics may appear chaotic. If the focus is on phenomena at a particular scale domain, studies
conducted at finer scales will fail to include important features of pattern or causal controls; studies restricted to
broader scales will fail to reveal the pattern or mechanistic relationships because such linkages are averaged out or are
characteristic only of the particular domain. Comparative investigations based on sampling the scale spectrum at
different points in relation to the distribution of scale domains and transitions (solid and dashed vertical arrows) will
exhibit different patterns. (B) If a reductionist approach is adopted to examine patterns found at a particular scale of
study, the findings (and inferences about causal mechanisms) will differ depending on how far the reductionism is
extended toward finer scales and how many domains are crossed (compare a, b, and c).
by factors operating on different scales (Hengeveld,
1987), and attempts to link these dynamics
directly without recognizing the scale differences
may lead to greater confusion than enlightenment.
The competitive interactions among species scaling
the environment in similar ways may be more
direct or symmetrical than those between
organisms that share resources but operate on
quite different scales. If we arbitrarily impose a
particular scale (e.g. quadrat size) on a community
of organisms that operate on different scales, we
truncate the interactions to different degrees for
different species.
Domains of scale
Scale-dependency in ecological systems may be
continuous, every change in scale bringing with it
changes in patterns and processes. If this is so,
generalizations will be hard to find, for the range of
extrapolation of studies at a given scale will be
severely limited. If the scale spectrum is not
continuous, however, there may be domains of
scale (Fig. 4a), regions of the spectrum over which,
for a particular phenomenon in a particular ecological
system, patterns either do not change or
change monotonically with changes in scale.
Domains are separated by relatively sharp transitions
from dominance by one set of factors to
dominance by other sets, like phase transitions in
physical systems. Normally well-behaved
deterministic systems may exhibit unpredictable
behaviour at such transitions (Kitchell et al.,
1988), and nonlinear relations may become unstable
(O'Neill, personal communication). The
resulting chaos makes translation between
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393 domains difficult (Heaps & Adam, 1975; May,
Scale in 1989). The argument over the relative merits of
ecology linear versus nonlinear models in ecology (e.g.
Patten, 1983) may reflect a failure to recognize the
differences in system dynamics within versus
between domains.
How may we recognize domains of scale in a
way that avoids the arbitrary imposition of preconceived
scales or hierarchical levels on natural
variation? Several statistical approaches are based
on the observation that variance increases as
transitions are approached in hierarchical systems
(O'Neill et al., 1986). If quadrats in which plant
species abundances have been recorded are aggregated
into larger and larger groupings, the variance
of differences in abundance between pairs of
contiguous groups fluctuates as a function of group
size (scale). Peaks of unusually high variance
indicate scales at which the between-group differences
are especially large, suggesting that this may
represent the scale of natural aggregation or
patchiness of vegetation in the communities
(Greig-Smith, 1952, 1979), the boundary of a scale
domain. Similar techniques may be used to
analyse data gathered on continuous linear transects
(Ludwig & Cornelius, 1987). Coincidence in
the variance peaks of different features of the
system (e.g. plants and soil nutrients, seabirds and
their prey) may indicate common spatial scalings
and the possibility of direct linkages (Greig-Smith,
1979; Schneider & Piatt, 1986). For a series of point
samples, the average squared difference (semivariance)
or the spatial autocorrelation between
two points may be expressed as a function of the
distance between them to estimate the scale of
patchiness in a system (Sokal & Oden, 1978;
Burrough, 1983). Other investigators have used
spectral analysis (Legrende & Demers, 1984) or
dimensional analysis (Lewis & Platt, 1982). Obviously,
the degree to which any of these methods
can reveal scales of spatial patterning is sensitive
to grain and extent.
Another approach involves the application of
fractal geometry (Mandelbrot, 1983; Peitgen &
Saupe, 1988) to ecological patterns. In many
physical systems, such as snow crystals, clouds, or
flowing fluids, the configuration of patterns differs
in detail at different scales but remains statistically
'self-similar' if the changes in pattern
measurements are adjusted to the changes in
measurement scale (Burrough, 1983; Hentschel &
Procaccia, 1984; Nittman et al., 1985). The way in
which detail differs with scale is characterized by
a fractal dimension, D, which indexes the scaledependency
of the pattern. Statistical self-similarity
of patterns (constant D) occurs when processes
at fine scales propagate the patterns to
broader scales, although self-similar patterns may
also arise from the operation of different but
complementary processes (Milne, 1988). A change
in the fractal dimension of a pattern, on the other
hand, is an indication that different processes or
constraints are dominant. Regions of fractal selfsimilarity
of pattern may therefore represent
domains of scale, whereas rapid changes in fractal
dimension with small changes in measurement
scale (e.g. the landscape patterns analysed by
Krummel et al., 1987 or Palmer, 1988) may
indicate transitions between domains. There is a
relationship between the sizes and movement
patterns of organisms and the fractal dimensions
of their habitats (Morse et al., 1985; Weiss &
Murphy, 1988, Wiens & Milne, in press), so it may
be possible to define ecological neighbourhoods or
domains using functions that combine allometry
and fractals.
Domains of scale for particular pattern-process
combinations define the boundaries of generalizations.
Findings at a particular scale may be
extrapolated to other scales within a domain, but
extension across the transition between domains
is difficult because of the instability and chaotic
dynamics of the transition zone. Measurements
made in different scale domains may therefore not
be comparable, and correlations among variables
that are evident within a domain may disappear or
change sign when the scale is extended beyond the
domain (as in the examples of species associations
given on p. ?). Explanations of a pattern in terms of
lower-level mechanisms will differ depending on
whether we have reduced to a scale within the
same domain, between adjacent domains, or
across several domains (Fig. 4b). The peril of
reductionism in ecology is not so much the prospect
that we will be overcome by excessive detail
or distracted by local idiosyncrasies but that we
will fail to comprehend the extent of our reduction
in relation to the arrangement of domains on a
scale spectrum.
Of course, not all phenomena in all systems will
exhibit the sort of discontinuities in scaledependence
necessary to define domains. Some
phenomena may change continuously across
broad ranges of scale. The boundaries of even
well-defined domains may not be fixed but may
vary in time, perhaps in relation to variations in
resource levels. The notion of domains, like other
conceptual constructs in ecology, may help us to
understand nature a bit better, but it should not
become axiomatic.
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394 Developing a 'science of scale' in ecology
J. A. Wiens
Recently, Meentemeyer & Box (1987) have called
for the development of a 'science of scale' in
ecology, in which scale is included as an explicitly
stated variable in the analysis. I think that we must
go further, to consider scaling issues as a primary
focus of research efforts. Instead of asking how our
results vary as a function of scale, we should begin
to search for consistent patterns in these scaling
effects. How does heterogeneity affect the size of
scale domains? Are the ecological neighbourhoods
of organisms in high-contrast landscapes
scaled differently from those in areas where the
patch boundaries are more gradual? Are there
regularities in the transitions between orderly and
seemingly chaotic states of ecological systems
with changes in scale, in a manner akin to turbulence
in fluid flows? Do selective forces influence
how organisms scale their environments, so
that particular life-history traits are related to
responses to particular scales of environmental
patchiness? If one adjusts for the size differences
between organisms such as a beetle and an antelope
that occur in the same prairie, can they then
be seen to respond to the patch or fractal structure
of the 'landscapes' they occupy in the same way?
Are differences between them interpretable in
terms of differences in their physiology, reproductive
biology, or social organization? Does the
spatial heterogeneity of soil patterns at different
scales have different effects on how forest ecosystems
respond to climatic changes? Is the spread
of disturbances a function of the fractal structure of
landscapes? Does nutrient redistribution among
patches at fine scales lead to instability or stability
of nutrient dynamics at broader scales?
To address such questions, we must expand and
sharpen the ways we think about scaling. Our
ability to detect environmental heterogeneity, for
example, depends on the scale of our
measurements, whereas the ability of organisms to
respond to such patchiness depends on how they
scale the environment. Proper analysis requires
that the scale of our measurements and that of the
organisms' responses fall within the same domain.
Because of this, however, the 'proper' scale of
investigation is usually not immediately apparent.
Moreover, the ecological dynamics within a
domain are not closed to the influences of factors at
finer or broader domains; they are just different.
Ecologists therefore need to adopt a multiscale
perspective (Legrende & Demers, 1984; Clark,
1985; Wiens et al., 1986a; Blondel, 1987; Addicott
et al., 1987). Studies conducted at several scales or
in which grain and extent are systematically
varied independently of one another will provide
a better resolution of domains, of patterns and
their determinants, and of the interrelationships
among scales.
We must also develop scaling theory that
generates testable hypotheses. One particular
focus of such theory must be on the linkages
between domains of scale. Our ability to arrange
scales in hierarchies does not mean that we
understand how to translate pattern-process relationships
across the nonlinear spaces between
domains of scale, yet we recognize such linkages
when we speak of the constraining effects of
hierarchical levels on one another or comment on
the openness of ecological systems. Perhaps there
is a small set of algorithms that can serve to
translate across scales. Discovering them requires
that we first recognize that ecological patterns and
processes are scale-dependent, that this scaledependency
differs for different ecological
systems and for different questions that we ask of
them, that ecological dynamics and relationships
may be well-behaved and orderly within domains
of scale but differ from one domain to another and
become seemingly chaotic at the boundaries of
these domains, and that an arbitrary choice of
scales of investigation will do relatively little to
define these scaling relationships.
Acknowledgments
A Katharine P. Douglass Distinguished
Lectureship at Rocky Mountain Biological Laboratory
provided the atmosphere and the impetus to
focus my thinking about scaling, and I thank the
staff of the laboratory for their hospitality and Mrs
Douglass for endowing the lectureship. Paul
Dayton, Kim Hammond, Victor Jaramillo, Natasha
Kotliar, Bruce Milne, Bob O'Neill, Eric Peters,
LeRoy Poff, Rick Redak, Bill Reiners, David
Schimel, Dick Tracy, Monica Turner, James Ward,
and Greg Zimmerman commented on the manuscript
and agreed on almost nothing. Si Levin, Bob
May, Bruce Milne, and Bob O'Neill shared unpublished
manuscripts. Ward Watt provided
useful editorial suggestions. My investigations of
ecological scaling are supported by the United
States National Science Foundation (BSR-
8805829) and Department of Energy (DE-FG02-
88ER60715).
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Received 9 December 1988; revised 2 February 1989;
accepted 7 February 1989
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