ECOGRAPHY 25: 626–640, 2002
A balanced view of scale in spatial statistical analysis
J. L. Dungan, J. N. Perry, M. R. T. Dale, P. Legendre, S. Citron-Pousty, M.-J. Fortin, A. Jakomulska,
M. Miriti and M. S. Rosenberg
Dungan, J. L., Perry, J. N., Dale, M. R. T., Legendre, P., Citron-Pousty, S. Fortin,
M.-J., Jakomulska, A., Miriti, M. and Rosenberg, M. S. 2002. A balanced view of
scale in spatial statistical analysis. – Ecography 25: 626–640.
Concepts of spatial scale, such as extent, grain, resolution, range, footprint, support
and cartographic ratio are not interchangeable. Because of the potential confusion
among the definitions of these terms, we suggest that authors avoid the term ‘‘scale’’
and instead refer to specific concepts. In particular, we are careful to discriminate
between observation scales, scales of ecological phenomena and scales used in spatial
statistical analysis. When scales of observation or analysis change, that is, when the
unit size, shape, spacing or extent are altered, statistical results are expected to
change. The kinds of results that may change include estimates of the population
mean and variance, the strength and character of spatial autocorrelation and spatial
anisotropy, patch and gap sizes and multivariate relationships. The first three of these
results (precision of the mean, variance and spatial autocorrelation) can sometimes be
estimated using geostatistical support-effect models. We present four case studies of
organism abundance and cover illustrating some of these changes and how conclu-
sions about ecological phenomena (process and structure) may be affected. We
identify the influence of observational scale on statistical results as a subset of what
geographers call the Modifiable Area Unit Problem (MAUP). The way to avoid the
MAUP is by careful construction of sampling design and analysis. We recommend a
set of considerations for sampling design to allow useful tests for specific scales of a
phenomenon under study. We further recommend that ecological studies completely
report all components of observation and analysis scales to increase the possibility of
cross-study comparisons.
J. L. Dungan ( jdungan@gaia.arc.nasa.go
), MS 242-2, NASA Ames Research Center,
Moffett Field, CA 94035-1000, USA. – J. N. Perry, Plant and In
ertebrate Ecology
Di
., Rothamsted Experimental Station, Harpenden, Herts, U.K. AL5 2JQ. – M. R. T.
Dale, Dept of Biological Sciences, Uni
. of Alberta, Edmonton, AB, Canada T6G 2E9.
– P. Legendre, De´pt de Sciences Biol., Uni
. de Montre´al, C.P. 6128 succ. A,
Montre´al, QC, Canada H3C 3J7. – S. Citron-Pousty, Social Science Statlab, Yale
Uni
., 140 Prospect St., P.O. Box 208208, New Ha
en, CT 06520-8208, USA. – M.-J.
Fortin, Dept of Zoology, 25 Harbord St., Uni
. of Toronto, Toronto, ON, Canada
M5S 3G5. – A. Jakomulska, Remote Sensing of En
ironment Lab., Fac. of Geography
and Regional Studies, Uni
. of Warsaw, 26/28, PL-00-927 Warsaw, Poland. – M.
Miriti, Dept of E
olution, Ecology and Organismal Biology, The Ohio State Uni
.,
1735 Neil A
e., Columbus, OH 43210-1293, USA. – M. S. Rosenberg, Dept of
Biology, Arizona State Uni
., P.O. Box 871501, Tempe, AZ 85287-1501, USA.
Technological advances have improved researchers’ ca-
pacity to observe phenomena that occur over very small
(
10−9 m) to very large (
1014 m) extents. The
increased use of new tools has created opportunities for
collaboration among researchers from previously inde-
pendent fields such as geology, cartography and ecol-
ogy. As the interests of these distinct fields continue to
merge, the need for consistent, conforming terminology
becomes increasingly important (Silbernagel 1997,
Jenerette and Wu 1999, Csillag et al. 2000). ‘‘Scale’’ is
one term that has gained great currency in ecology
during the past decade (Wiens 1989, Levin 1992,
Accepted 6 February 2002
Copyright © ECOGRAPHY 2002
ISSN 0906-7590
ECOGRAPHY 25:5 (2002)626

Ehleringer and Field 1993, Peterson and Parker 1998,
Gardner et al. 2001), yet this term has multiple, some-
times contradictory meanings.
One scale concept with a long tradition in geography
is map scale, a cartographic ratio referring to the
relationship between the distance or area represented
on a map to the corresponding real-world distance or
area. In landscape ecology, scale has the disjunctive
definition of ‘‘grain and extent’’ (Turner 1989). The
term ‘‘resolution,’’ commonly used in remote sensing, is
defined as the smallest object that can be reliably
detected. A geostatistical term, ‘‘support,’’ has been
used since the 1960s to refer to an n-dimensional vol-
ume, including its geometrical shape, size and orienta-
tion, within which average values of a variable may be
computed (Olea 1990). Schneider (1994) devotes an
entire text to concepts of spatial scaling in ecology. In
fact, the word scale has a long and varied list of
synonyms, including several more meanings in mathe-
matics and statistics. Concepts such as cartographic
ratio, grain, extent, resolution, support, range, variance
and footprint have all been used as synonyms of scale
in one context or another.
The purpose of this paper is to present a balanced
view of scale terms by considering their specific mean-
ings and their relationships to one another. We identify
some of the most prevalent scale terms in ecology and
propose that their definitions can be best understood
within three categories or dimensions. We then review
how changing scales within two of these categories
(sampling and analysis) can make a substantial differ-
ence to the inferences about the third category (phe-
nomena). The relevance of changing scales is further
discussed using four case studies. Finally, we recom-
mend sampling design considerations that are specific
to these dimensions of scale.
To provide a framework to discuss scale terms and to
provide a means of reducing potential confusion over
myriad definitions, we distinguish among three different
categories to which spatial scale-related terms may be
applied: 1) the phenomenon being studied, for example
the spatial structure of vegetation and the processes
that affect it; 2) the spatial units or sampling units used
to acquire information about the phenomenon, for
example quadrats on the ground or pixels in an image;
and 3) the analysis of the data, used to summarize them
or make inferences. The phenomenon, sampling and
analysis categories can be thought of as three dimen-
sions to which scale concepts pertain (Fig. 1). We will
illustrate this idea with a simple example.
Consider a community of crustose lichens growing
on a large smooth plane rock surface (Fig. 2). For the
purposes of illustration, we will discuss a structurally
simple system that is essentially two-dimensional. We
will pretend that there is no environmental variability in
this system, although in real saxicolous communities,
differences in environmental conditions on a single rock
face may determine where particular lichen species are
found. Plant communities typically have many other
complexities in their physical pattern arising from verti-
cal structure and from variation in environmental (to-
pographic, hydrologic, soil, climatic, etc.) variables.
Fig. 1. Dimensions of scale concepts.
Fig. 2. Idealized rendering of a community of crustose lichens
growing on a 27×27 cm area of rock, modified from Dale
(1999), p. 17. There are five species present, represented by
shaded polygons or tiles. Black polygons represent bare rock
(no lichen present).
ECOGRAPHY 25:5 (2002) 627