Vol. 144, No. 5 The American Naturalist November 1994
SCALE DEPENDENCE AND THE SPECIES-AREA RELATIONSHIP
MICHAEL W. PALMER* AND PETER S. WH1TEtI
*Department of Botany, Oklahoma State University, Stillwater, Oklahoma 74078; tDepartment of
Biology CB#3280, University of North Carolina, Chapel Hill, North Carolina 27599-3280
Submitted June 7, 1993; Revised November 22, 1993; Accepted Januaty 25, 1994
Abstract.-The complex relationship between species richness and area can be simplified by
decomposing spatial scale into its components: grain, extent, and number of samples. We designed
a 256 x 256-m study grid in the Oosting Natural Area in the Duke Forest, Orange
County, North Carolina, such that the effects of these components can be disentangled. We
found that grain, extent, and the number of samples all influenced the species-area relationship,
although the effects of grain were dominant. We also found that species richness patterns were
neither self-similar nor hierarchical. The degree to which diversity occurs in "hot spots" increases
as a function of both grain and extent, but diversity hot spots tend to persist across a
wide range of grains.
Understanding how and why species richness varies over space and time is a
major endeavor in ecology. One of the most studied relationships in all of ecology
is that between species richness and area sampled, or the species-area curve.
The shape of the species-area curve has been used to infer biological processes
such as disturbance (Lawrey 1991), competition (Leps 1990), and division of
niche space (Sugihara 1980). The relationship has been used to define the "Iminimum
area" of a community and thus as a tool for delineating community types
(Cain 1938; Rice and Kelting 1955; Oosting 1956; Goldsmith and Harrison 1976;
Kershaw and Looney 1985; Colinvaux 1993). The species-area curve is central
to the theory of island biogeography (MacArthur and Wilson 1963, 1967; MacArthur
1965; Patrick 1967; Williamson 1981, 1988) and hence also to the science of
preserve design (Diamond and May 1981; Higgs 1981; Dzwonko and Loster 1989;
Bierregaard et al. 1992). Furthermore, the species-area curve has been proposed
as a means to estimate the biodiversity of large regions or preserves (Evans et
al. 1955; Williams 1964; Kilburn 1966; Hubbell and Foster 1983; Lauga and Joachim
1987; Westfall et al. 1987; Gentil and Dauvin 1988; May 1988; Palmer 1990a;
Gitay et al. 1991; Grassle and Maciolek 1992).
Numerous attempts have been made to find the functional form of the speciesarea
curve (see, e.g., Gleason 1922, 1925; Arrhenius 1923; Williams 1964; Williamson
1981); some of these functions are justified theoretically (Williams 1964;
May 1975; Coleman 1981; Williamson 1981). Despite the theoretical, historical,
and applied importance of the species-area curve, it is very difficult to predict a
t Please address all correspondence to M.W.P. E-mail: M.W.P., carex@osuunx.ucc.okstate.edu;
P.S.W., pswhite.ecology@mhs.unc.edu.
Am. Nat. 1994. Vol. 144, pp. 717-740.
? 1994 by The University of Chicago. 0003-0147/94/4405-0001$02.00. All rights reserved.
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718 THE AMERICAN NATURALIST
priori what the. functional form of the relationship should be (Williams 1964;
Williamson 1981). To a large degree, this is because area itself is a complex
variable. While some authors believe that area (or, more generally, spatial scale)
should be determined according to the properties of organisms (Addicot et al.
1987; Morris 1987; Cornell and Lawton 1992; Fahrig 1992), others argue that scale
should be studied operationally (i.e., investigator defined) so that pattern can be
inferred later (Allen 1987; Turner et al. 1989a, 1989b; Reed et al. 1993); we employ
the latter approach here.
Spatial scale can be decomposed into several components (Addicot et al. 1987;
Turner et al. 1989b; Kotliar and Wiens 1990; Allen and Hoekstra 1991; Milne
1991; Reed et al. 1993). The minimum scale sampled (often the size of individual
quadrats) in a study is considered the grain. The maximum scale (e.g., the farthest
distance between quadrats) is the extent. The number of sampled units is another
important component. Other components of scale (not considered in this article)
include the shape of quadrats and geometry of placement. Scale dependence is
defined as the degree to which ecological phenomena vary as a function of grain,
extent, or other components of scale.
The purpose of this article is to evaluate the scale dependence of species richness
in a forest that is sampled at a series of different grains and extents. We
intend to demonstrate that species-area curves can have a wide range of shapes
within a single tract of forest and that although it is useful to decompose scale
into its components, it is the interaction between the components that determines
the overall relationships. In particular, we address the following questions: To
what degree is the species-area relationship influenced by grain versus extent
versus the number of quadrats? Does species richness vary more or less than
random expectation, and does this variation depend on grain and/or extent? Do
spots of particularly high (or low) richness tend to persist across spatial scales?
Is spatial variation in richness self-similar, hierarchical, or neither?
STUDY SITE
This study was performed in the Oosting Natural Area, part of the Duke Forest
in Orange County, North Carolina. The Natural Area consists of a heterogeneous
assemblage of forest communities, some dominated by species typical of anthropogenic
disturbance (e.g., Pinus taeda, Liriodendron tulipifera), some dominated
by mesic forest species (e.g., Acer rubrum, Liquidambar styraciflua, Fagus
grandifolia), and some tending more toward the xeric (Quercus alba, Quercus
rubra, Carya tomentosa). However, community boundaries in the Oosting Natural
Area range from poorly delineated to nonexistent. The study site is described
in more detail by Reed et al. (1993).
FIELD METHODS
Although quadrats or releves are often subjectively placed within homogeneous
regions (Braun-Blanquet 1932; Kilburn 1966; Mueller-Dombois and Ellenberg
1974; Kershaw and Looney 1985; Allen and Peet 1990), such placement is not
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SCALE DEPENDENCE AND SPECIES-AREA CURVES 719
L v '-- 1- l __
FIG. 1 -Diagram of the study grid
always desirable. In particular, since heterogeneity of sites may be a major determinant
of the species-area relationship (Williamson 1981, 1988; Brown 1988), it
is essential that the location of the study site not be based on the assumption
of homogeneity. This is especially important since few landscapes consist of
homogeneous habitats. The sampling grid was randomly located, with the only
constraint being that it fit entirely within the preserve. Most of the major habitats
in the preserve (except for young pine forests and broad floodplains) are represented
in the study grid.
The sampling grid consists of 256 16 x 16-in modules (fig. 1). A nested series
of square quadrats (with linear dimensions of 0. 125 m, 0.25 m, 0.5 m, m, 2 m,
and 4 m) is located in the southwestern corner of each module. Larger quadrats
(with dimensions of 8 m and 16 m) were studied in the central 100 modules of
the grid. Three modules (the three fine grids in fig. 1) were randomly selected for
more intensive study: in these, every square meter (including quadrats of dimensions
0.125 m, 0.25 m, and 0.5 m nested in the southwest corner) was studied.
There are thus three distinct data sets: all 256 modules, the central 100 modules,
and the three fine-scale grids. If the results from the different data sets are qualitatively
similar, we will only report on one of them.
In the remainder of this article, the size of each nested quadrat will be considered
the quadrat's level; see table 1 for details. In May and June of 1989, the
presence of each vascular plant species was recorded for each of the quadrats
described above. This time was chosen because the remains of spring ephemeral
plants and the first leaves of late-season plants are both clearly identifiable (those
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720 THE AMERICAN NATURALIST
TABLE 1
THE LEVEL AND SIZE OF QUADRATS USED IN THE
GRID ILLUSTRATED IN FIGURE I
Linear Dimensions Area
Level (m) (m 2)
1 .125 x .125 1/64
2 .25 x .25 1/16
3 .5 x .5 1/4
4 1.0 x 1.0 1
5 2.0 x 2.0 4
6 4.0 x 4.0 16
7 8.0 x 8.0 64
8 16.0 x 16.0 256
late-season plants that were difficult to identify, particularly graminoids and composites,
were flagged in May and June and identified later during several return
trips in autumn).
Grain and extent are areal concepts, but they are more conveniently expressed
in terms of linear measurements for the purposes of this study. By choosing the
size of quadrats in the study and/or by selectively aggregating adjacent modules,
grain can vary from 0.125 m to 160 m (equivalent to the completely inventoried
central area of 10 x 10 modules). Extent can vary from 2 m (by studying adjacent
1 x 1-m quadrats in any of the three intensive modules) to 256 m. Note: in this
study, "extent" is considered the maximum distance between quadrats in the
N-S and E-W directions; technically the extent could reach 2562 m in the NE-SW
or NW-SE direction.
Spatial Dependence and Statistics
Although the research design allows for a range of grains and extents, statistical
inference is limited because quadrats are not independent (this is a limitation of
any spatially based study, not just this one). Spatially based sampling typically
reveals spatial dependence (Burrough 1983a, 1983b, 1987; Palmer 1988, 1990b;
Legendre and Fortin 1989; Palmer and Dixon 1990; Lechowicz and Bell 1991),
which means that nearby quadrats are on the average more similar to each other
than distant quadrats. Any study with nested quadrats runs into another kind of
dependence: the data present in one grain contribute to the data of the next
highest grain. Unless somehow corrected, any kind of dependence in data will
make inferential statistics (i.e., the use of P values) biased. The analyses used
here in comparing grain and extent are of necessity complex, and it is unclear how
one would correct for dependent data. Therefore, the results will be presented for
their descriptive value only, and no formal attempt will be made to test statistical
hypotheses.
RESULTS
A total of 224 vascular plant species were encountered in the study grid, representing
approximately 23% of the species present in the Duke Forest (Palmer
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SCALE DEPENDENCE AND SPECIES-AREA CURVES 721
TABLE 2
THE MOST FREQUENT SPECIES ENCOUNTERED IN QUADRATS OF LEVEL
6 OF ALL 256 MODULES
No. of
Taxon Quadrats
Acer rubrum L. 256
Cornus fiorida L. 249
Desmodium nudiflorunm (L.) DC 242
Smilacina racemosa (L.) Desf. 233
Cercis canadensis L. 232
Viburnum rafinesquianulm Schultes 232
Galiumn circaezans Michaux 228
Polygonatum biflorum (Walter) Ell. 227
Carya ovata (Miller) K. Koch 227
Vitis rotundifolia Michaux 223
Liriodendron tulipifera L. 205
Phryma leptostachya L. 200
Prunus serotina Ehrhart 200
Euonymus americanus L. 199
Botrychium virginianum (L.) Swartz 183
Liquidambar styraciflua L. 173
Parthenocissus quinquefolia (L.) Planchon 168
Quercus alba L. 147
Quercus velutina Lam. 142
Sassifras albidum (Nuttall) Nees 130
Pinus taeda L. 129
Quercus rubra L. 119
Carya tomentosa (Poiret) Nuttall 115
Juniperus virginiana L. 110
Vitis aestivalis Michaux 96
Chimaphila maculata (L.) Pursh 94
Viola pedata L. 90
Carpinus caroliniana Walter 86
Sanicula gregaria Bicknell 86
Fagus grandifolia Ehrhart 86
Morus rubra L. 85
Ruellia caroliniensis (Walter) Studel 83
Amphicarpa bracteata (L.) Fernald 82
Prenanthes altissima L. 80
Viburnum acerifolium L. 78
Carya glabra (Miller) Sweet 75
Sanicula smallii Bicknell 72
Carex nigromarginata Schweinitz 68
NOTE.-Not shown are 186 species of lesser frequency. For the
most part, these species are also the most frequent at other levels
and in the central 100 modules.
1990d). The most frequently encountered species are listed in table 2. An electronic
copy of the data set is available upon request to M.W.P.
The Species-Area Curve
Even for the analysis of a single data set, there are numerous ways to construct
species-area curves (Cain 1938; Williams 1964; Westfall et al. 1987; Magurran
1988; Quinn and Harrison 1988; Lawrey 1992). One method is to add quadrats
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722 THE AMERICAN NATURALIST
sequentially and count the cumulative number of species encountered (see, e.g.,
Rice and Kelting 1955; Kikuchi 1987; Magurran 1988; Thiollay 1990). Since this
method is highly sensitive to the order in which quadrats are added, we chose to
calculate the average of the species-area curves for 200 random orders of quadrats,
sampled without replacement (see Palmer 1991). This was performed separately
for each quadrat level (fig. 2). For ease of visual interpretation, area is
plotted on a logarithmic scale.
Figure 2 illustrates that grain (level) has a profound effect on the species-area
relationship. At a fixed area, decreasing grain increases the number of quadrats
while at the same time increasing the number of species sampled. The curves are
remarkably parallel and evenly spaced from each other. The curves for higher
levels are more log-linear than those at lower levels, which indicates a profound
but gradual change in slope. The curves for all 256 modules (fig. 2A) are much
steeper and higher than the corresponding curves for the central 100 modules
(fig. 2B). There is clearly no tendency for any of the species-area curves to level
off to a horizontal asymptote.
Figure 2 also illustrates that sequentially adding nonnested quadrats causes a
much faster rate of species gain than does increasing area in a series of nested
quadrats (i.e., the line connecting the bottom of the curves).
Variability in species-area curves within a given level is illustrated in figure 3
for all 256 modules (the results for the central 100 modules are qualitatively
similar and are not shown). These shapes can be considered "envelopes" within
which almost all of the possible species-area curves would fall. The top curve for
each level represents the average of the 25 highest species-area curves (out of
1,000 random quadrat sequences). The bottom curve is the average of the 25
lowest species-area curves. The fact that these curves meet toward the upper
right is a trivial consequence of the fact that all quadrats at that level have been
sampled. Figure 3 illustrates that variability in species-area curves can be very
substantial; the envelopes for different levels can overlap considerably. However,
the envelopes do not overlap at the extreme left and right ends.
Extent and Species Richness
The influence of extent on species richness can be evaluated directly by observing
how the distance between one quadrat and a second effects the number of
species that are present in the second quadrat but not the first (i.e., the number
of "new" species). Figure 4 demonstrates that extent has practically no effect
on new species at low grains but has a positive effect at large grains. Thus, there
is a substantial interaction between grain and extent in determining richness.
The relative effects of grain and extent are also illustrated in figure 5. This
figure represents the number of species encountered in all possible combinations
of four equal-sized quadrats arranged in a square. The roughly triangular arrangement
of these curves is a consequence of the fact that extent is constrained to
be no less than twice the grain. The right end of these curves seem to have most
variation: however, this is probably a manifestation of the "hole effect" (Journel
and Huijbregts 1978; Hohn 1988; Isaaks and Srivastava 1989), a statistical artifact
caused by pseudoreplication at large extents.
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A11 256 modules
200 I
L 100
e ..
150/ /X X
10 ? 4///~/
.0625 .25 1 4 16 64 256 1024 4096 16384
Area sampled (square meters)
Central 100 modules
200
B
7
150
,. 100
/3
50 2
.0625 .25 1 2 16 62 256 1022 2066 16384
Area sampledJ (square meters)
FIG. 2.-Species-area curves in the study grid. Each curve represents the average of 200
different species-area curves, each with a different random order of quadrats. The lightercolored
curve connecting the lower ends of each curve represents the average species-area
curve obtained by expanding the level (sensu table 1) of the nested quadrats. A, All 256
modules; B, the central 100 modules. Numbers above each grid represent the quadrat level;
see table 1.
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724 THE AMERICAN NATURALIST
All 256 modules
200
150
4
(D
L 100
50
.0625 .25 1 4 16 64 256 1024 4096 16384
Area sampled (square meters)
FIG. 3.-Envelopes bounding species-area curves. For each level, the upper curve represents
the average of the highest 25 species-area curves, and the lower curve represents the
average of the lowest 25 species-area curves, out of 1,000 separate species-area curves with
different random quadrat sequences.
In figure 5, the far left point of each curve for each level indicates the situation
in which the four quadrats are directly abutting: In other words, it is the richness
of the quadrat of the next highest level (twice the length, four times the area).
The initial slope of the curves in figure 5 is therefore not merely an effect of
extent but also an effect of disaggregation, or of making quadrats discontinuous.
The slope gauge in the upper left of figure 5 lets us evaluate how many species
are added by doubling the linear dimensions of extent (or quadrupling the area
of extent). Extent has an effect on species richness: the curves are ascending for
most of their length. However, if we ignore the hole effect and the effects of
disaggregation, extent has only a minor effect: the slope corresponds, at most,
to around five new species per doubling. Doubling grain, on the other hand, adds
from 5-35 species, with 10-25 species being most typical.
It is interesting that the curves for the central 100 modules and for all 256
modules largely coincide. The lack of coincidence of the larger grains in the
intensive modules with the corresponding grains for the larger grids is probably
because, by chance, the intensive modules are slightly richer than the average
module.
Variation in Species Richness
Variation in species richness, like mean species richness, is likely to vary as a
function of spatial scale. The ratio of observed variance in richness to expected
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SCALE DEPENDENCE AND SPECIES-AREA CURVES 725
Central 100 modules All 256 modules
20 , 20 - - l
8
7
15 15 6
10 _15~~~~~~~~~~~~~~~~~~
5 35 -3
2 --___ _ __ _ _2
_________._,_i_.____ ~~1
-0o
0 614 1'28 1'92 2'56 0 64 126 1 2 2 6
distance between plots (meters) d2stance between plots (meters)
FIG. 4.-The number of new species encountered in a second quadrat but not in the first,
as a function of the distance between quadrats. The level is indicated by the number to the
right of the curve (see table 1). These curves represent the average over all possible pairs
of quadrats of a given level in a given distance class; distance classes were determined by
rounding distance down to the nearest meter. Vertical bars indicate SEs of the mean. Each
pair of quadrats is actually included twice, because the number of species found in A but
not B is typically not the same as the number found in B but not A.
variance in richness (under the null model of no associations between species),
or the variance test, is a useful way to evaluate the magnitude of variation in
richness (Schluter 1984; Palmer 1987, 1990c). The expected variance in species
richness under the null model (see Schluter 1984 and Palmer 1987 for justification)
is calculated as zpi(l - Pi)? where Pi is the proportion of quadrats occupied by
species i and the summation is over all the species in the study.
- The overall study grid (fig. 1) can be decomposed into a very large number of
subgrids of varying grain and extent. We can thus evaluate variation in species
richness as a function of grain and extent. The results in figure 6 are for subgrids
of 16 quadrats consisting of four equidistant rows and four equidistant columns,
with the distance between rows equaling that between columns. Grain is the size
of the quadrats, and distance is the distance between the beginning of one row
(or column) and the beginning of the next row (or column). Extent is thus closely
related to "distance"; namely, extent = 4 x distance + grain. The results in
figure 6 represent the average of all possible subgrids of the indicated grain and
distance.
Figure 6A illustrates the results of the variance test for the 16-quadrat subgrids
derived from the entire 256 module study grid. In general, grains less than 1 m
have values of the variance ratio close to one, which indicates that richness does
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726 THE AMERICAN NATURALIST
80
64
160- 48
15 species/doubling
140-/
10 soecies/doubling 32
e 120- 5 snec2es/doubling
a: 0 species/doubling
100- 6
a)
ci ~ ~ ~ ~ ~~~~~~~78/
e)80-460 - 5.,;
4 ------4
40 t = > / 4
20
.25 .5 1 2 4 8 16 32 64 128 256
Extent (m)
FIG. 5.-The average richness observed in all possible combinations of four equal-sized
quadrats arranged in a square. Fine lines represent the average of the three intensive grids,
dark thick lines represent the central 100 modules, and light thin lines represent all 256
modules. The grain, in meters, is to the right of each curve. Large grains were obtained by
aggregating adjacent modules. The slope gauge in the upper left lets us evaluate how many
species are added by doubling the linear dimensions of extent.
not vary much more than random expectation. However, variation in richness
increases dramatically with grain, for grains of 1 m and greater. This means there
is an increasing tendency for richness to occur in "hot spots" as grain increases.
As before, extent does not have as profound an effect as does grain, but when
distance exceeds 48 m, species richness is much more variable than at lesser
distances (at least for large grains). This means that increasing extent increases
the degree to which one can find hot spots in richness.
Similar results can be seen for the central 100 modules (fig. 6B). Variation in
richness is close to the null expectation for grains less than a meter, and it increases
dramatically at larger grains. There is an interesting leveling off (or perhaps
even a decline) in the variance ratio of grains between 4 m and 8 m and a
dramatic increase at 16 m. This leveling does not imply that the size of a diversity
hot spot is around 4-8 m, because the increase at 16 m suggests that hot spots
are more distinctive on that scale; all it means is that diversity patterns are
relatively scale-neutral at that size. As in figure 6A, there is not much difference
between a distance between rows of 16 m and 32 m.
The results of the variance test for the smaller, intensive modules (not illustrated
here) revealed values of the variance ratio close to one, which indicates
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All 256 modules
4
3
w
> 2
0
.125 .25 .5 1 2 4 8 16
Grain (meters)
B
Central1 00 modules
4
3
w
> 2
1
.125 .25 .5 1 2 4 8 16
Grain (meters)
FIG. 6.-The ratio of observed species richness to expected species richness, as a function
of grain. Vertical bars indicate standard errors. A, Results for 16-quadrat subgrids of all 256
modules. Lines ranging from dark to light indicate distances (where distance is as in fig. 6)
of 16 m, 32 m, 48 m, and 64 m, respectively. B, Results for 16-quadrat subgrids of the central
100 modules. The dark line indicates a distance of 16 m, and the light line indicates 32 m.
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728 THE AMERICAN NATURALIST
9
8
7
o 5
C: 4
-.1
1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6
1 2 3 4 5 6
FIG. 7.-Correlation coefficients (r) of species richness in quadrats of one level (the single
large number at the bottom of each panel) with richness in quadrats of other levels in the
same module (the six smaller numbers). Vertical bars indicate 90% confidence intervals. The
correlation coefficient of each level with itself is necessarily equal to one.
that richness was not more variable than random expectation. Neither grain nor
extent revealed any consistent trends.
Cross-Scale Richness Correlations
Figure 7 displays the strength of correlation between species richnesses at
different grains, for the data from all 256 modules. Species richness at a given
grain is strongly correlated with richness at the next largest (and next smallest)
grain but much less strongly correlated with richness at much larger and smaller
grains. The decline in the correlation is a gradual function of change in grain.
Another way of interpreting figure 7 is that diversity hot spots (regions of high
richness) tend to persist (within limits) as one changes grain: a quadrat will tend
to be species-rich if it is nested within a species-rich quadrat that is larger; conversely,
a quadrat that includes a smaller species-rich plot will also tend to be
rich. The same patterns hold for low-diversity spots. These patterns are hardly
surprising and somewhat artifactual: the number of species in any quadrat is
constrained to be no less than the number of species in any included quadrat.
Figure 7 also reveals that changing scale is not always symmetrical: for example,
richness at level 3 is more strongly correlated with richness at level 4 than
it is with richness at level 2. The decline in the correlation as one increases grain
from level 1 is significantly more precipitous than the decline as one decreases
grain from level 6.
Correlations for the central 100 modules (not shown) are qualitatively similar
to those in figure 7. The major quantitative differences are that correlations are
much weaker (probably since much less area is covered) and the confidence
intervals are broader (since there are fewer samples).
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SCALE DEPENDENCE AND SPECIES-AREA CURVES 729
DISCUSSION
Disaggregation of Quadrats
The study grid used in this research allows much flexibility in altering grain,
extent, and total number of quadrats. However, these three components of area
cannot be varied completely independently. For example, if the total area in a
group of quadrats is held constant, decreasing grain is necessarily accompanied
by an increase in number of quadrats (and increasing grain is accompanied by a
decrease in number of quadrats). In this case, decreasing grain can be considered
disaggregating the sampled area.
Disaggregation of area appears to have a remarkably constant effect (fig. 2).
Species-area curves for different grains are parallel- and evenly spaced. This
means that a given amount of disaggregation is accompanied by a more or less
constant increase in the number of species, over a wide range of areas sampled
and grains. The constancy implies that there is some regular, underlying process
relating richness to disaggregation. This process need not be complex: a number
of simple processes (such as fragmentation, fracturing, curdling, and Brownian
motion) have been shown to produce patterns that are constant over wide ranges
of spatial scales (Burrough 1981, 1983a, 1983b; Mandelbrot 1983; Feder 1988;
Petigen and Saupe 1988; Lauwerier 1991).
Zacharias and Brandes (1990) found that disaggregation had a reasonably constant
effect on species richness of woodlots, on spatial scales much larger than
those considered here. Dzwonko and Loster (1989) also studied woodlots on
larger scales, but they found that the effects of disaggregation on richness were
location- and area-dependent.
The regularity of figure 2 means we can partially decompose the species-area
curve into some of its components. In particular, we can answer the following
question: Given a cumulative species-area curve of randomly added quadrats
with constant grain, how much of the increase is due to pure area effects, and
how much is due to increasing the number of nonnested quadrats?
Figure 8 represents an idealized version of the region of figure 2 in which the
species-area curves are linear, parallel, and equidistant. We wish to determine
the degree to which the difference between R3 and RI is caused by increasing
area as compared to increasing number of samples. Let us define the following
terms: 0 is the "original" number of species in N quadrats of size G; G is the
grain of the square quadrat, measured in length of side; N is the number of
quadrats sampled (not on the graph); A is the total area sampled, or G2N; and F
is a (dimensionless) scale factor-it is the amount by which area is increased or
decreased. In our study, F = 4 because each level is fourfold the area of the
previous level. In addition, D is the number of new species encountered by disaggregating
a given sample into F times the number of original quadrats (each new
quadrat with an area G2IF). Finally, S is the factor by which we would have to
decrease quadrat size to have the same number of species, if the number of
quadrats was increased F-fold.
Given these definitions, table 3 lists the equations for species richness of four
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730 THE AMERICAN NATURALIST
GE G2
E
a)
C.)
0
a)
n
E
EQUATIONS FOR SPECIES RICHNESS AT THE FOUR MARKED POINTS ON
FIGURE 8
Point Quadrat No. of Total Species
on Graph Area Quadrats Area Richness
R1i G N A 0
R2 G2/F NXF A O+D
R3 G2 N XF A XF O0+DF/S
R4 G2 x F N A E X 0F?O+RDF/S-D
NOTE- The number of species is calculated on the assumption
that the lines are parallel and equidistant. A iS always G2N.
points (R1-R4) illustrated in figure 8. Our original question-Given a cumulative
species-area curve of randomly added quadrats with constant grain, how much
of the increase is due to pure area effects, and how much is due to increasing
the number of quadrats? can now be more precisely formulated: How much of
(R3 - Ri) is due to increasing A by F, and how much is due to increasing N by
F? The proportion due to increasing area, PA' 15
PA = (R4 - R1)/(R3 - Ri).
Substituting in the equations from table 3, this equation simplifies to
PA = 1 - S/F.
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SCALE DEPENDENCE AND SPECIES-AREA CURVES 731
The proportion due to increasing the number of quadrats is
PN = (R2 - R1)/(R3 - RI),
which simplifies to
PN= SIF.
In figure 2, PN is the ratio of the horizontal distance between species-area curves
to the horizontal distance indicating a fourfold difference in area and approximately
equals 0.35. Therefore, PA = 0.65.
We can conclude that most (approximately two-thirds) of the species-area
curve from sequentially added quadrats is actually caused by increasing area,
but the proportion caused by increasing the number of quadrats (approximately
one-third) is far from negligible!
The arguments outlined above only pertain to the equidistant and parallel portions
of the species-area curves, and therefore they do not explain why the overall
shapes of the curves vary dramatically but gradually from small to large grains.
In particular, species-area curves for small grains begin with very low slopes. To
some degree, this can be considered a trivial result: since richness cannot be less
than zero, a zero asymptote seems reasonable. Even so, it is theoretically possible
for the curves to start near zero species and then rise with initially steep slopes.
Why does this not happen? We suspect that smaller grains are of the same
magnitude as the size of individual organisms (or individual clumps of organisms)
and that the total species richness is constrained by the number of individuals
that can fit into the quadrat. In order to test whether this is a reasonable explanation,
we performed computer simulations of species-area curves on two hypothetical
landscapes: one in which each 1 m x 1 m of the landscape was randomly
assigned to one of 256 species, and another in which each 4 m x 4 m of the
landscape was thus assigned.
Figure 9 illustrates the species-area curves (calculated as in fig. 2) from these
hypothetical landscapes. The curviliiiearity of the upper portion of the some of
the curves (not seen in fig. 2) may be caused by the lack of spatial trends in the
simulated landscapes or by differences in the frequency distributions of species.
On the other hand, the inflections in the lower part of some of the curves bear a
striking resemblance to those in figure 2.
For levels much less than the size of the individual (i.e., levels 1 and 2 for
both landscapes, level 3 of the large-individual landscape), the curves are almost
indistinguishable. For these curves, the number of species encountered is almost
solely dependent on the number of independent quadrats. As the level increases
to a scale much larger than the individual, the curvilinearity of the lower part of
the curve disappears (though not entirely for the large-individual landscape). The
results from these simulations suggest that the average size of individual organisms
or clumps (i.e., Kershaw and Looney's [1985] "morphological pattern") is
a plausible explanation for the existence and position of the lower inflection in
the species-area curve.
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732 THE AMERICAN NATURALIST
Simulated Species
200/
150 /
U /0-0/
50/ /
.0625 .25 1 4 16 64 256 1024 4096 16384
Area sampled (square meters)
FIG. 9.-Simulated species-area curves from two hypothetical landscapes v
size of individuals. Curves were generated as in fig. 2. Thin lines, individuals are 1 m on a
side; thick lines, individuals are 4 m on a side.
Grain and Extent
This study demonstrates that the species-area relationship is heavily influenced
by grain, especially at small extents. Grain has a very strong influence on the
number of species added by sampling a second quadrat (fig. 4) and on the number
of species in groups of four quadrats (fig. 5). Increasing grain also strongly increases
the patchiness of richness, that is, the degree to which vari-ation in richness
exceeds random variation (fig. 6).
Although grain has the largest effect, extent has an important but subtle influence.
Species are added more quickly to the species-area curve if the extent is
the entire study grid rather than just the central 100 modules (fig. 2). Extent
increases the number of species encountered by sampling a second quadrat (fig.
4). Extent can increase the number of species encountered in subgrids of the
study grid (fig. 5). Extent slightly increases the patchiness of richness (fig. 6).
The effects of extent in promoting richness are probably related to distance
decay in the environment. Distance decay (also known as spatial dependence or
the "reddened spectrum" sensu Williamson 1988) is an almost universal property
of spatially based data (Burrough 1983a; Robertson 1987; Palmer 1988, 1990b,
1990c, 1992; Legendre and Fortin 1989; Lechowicz and Bell 1991) and describes
the situation in which nearby environments are generally more similar to each other
than distant environments. If distant environments are different, then they will
on the average contain more species in aggregate than nearby environments (on
the assumption that organisms exhibit some habitat or microhabitat specificity).
Grain and extent interact in affecting richness. Increasing the distance between
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SCALE DEPENDENCE AND SPECIES-AREA CURVES 733
quadrats only increases the number of new species if the grain is large (fig. 4).
The ratio of observed to expected species richness does not differ among different
extents, except for large grains (fig. 6). This interaction between grain and extent
demonstrates that we cannot fully understand the effects of changing scale until
we understand the roles played by the different components of scale.
Scale Decay
Since the decline in the correlation between species richnesses at different
grains is a gradual function of increasing or decreasing grain (fig. 7), clearly
species richness is not determined by forces operating on crisply defined spatial
scales. Rather, there is a "scale decay" that is directly analogous to "distance
decay," and scale domains (the range of spatial scales over which a process
operates) of richness are broad and poorly defined. This is consistent with results
from other studies (Shmida and Wilson 1985; Auerbach and Shmida 1987;
Rejm'anek and Rosen 1988; Palmer 1990b, 1990c; Reed et al. 1993).
Since correlations in richness are not a symmetrical function of scale (fig. 7),
we can also conclude that richness patterns are not strictly statistically self-similar in
the sense of fractal geometry (Mandelbrot 1983; Feder 1988; Petigen and Saupe 1988).
Randomness on the Small Scale
The literature is ambiguous as to how spatial scale should affect the degree to
which community structure departs from randomness. Some authors suggest that
on the scale of individual organisms, interactions between individuals should lead
to strong departures from randomness (Connor and Bowers 1987; Thorhallsdottir
1990; Watkins and Wilson 1992). Agnew and Gitay (1990) suggest that species-rich
systems should have strong small-scale structure. On the other hand, Rogers
(1993) specifically looked for such small-scale patterns and failed to detect them.
Ricklefs (1987) and Cornell and Lawton (1992) argue that larger-scale forces are
the prime determinants of local patterns, while Willems et al. (1993) argue that
an understanding of the small-scale dynamics is essential. Wiegleb et al. (1989)
and Reed et al. (1993) suggest small-scale patterns may be too "noisy" to allow
their detection.
The analyses presented here show that variation in species richness does not
vary substantially from random expectation at small grains and extents (fig. 6).
However, it is not possible to determine whether this is due to a lack of interactions
among intervals or to the statistical problems of a smaller sample of individuals
and species on small scales.
Spatial Hierarchies
A large body of literature suggests that the spatial structure of nature is intrinsically
hierarchical (Krummel et al. 1987; Ricklefs 1987; Kotliar and Wiens 1990;
Peterson and Pickett 1990; Barrange and Campos 1991; Kolasa and Rollo 1991;
O'Neill et al. 1991; Holling 1992; McLaughlin 1992). However, the analyses presented
here are inconsistent with a hierarchical view of spatial pattern. There are
no breakpoints or "thresholds" (sensu Gardner et al. 1989; Meentemeyer 1989)
at well-defined scale intervals, within the range of spatial scales studied. The
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734 THE AMERICAN NATURALIST
results are more consonant with the view that patterns change gradually and
continuously as a function of scale (Levin 1987; Williamson 1988; Hengeveld
1990; Lechowicz and Bell 1991; Virkkala 1991; Reed et al. 1993).
Location Dependence
As previously stated, it was extremely important for the study grid not to be
placed using a criterion of homogeneity. As a consequence, a number of "unusual"
microsites were included in the grid: a small stream runs through the
southwestern corner, a ridge of basic soils (possibly an ultramafic intrusion) runs
through the eastern half, and tree-fall gaps are widely scattered throughout (see
Reed et al. 1993 for a more complete description).
The particular results of this study are caused by the particular spatial distributions
of particular microsites. In other words, the results are location-dependent.
Location dependence is particularly reflected the erratic behavior of the right end
of the curves in figure 5; as previously mentioned, this behavior is termed the
hole effect.
We believe that, in general, the probability of encountering unusual microsites
(of any sort) in a study such as this is close to unity (by analogy, the chance of
any particular coincidence occurring is vanishingly small, but since there is an
astronomical number of potential coincidences, coincidences happen every day).
The hole effect will never disappear, and location dependence as a phenomenon
may be location-independent. To truly understand location dependence, we
would need to develop an objective measure of "unusualness" and examine its
geometry (which would probably have fractal attributes).
The Species-Area Curve and Conservation Biology
As the science of conservation biology is maturing, scientists are becoming
increasingly aware of how little we actually know about biodiversity (May 1988;
Erwin 1991; Gaston 1991a, 1991b; Kangas 1992). However, we do know that it is
being depleted at astonishing rates (Reid 1992; Whitmore and Sayer 1992; Myers
1993). Since the ratio of field biologists to species on this planet is very low, it is
extremely unlikely that we will ever know enough about the particulars of the
planet's biota to formulate a conservation strategy targeted to each taxon and region.
We thus must attempt to make generalizations about the distribution of biodiversity
and about how biodiversity might be evaluated when our evidence is limited.
The species-area curve holds much promise as a tool in conservation biology.
The species-area curve has already played an important role in island biogeography
theory (MacArthur and Wilson 1963, 1967; MacArthur 1965; Williamson
1981). To a large degree, the discipline of conservation biology emerged from
this theory (Hoehne 1981; Harris 1984; Quinn and Hastings 1987; Quinn and
Harrison 1988). One important example of how the species-area relationship has
influenced conservation biology is the "single large or several small" (SLOSS)
debate, which addressed the question about whether it is better to arrange a fixed
amount of preserve area in a single large or several small preserves (Wright and
Hubbell 1983; Soule and Simberloff 1986; Blake and Karr 1987; Woolhouse 1987;
Loman and von Schantz 1991). Although the debate has never been resolved per
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SCALE DEPENDENCE AND SPECIES-AREA CURVES 735
se, it has moved on to more detailed issues such as the ideal arrangement of
preserves, optimizing forestry practices, the presence of corridors, and buffer
zones (Harris 1984; Noss and Harris 1986; Ehrenfeld and Schneider 1991; Harris
and Atkins 1991; Noss 1991; Spellerberg 1991; Inglis and Underwood 1992). Even
though SLOSS may not be debated any longer, its "descendents" still rely on
the existence of a species-area relationship.
The results of this study indicate that although the species-area relationship
can be quite complex, it does possess certain regularities. If this can be shown
to be the case for much larger regions, there is much promise in applying the
species-area curve to questions of preserve design.
The species-area curve has also been used in estimating species richness in
large regions such as preserves (Evans et al. 1955; Williams 1964; Kilburn 1966;
Lauga and Joachim 1987; Westfall et al. 1987; Gentil and Dauvin 1988; Gitay et
al. 1991; Baltan'as 1992; Grassle and Maciolek 1992). By fitting a function to the
species-area curve, one could potentially extrapolate to an area much larger than
the area sampled. However, it is clear from figures 2 and 4 that there is no such
thing as the species-area curve for a given location. Rather, there is a suite of
species-area curves, each with its own characteristics. In theory, all of the species-area
curves for a given region should converge at two points: (area = 0,
richness = 0) and (area = area of the entire region, richness = total richness of
the region). We are very interested in estimating the latter point, because it
represents the region's biodiversity. Unfortunately, the species-area curves in
this study do not show any evidence of converging to the right into a single point
(fig. 2). The envelopes for these curves (fig. 3) indicate a wide range of allowable
species-area curves, even for a particular grain and extent; these curves may
point in different directions. Thus it is misleading to use species-area curves to
estimate the number of species in a large region. Studies on similar forests have
shown that species-area curve methods tend to estimate species richness poorly
(Kilburn 1966; Palmer 1990a).
Nevertheless, the fact that the species-area relationship can be decomposed
into its components (figs. 2, 5, 9) is grounds for optimism: simple species-area
models can potentially be improved to include some of the complexities of scale.
CONCLUSIONS
We have demonstrated that the positive relationship between species richness
and area is influenced by grain, extent, and the number of samples in the Oosting
Natural Area. Of these, grain is the most important. However, the species richness
at a given area is determined by an interaction between the various components
of scale. Despite this complexity, the species-area relationship exhibits
marked regularities, which suggests fairly simple underlying causes. It remains
to be demonstrated that such regularities exist at much larger grains and extents.
ACKNOWLEDGMENTS
This research was carried out under support from the North Carolina Botanical
Garden. Data analysis and manuscript preparation were assisted by a grant from
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736 THE AMERICAN NATURALIST
the Oklahoma State University College of Arts and Sciences. K. Doyle, S. D.
McAlister, I. L. Palmer, S. S. Palmer, R. A. Reed, M. Robinson, and K. Wolf
assisted in establishing the grid and collecting the data. Discussions with S. D.
McAlister, J. Nekola, R. K. Peet, T. Phillippi, and R. A. Reed and the comments
of two anonymous reviewers improved our presentation of these ideas.
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