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Behavior of vegetation sampling methods in the presence of spatial
autocorrelation
Sarah C. Goslee
USDA-ARS Pasture Systems and Watershed Management Research Unit, Bldg. 3702 Curtin Road, Uni-
versity Park, PA 16802, USA; (e-mail: Sarah.Goslee@ars.usda.gov; phone: +814-863-0887; fax: +814-
863-0935)
Received 5 March 2004; accepted in revised form 25 February 2005
Key words: Cover, Frequency, Modified Whittaker plot, North Carolina Vegetation Survey, Species-area
curves, Transect
Abstract
Spatial autocorrelation in vegetation has been discussed extensively, but little is yet known about how
standard plant sampling methods perform when confronted with varying levels of patchiness. Simulated
species maps with a range of total abundance and spatial autocorrelation (patchiness) were sampled using
four methods: strip transect, randomly located quadrats, the non-nested multiscale modified Whittaker plot
and the nested multiscale North Carolina Vegetation Survey (NCVS) plot. Cover and frequency estimates
varied widely within and between methods, especially in the presence of high patchiness and for species with
moderate abundances. Transect sampling showed the highest variability, returning estimates of 19–94%
cover for a species with an actual cover of 50%. Transect and random methods were likely to miss rare
species entirely unless large numbers of quadrats were sampled. NCVS plots produced the most accurate
cover estimates because they sampled the largest area. Total species richness calculated using semilog
species-area curves was overestimated by transect and random sampling. Both multiscale methods, the
modified Whittaker and the NCVS plots, overestimated species richness when patchiness was low, and
underestimated it when patchiness was high. There was no clear distinction between the nested NCVS or
the non-nested modified Whittaker plot for any of the measures assessed. For all sampling methods, cover
and especially frequency estimates were highly variable, and depended on both the level of autocorrelation
and the sampling method used. The spatial structure of the vegetation must be considered when choosing
field sampling protocols or comparing results between studies that used different methods.
Introduction
Early ecologists assumed that vegetation was uni-
form, or oriented along a simple gradient, and
designed their sampling methods accordingly
(Greig-Smith 1979; Legendre and Fortin 1989).
Methods employing a series of equally-sized
quadrats, whether placed systematically or
randomly located, were widely used. The major
concerns were with the number, size and shape of
quadrats needed to characterize a particular veg-
etation type (Clapham 1932; Cain 1938; Rice and
Kelting 1955). Ecologists now realize that most if
not all communities are spatially structured, and
that sampling and analysis methods must be ro-
bust to varying levels of spatial autocorrelation as
Plant Ecology (2006) 187:203–212 Springer 2006
DOI 10.1007/s11258-005-3495-x
expressed by patchiness in the underlying species
distributions (Levin 1992; Legendre 1993).
Most practitioners now realize that spatial
autocorrelation interferes with standard statistical
tests, and are familiar with statistical methods to
overcome this complication (e.g. Dale and Fortin
2002; Legendre et al. 2002). Considerable effort
has been devoted to developing sampling designs
and statistical techniques to detect and quantify
spatial pattern, especially as it relates to the mea-
surement of species diversity (Fortin et al. 1989;
Dutilleul 1993; Bellehumeur and Legendre 1998;
Legendre et al. 2002). Although the potential
importance of spatial autocorrelation in field
sampling has been acknowledged (Stohlgren et al.
1995), little quantitative information is available
about the effect of patchiness in vegetation on the
measurement of common community attributes.
Ecologists continue to debate the appropriate
shape of sampling areas, but attention has shifted
to sampling schemes that incorporate subplots of a
range of sizes. Multiscale methods are better-sui-
ted to patchy environments, and reduce or elimi-
nate concerns about choosing the appropriate
spatial resolution (Peet et al. 1998). The increased
use of multiscale methods reflects interest in pat-
terns of species richness and abundance at different
scales (Stohlgren et al. 1995; Peet et al. 1998). Both
nested plot designs, with overlapping subquadrats,
and non-nested plot designs have been proposed.
The modified Whittaker plot, developed by
Stohlgren et al. (1995), is a widely-adopted non-
nested method. All subplots are contained within
the outermost sample region, but there is no
overlap between other subplots, so I have de-
scribed this as ‘non-nested’ even though it is truly
minimally nested (Figure 1a). The NCVS uses a
nested multiscale design with complete overlap
between subplots of different sizes (Figure 1b; Peet
et al. 1998). These newer methodologies have been
developed to match advances in our understanding
of the nature of spatial structure in vegetation, but
both systematic and random quadrat methods are
still widely used, especially when little is known in
advance about the structure of the vegetation
(Legendre et al. 2002).
Although multiscale designs are intended to
address spatial patterning in vegetation, there has
been little systematic comparison of their benefits
in the presence of varying levels of autocorrela-
tion. There have been a number of studies com-
paring aspects of the performance of vegetation
sampling methods under field conditions, but none
have explicitly examined autocorrelation (e.g.
Bourdeau 1953; Stohlgren et al. 1998; Barnett and
Stohlgren 2003; Korb et al. 2003; Leis et al. 2003).
Instead of repeating these trials with field data, I
chose to use simulated species distributions. Un-
like field sampling, with simulated data the level of
autocorrelation, the abundance of each species
and the actual number of species are known ex-
actly, so the performance of each sampling design
under a range of conditions can be assessed.
The main objective of this study was to compare
species cover and species frequency estimated by
four methods, two quadrat (random and system-
atic) and two multiscale (nested and non-nested),
given plant species of different size, abundance,
and level of spatial autocorrelation. A secondary
objective was to examine the effects of autocorre-
lation on species-area curves and estimates of total
richness. This information provides a baseline for
comparison of results from studies using different
methods, and for evaluating the suitability of a
particular sampling design for a variety of condi-
tions.
Methods
Four sampling methods were selected:
systematically-located quadrats, randomly-located
quadrats, a non-nested multiscale and a nested
multiscale scheme. The systematic quadrat method
used a strip transect of 1 ·1 m quadrats running
the length of the simulated area, for a total of fifty
1m
2
quadrats. The start point of the transect was
randomly chosen. The random method used the
same size and number of quadrats, but they were
placed randomly with no overlap. Species cover
was recorded for each quadrat.
The non-nested design used was the modified
Whittaker plot (Figure 1a; Stohlgren et al. 1995).
The total area sampled was 20 ·50 m. Species
cover was recorded within ten 2 ·0.5 m quadrats.
Species presence was recorded for progressively
larger rectangular plots: two of 2 ·5 m, one of
5·20 m, and a final plot of 20 ·50 m that
encompassed all the smaller plots.
The NCVS design was a nested design that
covered the same total area as the modified
Whittaker plot, but divided the area differently
204
(Figure 1b; Peet et al. 1998). The entire 50 ·20 m
area was divided into ten 10 ·10 m plots, in which
cover was recorded. Four of these plots contained
two sets of square nested subplots with areas of 10,
1, 0.1, and 0.01 m
2
. Species presence was recorded
for these subplots.
Simulations
The gstat package for R was used to simulate
species distributions with varying spatial autocor-
relations, revealed as patchiness in the distribution
of individuals (Pebesma 2001, 2004; R 1.8, R
Project for Statistical Computing). The spatial
correlation was quantified by an exponential
variogram model, and ten levels of patchiness were
created by varying the effective range (range = 0,
2, 5, 10, 15, 20, 25, 35, 50, 100). The variogram was
used as the basis for an unconditional kriging
simulation at gridded prediction locations. The
sequential gaussian simulation algorithm in the
gstat package was used to generate multiple real-
izations at the grid notes. The resulting continuous
variables were sliced to create simulated species
with one of eight possible levels of abundance by
defining all grid cells less than the cutoff value to
be occupied, and the remainder to be vacant
(abundance = 0.1, 1, 5, 10, 25, 50, 75, 90% cover).
For binary samples such as these derived presence/
absence grids, the level of spatial autocorrelation
or patchiness is shown by ‘clumping’ of the species
distributions across the simulated area (Figure 2).
The vegetation sampling schemes consisted of
plots and subplots of predetermined sizes, so a
scale had to be imposed on the simulated data. A
grid cell or pixel is the lower limit of resolution of
the sampling (the minimum size of a plant). Pre-
liminary simulations using a range of resolutions
(grain sizes of 1–20 pixels/m), conducted by sim-
Figure 1. Multiscale sampling methods. (a) Modified Whittaker plot sampling method (Stohlgren et al. 1995). Cover is estimated
within ten 1 m
2
quadrats, and species lists are recorded for each of the larger plots. (b) North Carolina Vegetation Survey (Peet et al.
1998) scheme. Cover is recorded within ten 100 m
2
plots, and species lists are recorded for each of the smaller subplots.
205
ulating a 20 ·50 m grid of the appropriate number
of pixels, demonstrated that varying the plant size
within this range made little difference to the pat-
terning of the simulated vegetation, so only the
results of the 10 pixel/m simulations are presented
here (plants with a minimum size of 10 ·10 cm).
The grid used was thus 200 ·500 pixels, since the
maximum size of a sampling plot was 20 ·50 m.
The single-species simulations used 10 levels of
patchiness and 8 species abundances (80 combi-
nations), and each had 100 repetitions. The four
sampling methods were applied to each, so that
total frequency and total cover as estimated by
each could be compared to the actual values.
Simulated species were combined into ‘commu-
nities’ by randomly selecting two species from each
abundance level for a given level of autocorrela-
tion. This process resulted in fifty sets with 16
species of varying abundance but identical levels of
patchiness. For the random and transect data, the
cumulative species richness curve was used to
estimate total richness in the 20 ·50 m area.
Species-area curves were calculated from the sub-
plots of the modified Whittaker and NCVS
schemes, and again used to estimate total species
richness. Both semilog [richness log(area)] and
log-log [log(richness)log(area)] forms of the
species area curve were calculated.
Figure 2. Simulated species distributions with 10% abundance and ten levels of autocorrelation (patchiness) determined by the range
value for an exponential variogram.
206
Results and discussion
The NCVS plot provided a perfect mean cover
estimate because cover is measured across the
entire area (mean of ten 100 m
2
quadrats). The
transect and random sample estimates are the
means of fifty 1 m
2
quadrats, and the modified
Whittaker estimate is the mean of ten 1 m
2
quadrats. If no spatial autocorrelation is present,
these three methods give equivalent values with
high accuracy and precision, as shown in
Figure 3a. As the level of patchiness increases,
the range of the species cover estimates also in-
creases. Transect sampling was most affected by
autocorrelation; species with a high autocorrela-
tion and true abundance of 50% had measured
cover of 19–94% from fifty quadrats (Figure 3b).
Random sampling was less affected, with a range
of 36–64%. Because it only samples ten 1 m
2
quadrats, the modified Whittaker plot produced
less-accurate cover estimates than the random
sample, although it did perform better than the
transect sample (range 28–76%). When only ten
quadrats from the random and transect samples
were considered instead of all fifty, the modified
Whittaker plot and the random samples pro-
vided similar estimates of cover, and both
were much more accurate than the transect
sample.
Frequency estimates were more affected by the
level of patchiness than by sampling method.
Estimates from transect sampling had the greatest
variability, followed by random and modified
Whittaker, and NCVS estimates were the most
precise (Figure 4). Frequency estimates from
NCVS sampling tended to be higher than those
obtained by other methods because of the larger
size of the subplots.
Figure 3. Comparison of strip transect, random quadrat, modified Whittaker plot and North Carolina Vegetation Survey sampling
methods at low (range = 0) and high (range = 100) levels of autocorrelation for four levels of species abundance.
207
Rather than present similar data for all four
methods, I chose random sampling as representa-
tive of the effects of autocorrelation on measured
plant frequency (Figure 5). The more uniform the
distribution, the higher the frequency. With no
autocorrelation, all species with abundance >10%
had a measured frequency of one using any
method. At very high abundances, the frequency
was near one regardless of the autocorrelation,
while the frequency estimates for low and moder-
ately abundant species varied widely. The effects of
spatial autocorrelation on apparent cover and
frequency were most pronounced at intermediate
abundances, since 0 and 100% provide hard limits
on plant cover. Rare species are unlikely to be
found regardless of the sampling method or spatial
distribution, while abundant species will always be
found.
The format of the modified Whittaker and
NCVS plots is fixed, but researchers often choose a
certain number of quadrats for random and tran-
sect sampling. Simulation results can help to
choose an appropriate number of quadrats
(Table 1). Random sampling is slightly more effi-
cient than transect sampling, but both are poor at
locating rare species, especially if any autocorre-
lation is present. With random sampling from a
species distribution based on a variogram with
range = 20 and an abundance of 1%, at least 30
quadrats are required to have a 95% chance of
encountering that species, and with transect sam-
pling at least 47 quadrats are required. Both
methods will find common species, even with few
quadrats. The numbers of quadrats needed to find
rare species are higher than often used to sample
an area of 20 ·50 m, suggesting that these meth-
ods seriously underestimate species richness. Field
studies support this conclusion; Jorgensen and
Tunnell (2001) found that quadrat methods missed
up to 30% of the plant species in their test area.
The multiscale plots can be used to estimate
frequency at a range of spatial scales (Figure 6).
Frequencies are always lower in smaller subplots,
and patchiness has the greatest effect on the
smallest subplots. The only exception is the
0.01 m
2
subplot of the NCVS scheme. This is the
same size as the pixel used in the simulations, so
frequency at this scale approximates the species
abundance. Similarly-sized subplots follow the
same curves for both modified Whittaker and
NCVS sampling schemes.
Log-log species area curves substantially
underestimated the number of species in 1000 m
2
,
so only semi-log curves will be considered further.
Cumulative richness curves from both transect and
random plots overestimated the number of species
in a 1000 m
2
area, especially at moderate and high
levels of autocorrelation (Figure 7). This was
Figure 4. The range of measured frequencies obtained by using strip transect, random quadrat, modified Whittaker plot and North
Carolina Vegetation Survey sampling methods on simulated species with high autocorrelation level and two levels of abundance.
208
expected, since it is known that species-area curves
constructed by aggregating samples have a higher
slope, and thus overestimate total richness (Ro-
senzweig 1995). Although the shape of the re-
sponse was somewhat different, both of the
multiscale sampling schemes overestimated the
total species richness at low autocorrelations, but
underestimated it at high levels. For both, a uni-
form species distribution led to a species-area
curve with low slope but high intercept, since even
the smallest plots found most species. With high
autocorrelation the slope was steeper but the
intercept was much lower.
The ‘communities’ used for calculating species
area curves are not representative of actual com-
munities. Usually there are a few abundant species
and many rare species, rather than equal numbers
across a range of abundances. Each species was
randomly distributed with respect to all other
simulated species, and all had the same level of
autocorrelation. In actual plant communities,
species distributions may show positive and neg-
ative associations and the effects of environmental
heterogeneity. The objective of this study was to
evaluate the effects of autocorrelation, not
hypotheses about the structure of plant commu-
nities, so this simplified community structure was
appropriate.
The modified Whittaker plot was the only
method examined with rectangular rather than
square quadrats. Preliminary investigation showed
that for this simulation study, plot shape made
little difference. In the presence of anisotropy, such
as an underlying environmental gradient, plot
shape could have a strong effect on observed
vegetation characteristics.
The choice of nested or non-nested plots has
been debated in the literature. The only differences
between the nested NCVS and the non-nested
modified Whittaker plots that were not attribut-
able to differing subplot sizes was in the species-
area curve predictions of total richness. Stohlgren
et al. (1995) stated that spatial autocorrelation has
a larger effect on overlapping subplots because a
Figure 5. The range of frequency estimates produced by random sampling of simulated species with four abundance levels at a range
of autocorrelation levels.
209
particular area is sampled more than once. Peet
et al. (1998) made the identical claim in reverse,
stating that the use of non-overlapping plots
ignores spatial autocorrelation in vegetation. The
simulation results here suggest that the two
methods do respond differently to spatial
Table 1. The number of quadrats (maximum of 50) needed to have at least a 95% chance of encountering a species with given
abundance and distribution.
Autocorrelation Species abundance (%)
0.1 1 5 10 25 50 75 90
a. Transect
0 27 3111111
2 46 5211111
5 –14541111
10 –28963211
15 – 48 16 12 4 1 1 1
20 – 47 24 14 9 4 1 1
25 – – 32 15 6 3 1 1
35 – – 38 23 10 3 2 1
50 – – 38 30 14 6 4 1
100 – – –4227134 1
b. Random
0 23 3111111
2 – 5211111
5 –13432111
10 –16642111
15 – 29 10 5 3 2 1 1
20 – 30 10 7 3 2 1 1
25 – 39 15 7 3 2 1 1
35 – 48 13 10 4 3 1 1
50 – – 19 10 5 2 1 1
100 – – 22 11 6 3 2 1
A dash marks denote species which were not found after sampling 50 quadrats.
Figure 6. Frequency estimates produced by sampling at different spatial scales using the modified Whittaker and North Carolina
Vegetation Survey schemes for species with 10% actual abundance.
210
autocorrelation, but that the differences are negli-
gible in anisotropic environments. It is more
important to note that both methods overestimate
species richness in vegetation with low autocorre-
lation, but underestimate it with high autocorre-
lation.
The findings from this simulation study on cover
and frequency estimates accord with what is known
from field experiments. All sampling methods
encounter dominant species, but random and
transect methods are more likely to miss rare species
than methods that cover a larger area (Bourdeau
1953; Stohlgren et al. 1998; Jorgensen and Tunnell
2001; Barnett and Stohlgren 2003; Korb et al. 2003).
The drawback is that larger multiscale methods are
slower to lay out and sample in the field (Stohlgren
et al. 1998; Korb et al. 2003).
Conclusions
In vegetation, the degree of underlying spatial
autocorrelation is expressed by patchiness in the
species distribution, and can be modeled by vary-
ing the effective range of the variogram used as the
basis for a kriging simulation. Using simulated
species distributions to test the choice of sampling
method demonstrated that transect methods
especially responded poorly to spatial autocorre-
lation. Randomly-located quadrats were more
efficient in highly patchy environments, but large
numbers of quadrats are needed for either method
if rare species must be located. Multiscale methods
were more robust to spatial autocorrelation, and
more effective at identifying rare species because of
the larger proportion of the total area sampled.
Cover and especially frequency estimates were
highly variable, and depended on both the level of
autocorrelation and the sampling method used. It
is difficult to meaningfully compare community
attributes obtained by different methods, and un-
der certain circumstances sampled results may
have little resemblance to actual values.
References
Barnett D.T. and Stohlgren T.J. 2003. A nested-intensity design
for surveying plant diversity. Biodivers. Conserv. 12: 255–
278.
Bellehumeur C. and Legendre P. 1998. Multiscale sources of
variation in ecological variables: modeling spatial dispersion,
elaborating sampling designs. Landscape Ecol. 13: 15–25.
Bourdeau P.F. 1953. A test of random versus systematic eco-
logical sampling. Ecology 34: 499–512.
Cain S.A. 1938. The species-area curve. Am. Midl. Nat. 19:
573–581.
Clapham A.R. 1932. The form of the observational unit in
quantitative ecology. J. Ecol. 20: 192–197.
Dale M.R.T. and Fortin M.-J. 2002. Spatial autocorrelation
and statistical tests in ecology. E
´coscience 9: 162–167.
Dutilleul P. 1993. Spatial heterogeneity and the design of eco-
logical field experiments. Ecology 74: 1646–1658.
Figure 7. Deviances [(observed valueexpected value)/expected] for species richness in 1000 m
2
estimated from data collected using
four different sampling methods.
211
Korb J.E., Covington W.W. and Ful P.Z. 2003. Sampling
techniques influence understory plant trajectories after res-
toration: An example from Ponderosa pine restoration. Re-
stor. Ecol. 11: 504–515.
Fortin M.-J., Drapeau P. and Legendre P. 1989. Spatial auto-
correlation and sampling design in plant ecology. Vegetatio
83: 209–222.
Grieg-Smith P. 1979. Pattern in vegetation. J. Ecology 67: 755–
779.
Jorgensen E.E. and Tunnell S.J. 2001. The effectiveness of
quadrats for measuring vascular plant diversity. Tex. J. Sci.
53: 365–368.
Legendre P. 1993. Spatial autocorrelation: trouble or new
paradigm? Ecology 74: 1659–1673.
Legendre P. and Fortin M.-J. 1989. Spatial pattern and eco-
logical analysis. Vegetatio 80: 107–138.
Legendre P., Dale M.R.T., Fortin M.-J., Gurevitch J., Hohn
M. and Myers D. 2002. The consequences of spatial structure
for the design and analysis of ecological field surveys. Ecog-
raphy 25: 601–615.
Leis S.A., Engle D.M., Leslie D.M.Jr., Fehmi J.S. and Kretzer
J. 2003. Comparison of vegetation sampling procedures in a
disturbed mixed-grass prairie. Proc. Oklahoma Acad. Sci. 83:
7–15.
Levin S.A. 1992. The problem of pattern and scale in ecology.
Ecology 73: 1943–1967.
Pebesma E.J. 2001. GSTAT User’s Manual. (gstat version
2.3.3). http://www.gstat.org.
Pebesma E.J. 2004. Multivariable geostatistics in S: the gstat
package. Comput. Geosci. 30: 683–691.
Peet R.K., Wentworth T.R. and White P.S. 1998. A flexible,
multipurpose method for recording vegetation composition
and structure. Castanea 63: 262–274.
Rice E.L and Kelting R.W. 1955. The species-area curve.
Ecology 36: 7–11.
Rosenzweig M.L. 1995. Species Diversity In Space and Time.
Cambridge University Press, Cambridge, UK.
Stohlgren T.J., Falkner M.B. and Schell L.D. 1995. A Modi-
fied-Whittaker nested vegetation sampling method. Vegetatio
117: 113–121.
Stohlgren T.J., Bull K.A. and Otsuki Y. 1998. Comparison of
rangeland vegetation sampling techniques in the Central
Grasslands. J. Range Manage. 51: 164–172.
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