Ecological Applications, 15(5), 2005, pp. 1761–1771
䉷 2005 by the Ecological Society of America
A TEST FOR COMMUNITY CHANGE USING A NULL MODEL APPROACH
JACOB SCHAEFER,1,4 KEITH GIDO,2
AND
MELINDA SMITH3,5
1
Department of Biology, Southern Illinois University Edwardsville, Edwardsville, Illinois 62026 USA
2Division of Biology, Kansas State University, Ackert Hall, Manhattan, Kansas 66506 USA
3National Center for Ecological Analysis and Synthesis, 735 State St., Suite 300, Santa Barbara, California 93101 USA
Abstract. Quantifying patterns of temporal or spatial change in community structure
is critical for assessing the impact of disturbances on biological systems and the stability
of ecosystems. Detecting change in communities can be problematic, however, because of
the inherent variability of systems and limitations of commonly used methods, such as
similarity indices and ordination that do not explicitly test a hypothesis. Here we present
empirical data to show a strong relationship between species mean abundance and variability
across three broad taxonomic groups (plants, zooplankton, and fish). These statistical relationships were then used to construct null models of expected community variability that
were used to test against the observed temporal change of these communities. We evaluated
the ability of this approach to detect significant temporal change above that associated with
random variation with nine communities (three Midwestern stream fish, three north temperate zooplankton, and three tallgrass prairie plant), each having long-term data sets and
different expected levels of change. Nonrandom change was detected in 21.3% of samples
from the expected low-change communities, 52.6% in moderately changed communities,
and 60.4% in high-change communities. Thus, this approach was effective in detecting
change over time in those communities expected to change most. By using empirical relationships between species abundance and variability, this null model approach provides
ecologists and resource managers an objective tool, which can be used along with existing
community indices and statistical techniques to assess the type and magnitude of community
change with limited data sets.
Key words: community dynamics; disturbance; null model; population variability; simulation;
statistical method.
INTRODUCTION
Inherent variability in ecological communities can
limit our ability to link community change over space
or time to natural or anthropogenic disturbances (Tilman 1989, Grossman et al. 1990, Clarke and Warwick
1994, Matthews 1998, Collins 2000). In order for ecologists to relate such disturbances to community variability there needs to be more effective means for assaying the significance of the observed levels of change
above that of natural or random variation. Thus, key
problems facing ecologists are estimation of the
amount of background variation in community structure and determination of the biological significance of
deviations in community structure among samples
(Grossman et al. 1990, Clarke and Warwick 1994, Philippi et al. 1998, Micheli et al. 1999, Smith 2002, Bowman et al. 2003). Long-term data at a reference site or
at the same location taken prior to the disturbance are
Manuscript received 28 September 2004; revised 23 December 2004; accepted 25 January 2005; final version received 9
March 2005. Corresponding Editor: T. E. Essington.
4 Present address: Department of Biological Sciences, University of Southern Mississippi, Hattiesburg, Mississippi
39401 USA. E-mail: Jake.Schaefer@usm.edu
5 Present address: Department of Ecology and Evolutionary Biology, Yale University, New Haven, Connecticut 06520
USA.
ideal for addressing these problems. However, in most
cases, these data are either not available or lack adequate spatial or temporal replication (Tilman 1989, Philippi et al. 1998, Collins 2000). Moreover, when longterm data are available, most techniques are not optimal
for testing the null hypothesis that a community has
not changed over time. In this paper, we present a null
model approach to assess community change and then
test the approach with both simulated (random-walk)
data and empirical data from three different long-term
data sets (stream fish, zooplankton, and tallgrass prairie
plants).
There are a number of approaches that can be used
to quantify community change, including similarity indices and ordination (Washington 1984, Boyle et al.
1990, Warwick and Clarke 1991, Clarke 1993, Clarke
and Warwick 1994). Each of these approaches has
strengths and weaknesses depending on the questions
being asked, the temporal scope of the data, and the
fundamental properties of the community being examined. Consequently, researchers often rely on personal experience or some knowledge of the individual
indices for selection (Jongman et al. 1995). For example, if the data set being studied consists of a small
number (less than five) of samples in time, ecologists
often use an index of similarity or dissimilarity to quan-
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JACOB SCHAEFER ET AL.
tify community change. Quantitative similarity indices
provide an intuitive measure of the differences among
samples, but the behavior and sensitivity of the indices
are highly dependent on the properties (e.g., abundance
of dominant species) of the community (Faith et al.
1987, Boyle et al. 1990). Some authors recommend a
‘‘cut-off’’ based on mean values from a large number
of comparisons to indicate a biologically-relevant
change. For example, Matthews (1998) suggested that
a percent similarity index (PSI) of ⬎0.6 among interannual samples in a midwestern stream fish community
indicates a stable community. Because the responses
of these indices change among community types, comparing values among various communities (either
across geographic regions or taxonomic group) is troublesome at best. If samples are replicated and independent, standard parametric statistics can be applied
to similarity indices. A variety of bootstrap or randomization techniques have also been developed to generate confidence intervals for similarity indices (Rice
and Beland 1982, Ebeling et al. 1990, Solow 1993,
Smith 2002) or to permute a similarity/distance matrix
(Smith et al. 1990) to obtain a probability for the observed value. In addition, a multisample nonparametric
correlation (Kendall’s W) can be used to test for community stability through time (Grossman 1982; but see
Ebeling et al. 1990). However, a common requirement
for all of these approaches is a long-term data set. In
general, similarity indices as they are currently applied
are of limited use unless there is a means to explicitly
test the null hypothesis that a community has not
changed relative to random variability in community
structure.
If a data set with more samples in time than species
in the community is available, ordination or cluster
analyses can be helpful for detecting community
change. Ordination techniques allow one to quantify
the amount of change as well as the directionality (direction in ordination space) of change (Clarke and
Green 1988, Clarke and Warwick 1994, Legendre and
Legendre 1998). Matthews (1998) used the displacement or movement of points over time in ordination
space to quantify the amount and directionality of community change. More recently, Collins (2000) showed
divergence in plant communities in multivariate space
using autocorrelation (time-lag) analyses. However, the
biggest limitation of ordination techniques is they require a large number of samples across time.
Because of the problems mentioned above and the
persistent need for ecologists to detect community
change, we have developed a null model (Manley 1991,
Gotelli 2001, Gotelli and Entsminger 2003) approach
to assess community change that can be used with only
a few samples. Our approach is fundamentally different
from other randomization techniques in that it is based
on an empirical relationship between species abundance and coefficient of variation (CV) of abundance
over time for members of a community. Once quan-
tified, this relationship forms the basis of a null model
that predicts future community structure in the absence
of any change. We therefore define community change
as statistically significant change from a reference sample due to biotic or abiotic factor. Thus, our definition
of change includes, among other factors, covariation
among species, disturbance, and population trajectories.
Our null model is based on knowledge of initial community structure (e.g., one to six reference samples)
and the predicted variability of each species derived
from the relationship between abundance and CV of
abundance over time. Using randomly generated communities from this null model we can build frequency
distributions of community change metrics (similarity
indices and distances in ordination space). These distributions are then used to test the hypothesis that the
community has not undergone significant change over
time. Here, we present tests of this technique using
random-walk simulations and long-term (14–18 yr) annual sampling records for midwestern stream fishes, a
north temperate zooplankton community, and tallgrass
prairie plant communities.
METHODS
Raw data
We compiled long-term data (hereafter referred to as
training samples) for three different community types
to establish relationships between abundance and variation in abundance: midwestern stream fishes, north
temperate lakes zooplankton, and tallgrass prairie
plants. Stream fish data were taken from surveys in the
Red and Arkansas River basins by the Oklahoma Department of Environmental Quality (ODEQ). The
ODEQ collections included 31 sites sampled between
1977 and 1995 using a standardized sampling effort
(approximately 1 h; see Pigg et al. 1998 for sample
methodology). Twenty, 10-m seine hauls were taken at
each site with a 3 ⫻ 1.5 m (4.7-mm mesh) heavy-leaded
seine. Each site was sampled two to three times a year
and all data were pooled over the year and expressed
as the mean number of each species collected at each
site in a year.
Zooplankton data from seven Wisconsin lakes collected from 1986 to 2000 were compiled from the North
Temperate Lakes Long-Term Ecological Research
(NTL-LTER) database: Lake Allequash, Crystal Bog,
Crystal Lake, Sparkling Lake, Big Muskellunge Lake,
Trout Bog, and Trout Lake. Each lake was sampled at
least three times per year at nine depths using a 2 m
long Schindler-Patalas trap and with vertical tows using
a Wisconsin net. As with the stream fish samples, data
from all samples within a year were combined to give
a mean abundance for each species in each lake during
each year. At sites where yearly sampling effort
changed (for example, Big Muskellunge Lake had 18
samples per year in 1986–1989 and five samples per
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ASSESSMENT OF COMMUNITY CHANGE
year in 1990–2000) we randomly selected a subset of
samples, attempting to keep the number of samples per
season equal across years. Unresolved taxa were not
used in this analysis and typically consisted of a small
number of rare species (usually fewer than five).
Tallgrass prairie plant community data were compiled from the Konza Prairie LTER (KP-LTER) site
near Manhattan, Kansas. Before 1972, sites in this area
were burned at 2–3-yr intervals and grazed by cattle.
Beginning in 1972, watersheds on Konza Prairie have
been experimentally burned at 1-, 4-, or 20-yr intervals
(Knapp et al. 1998, Collins 2000). We gathered data
from two ungrazed watersheds subjected to each of
these three burn regimes. Permanent sampling plots
were established in 1983 and since then have been
sampled in the spring and fall of each year. Species
abundances were measured as percent cover as described in Gibson and Hurlbert (1987) and Collins
(2000). Data were combined for spring and fall samples
to give a maximum percentage cover for each species
during the growing season.
Relating abundance and variation in abundance
The establishment of the relationship between species mean abundance and variation in abundance (from
the training samples) through time is fundamental to
our approach. This relationship allows us to define the
predicted variability over time for each species based
on its abundance in a reference sample or samples.
McArdle et al. (1990) outlined the potential problems
of relating species mean abundance and variability in
abundance. To summarize, many measures of population variability are problematic due to the complexities
of spatial and temporal scales of sampling and the dependency on mean population size. A common measure
of population variability is SD(log[N]); however this
measure is undefined if zero abundance data are present, something quite common in ecological data sets
(Williamson 1984, McArdle et al. 1990). To correct for
zero data, SD(log[N ⫹ 1]) is often used, but this measure underestimates the true variance and the more zeros in the data set the greater the bias (Anscombe 1948,
McArdle et al. 1990). Coefficient of variation
(CV,[SD(N)]/Nmean) is a widely used and scale-free measure of variability that does not have the same problems
with zeros in the data.
By plotting the CV of abundance against log(mean
abundance), we can examine the relationship between
a species’ (or taxon) mean abundance and variation
through time. If the slope of this line is zero (a horizontal line), then variability in abundance is independent of mean abundance (McArdle et al. 1990). Because the denominator of CV is mean abundance, the
relationship between log(CV) and log(mean abundance)
is analogous to a residual analysis that evaluates variability as a function of an independent variable. An
inverse relationship between mean abundance and CV
in abundance has been demonstrated in a number of
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taxa including fish (Grossman et al. 1990, Winemiller
1996, Matthews 1998), mites (Ford 1938), spiders
(Schoener and Spiller 1992), moths (Spitzer and Leps
1988), and mammals (Windberg 1997). Because of the
generality of this relationship, we suggest these relationships can be used to predict species variability, and
when used in concert with Monte Carlo simulations,
can be used to evaluate the probability of community
change among sample points.
For each of the three community types, we calculated
mean abundance and CV in abundance for all species
in each of the training samples (raw data were linearly
transformed [⫻10 for fish and NTL-LTER, ⫻100 for
KP-LTER] so that all individual yearly species abundances were ⱖ1.0). For example, the NTL-LTER data
set consisted of seven lakes (Allequash Lake, Crystal
Bog, Crystal Lake, Muskellunge Lake, Sparkling Lake,
Trout Bog, and Trout Lake) that had 72, 93, 80, 86,
60, and 95 total species, respectively. Therefore, there
was a total of 561 species means and CVs for the NTLLTER data set from which we examined the relationship between abundance and variation in abundance.
The KP-LTER and stream fish data sets consisted of
878 and 761 species–site observations, respectively.
For each of the three community types, we fitted the
mean log(x ⫹ 1) abundance vs. CV with an exponential
decay function. There are a number of other techniques
for estimating population variances (e.g., McArdle et
al. 1990), but we chose this particular method because
it worked well for all three of our communities. Exponential decay functions had an r2 of 0.56 for the
stream fish data, 0.64 for the NTL-LTER data, and 0.65
for the KP-LTER data (Fig. 1a–c). These relationships
were used to predict CV in abundance over time for a
species based on its abundance in a reference sample.
Testing for community change
Within each of the three community types (fishes,
zooplankton, prairie plants), we selected one community with a high degree of change (HC), one with moderate change (MC), and one with low change (LC)
based on experimental manipulations (KP-LTER), published works, or observations by investigators (J. F.
Schaefer, K. B. Gido, and J. Pigg for stream fish, J.
Rusak for NTL-LTER) familiar with the communities
during the respective sample periods. For stream fishes,
we selected the Canadian River (HC), the Salt Fork of
the Arkansas (MC), and the Salt Fork of the Red (LC);
for NTL-LTER, we selected Crystal Lake (HC), Allequash Lake (MC), and Big Muskellunge Lake (LC);
for the KP-LTER, we selected plots that were burned
at 20-yr (HC), 4-yr (MC), and 1-yr (LC) intervals. We
expected the least change in the 1-yr burn based on
results presented by Collins (2000), who found these
communities exhibited the lowest amount of temporal
variation and turnover of species.
For each of these nine communities, we used the
following model to randomly generate potential com-
JACOB SCHAEFER ET AL.
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FIG. 1. The relationship between coefficient of variation
(CV) and mean abundance for each of the three communities.
Solid lines represent best-fit regression lines (r2 values
shown); dashed lines represent 0.5 ⫻ CV and 2.0 ⫻ CV.
munities based on species abundances in a reference
sample (first sample in time at one community) and
their predicted CV in abundance from training samples
for a community (Fig. 1). For a single randomly generated community, the model can be summarized as
follows:
Ai ⫽ R (x¯ i , SDi )
where Ai ⫽ the estimated abundance of species i in the
randomly generated community, R is a random number
drawn from a negative binomial distribution with a
mean abundance of species i in the reference sample
x̄i and a standard deviation (SDi) calculated from CVi.
Species with an abundance of zero in a reference sample but present in later samples were included in the
analysis and assigned the maximum CV for the community type and SD was calculated based on an arbitrary mean value of 1.0 (minimum abundance in transformed data).
Ecological Applications
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Once the predicted abundance and CV for each species in a community was established, 5000 communities were generated by the model and different community change metrics were calculated using each randomly generated community and the reference sample.
Sensitivity of the analysis to different levels of CV was
assessed by generating an additional 5000 communities
using half (0.5 ⫻ CV), and twice the expected CV (2.0
⫻ CV). Therefore, for each community we generated a
total of 15 000 randomly generated communities (Fig.
2). For all three community types, 93% (2043 out of
2200) of the CV values in training samples were within
the range of 0.5(predicted CV) and 2.0(predicted CV)
values (Fig. 1).
Community change over time was assessed by comparing expected community structure (randomly generated communities) to target samples (all samples
from a community taken after a reference sample). For
each simulation, the randomly generated communities
were compared to the reference sample using qualitative (Jaccard’s index) and quantitative (PSI, Bray-Curtis, and Morisita’s indices) similarity indices (Magurran
1988). Frequency distributions of each metric were
compiled for each community and level of variability
(CV, 0.5 ⫻ CV, and 2.0 ⫻ CV) and used to test the
significance of observed similarity index values (comparing the reference sample to target samples at a community; Fig. 2). Statistically significant community
change (i.e., target samples significantly different from
the reference sample) occurred if the observed change
for a given index was more extreme than 95% of the
values of that index for the randomly generated communities (Table 1).
Community change also was quantified using Euclidian distance in non-metric multidimensional scaling (NMDS) space. For each community and predicted
level of CV, a NMDS ordination was performed on a
matrix consisting of all target and reference samples
and the 1000 (5000 was not practical due to the computational intensity of NMDS) randomly generated
communities. We then calculated Euclidean distances
in NMDS space between the reference sample and all
randomly generated communities as well as the reference sample and the target samples. The distances
between the reference sample and randomly generated
communities formed a null distribution that we used
to test for significant change in the target samples. Any
target sample that had a Euclidean distance from a
reference sample greater than 95% of the randomly
generated communities was judged to have significantly changed (Fig. 2). Analyses were also performed
with a second ordination technique (DCA), however
results were similar to NMDS and are therefore not
presented below.
Accuracy of mean abundance in reference samples
Because the variance estimate for each species is
derived from its abundance in the reference sample or
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ASSESSMENT OF COMMUNITY CHANGE
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FIG. 2. Flow diagram illustrating the steps involved in assessing community change. The steps shown here would assess
community change from one reference sample using two metrics: (A) PSI and (B) distance in NMDS space. Results from
PSI and NMDS are from a simulation of Big Muskellunge Lake using the first year as the reference sample and 1.0 ⫻ CV.
The vertical line on each frequency histogram represents a 5% cutoff point used to determine significance of observed values:
PSI ⬍ 0.56 or NMDS distance ⬎1.39 for a target sample would indicate significant change from the reference sample. On
the NMDS plot (B), large circles represent target samples, and the black circle represents the reference sample.
samples, the accuracy of our approach relies on the
accuracy of this estimate. Although abundance measures for species from a single sample will reflect gross
differences in abundance across species, an average
abundance across multiple samples might better reflect
the abundance of a species in that particular environment. Thus, to assess the accuracy of the estimated
species abundance from a single sample or multiple
TABLE 1. Mean similarity of randomly generated communities compared to reference samples (first-year sample) using four
common similarity indices.
Community type
Stream Fish
Zooplankton
Tallgrass Prairie
Community name
Salt Fork of the Red River
Salt Fork of Arkansas
Canadian River
Big Muskellunge Lake
Allequash Lake
Crystal Lake
Annually burned
4-yr burn
Unburned
PSI
0.73
0.74
0.79
0.73
0.81
0.75
0.86
0.84
0.83
(0.34)
(0.41)
(0.42)
(0.64)†
(0.74)
(0.55)
(0.77)
(0.76)
(0.76)
Bray-Curtis index
0.59
0.63
0.63
0.72
0.80
0.74
0.83
0.82
0.81
(0.24)
(0.36)
(0.29)
(0.62)
(0.73)
(0.63)
(0.74)
(0.72)
(0.72)
Morisita’s index
0.86
0.86
0.89
0.88
0.81
0.88
0.96
0.97
0.97
(0.38)
(0.43)
(0.49)
(0.76)
(0.71)
(0.77)
(0.90)
(0.92)
(0.90)
Jaccard’s index
0.54
0.53
0.52
0.51
0.51
0.38
0.47
0.54
0.41
(0.43)
(0.42)
(0.40)
(0.44)
(0.43)
(0.31)
(0.42)
(0.49)
(0.36)
Notes: Numbers in parentheses are the critical values, where 95% of the generated communities had greater than or equal
similarity to the observed community (i.e., an observed community with a lower value would be significantly changed).
‘‘PSI’’ is the percent similarity index.
† Distribution is shown in panel A of Fig. 2.
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the grand mean divided by the mean abundance during
the given time interval. If the abundance for a time
period was greater than the grand mean we used the
reciprocal of the value. For example, if a species had
a grand mean abundance of 50 individuals, and an
abundance of 40 and 100 in the first two samples, the
deviation of the first sample would be 1.25 (50/40),
and 1.4 (70/50) for the first two samples combined. By
definition, the deviation values asymptote at 1.0 when
estimated means are equal to grand means. To quantify
how sensitive our approach is to different levels of
accuracy in forming reference samples, we ran simulations for each community using three different reference samples: (1) reference sample included only the
abundances from the first sample, (2) reference sample
included mean abundances from the first three samples,
and (3) reference sample included mean abundance
from the first six samples. These simulations were only
conducted at the predicted level of 1.0 ⫻ CV. Programs
for Monte Carlo simulations and associated calculations were written in the C programming language (see
Supplement).
Random walk simulations
FIG. 3. Summary of statistically significant change (bars;
left-hand vertical axes) and overall diversity (lines; right-hand
vertical axes) for the nine communities examined. Open circles represent years in which no community change was detected; closed symbols represent years in which change was
detected, with bars representing the number of metrics detecting change. Results shown are for expected level of variability (1.0 ⫻ CV) and one reference sample (first-year sample from each community). Annual, 4-year, and 20-year refer
to experimental burn cycles in Konze prairie plots; LC, low
change; MC, moderate change; HC, high change.
To assess the sensitivity of our approach, 100 30-yr
simulations for six stream fish communities were generated, each starting with 30 species (three species each
with a mean abundance of 2, 4, 8, 16, 32, 64, and 100;
two species each with a mean of 150, 200, and 250;
one species each with a mean of 500, 750, and 1000).
In the ‘‘no change’’ community, all species remained
unchanged and abundance data at each time step were
generated by a simple random walk. In the ‘‘two
changed’’ community, the most abundant species declined over time from a mean of 1000 to a mean of
two and the least abundant species increased from a
mean of two to 1000 while the mean abundance of the
other 28 species remain unchanged (random walk). The
‘‘six changed’’ and ‘‘12 changed’’ were similar except
the three or six most abundant species decreased while
the three or six least abundant increased. In the ‘‘six
extinct’’ and ‘‘12 extinct’’ simulations the six and 12
least abundant species went extinct while the other 24
or 18 more abundant species remained unchanged. For
each of the 600 simulations, the reference sample was
the first generated (time 1) and the target sample the
30th (data in between were not used). Analyses were
performed as described above using the CV–abundance
relationship for stream fish.
RESULTS
samples across time, we evaluated the deviation of
these estimates from the grand mean abundance across
all sample years.
For each time interval, we calculated the deviation
from the grand mean for each species and plotted the
mean deviation (⫾1 SE) for all species in that community. Deviation from the grand mean was defined as
Community change
Using the expected level of variation (1.0 ⫻ CV), the
three LC communities showed significant differences
between the reference samples and a target samples in
21.3% (49 out of 230) of the community ⫻ sample ⫻
metric combinations (Fig. 3). The MC and HC com-
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ASSESSMENT OF COMMUNITY CHANGE
1767
deviation of estimated species abundance from the
grand mean (mean for all stream fish species, Fig. 4a)
and deviations for individual species ranged from 1.0to 77-fold differences from the grand mean. By averaging six samples to form our estimate the mean deviations for KP-LTER, NTL-LTER and stream fish
were 2.9 (SE ⫽ 0.26), 2.1 (SE ⫽ 0.13), and 2.4 (SE ⫽
0.23) times the grand mean, respectively, and the maximum deviation for a species was 18.3-fold (mean
abundance over first 6 yr ⫽ 0.058, overall mean abundance ⫽ 1.063). For all three community types, the
deviation of estimated mean abundances were highest
with one to three years of data and dropped dramatically with four to six years of data. Increases in accuracy (decreased deviation) were not appreciable with
more than six years of data (Fig. 4).
Across all communities and metrics used, significant
change was detected more often when reference samples were based on one years data (38.4% of target
samples significantly changed) compared to three
(33.2%) or six years data (25.9%, Fig. 5). Using quantitative indices, the number of communities detected
as changed decreased as more samples were used to
form the reference sample (one year, 50.9%; three
years, 38.9%; and six years, 31.2%; Fig 5). The opposite trend was observed when using the qualitative
Jaccard’s index as a metric (one year, 0.7%; three years,
16.0%; and six years, 10.0%; Fig 5), due to the accumulation of rare species over time as more samples
were included in the reference sample. This effect was
most obvious in the zooplankton data where a typical
single year sample consisted of 36 species while the
full data matrix for these communities averaged 70
species.
FIG. 4. Accuracy of reference samples in estimating mean
abundance for each of the three community types. Values on
the x-axis represent the number of sample years used to calculate mean abundance. The y-axis represents the mean (⫾
SE ) deviation (estimated mean/actual mean) of the estimated
mean from the grand mean for all species in each of the three
community types.
Sensitivity to level of
CV
Across all communities and metrics used, community change was detected in 78.4% of target samples
using 0.5 ⫻ CV, 45.0% of target samples using 1.0 ⫻
munities showed significant differences in 52.6% and
60.4% of samples respectively (Fig. 3). Moreover, for
the MC and HC communities, there was often agreement among metrics in detecting change, as compared
to the LC communities. For example, community
change was detected in 11 samples for the LC NTLLTER but only four times by more than two metrics.
For the HC NTL-LTER data, community change was
detected in 13 samples and always by four metrics.
Accuracy of mean abundance in reference samples
Estimates of mean species abundance over time
asymptotically approached the grand mean as more
samples were included in the reference sample. Using
a single sample as an estimate of mean species abundance over time resulted in a maximum of a 6.8-fold
FIG. 5. Sensitivity (total number of communities detected
as significantly changed) of four similarity indices when species abundances in reference samples were estimated from
one-, three-, and six-year means.
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JACOB SCHAEFER ET AL.
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Random-walk simulations
Of the quantitative metrics, Bray-Curtis and Morisita’s metrics were most sensitive to changes in abundance in the random-walk simulations (Table 3). All
three of the quantitative metrics detected all simulated
communities as changed when 12 of the 30 species
either increased or decreased in abundance. Jaccard’s
index was only effective at detecting extinctions,
whereas the quantitative metrics did not consistently
detect change even when the 12 least abundant species
went extinct (Table 3).
DISCUSSION
FIG. 6. Sensitivity (percentage of communities detected
as significantly changed) of four similarity indices and Euclidian distance in NMDS space when variance in species
abundance from reference samples was based on 1.0, 0.5, and
2.0 times the coefficient of variation (CV). Species abundances from reference samples were based on the first-year
sample.
and 6.0% of target samples using 2.0 ⫻ CV (Fig.
6). In general, target samples found to be significantly
changed at the 2.0 ⫻ CV level were drastically changed.
Most (33 of 42) of the target samples detected as
changed at the 2.0 ⫻ CV level occurred at one of the
three HC sites. Conversely, communities where target
samples were not detected as changed at the 0.5 ⫻ CV
level would have been extremely stable. The Salt Fork
of the Red River community was the most stable in
this regard with only 33.7% (27 out of 80) of the target
sample/index combinations indicating change at the 0.5
⫻ CV level.
CV ,
Sensitivity of individual metrics
Combining all communities and CV levels, Euclidean
distance in NMDS space, PSI and Bray-Curtis indices
most often detected community change (61.2%, 51.7%,
and 45.7%, respectively), followed by Morisita’s
(40.9%) and Jaccard’s (16.29%; Fig. 6). PSI and BrayCurtis metrics were the most consistent in detecting
change (agreeing in 85.4% of samples), whereas results
from NMDS and Jaccard’s metrics differed the most
often (28.0%, Table 2). In general, results among quantitative similarity indices were more similar than
among NMDS and Jaccard’s index (Table 2).
Based on our knowledge of the data sets used in our
study, our approach provided an unbiased estimate of
natural variability that was used to test for community
change (significant difference between reference and
target samples). In each of our community types, we
detected change more often for HC communities than
at MC or LC communities. Extensive data sets like
those used in our analysis of LC, MC, and HC communities are helpful to demonstrate this technique;
however such data are often unavailable for communities of interest. Our intentions were to develop a null
model approach that can be used with a small number
of reference and target samples. Because it is a randomization technique there is no loss of statistical power with these small sample sizes (Solow 1993, Sokal
and Rolf 1994, Legendre and Legendre 1998).
The fundamental assumption made with our approach is that species variability (CV) in abundance
over time can be accurately predicted from abundance
estimates from reference samples. Given the strength
of the relationship between abundance and variation in
abundance for the species in the three community types
presented (stream fish, northern temperate lake zooplankton, and tallgrass prairie), this assumption appears
to hold across a wide range of community types and
is strong enough to generally assess change in the modeled communities. It is likely that similar relationships
can be established with other community types, given
the broad taxonomic range of organisms we examined
in this study and relationships reported from other systems and taxonomic groups (Ford 1938, Grossman et
al. 1990, Schoener and Spiller 1992, Winemiller 1996,
Windberg 1997, Matthews 1998). It also is possible
that the abundance CV in abundance relationships are
TABLE 2. The percentage of times that pairs of similarity metrics both detected either change
or no change in a sample (i.e., gave the same result) for all simulations with the first year
as the reference and 1.0 ⫻ CV.
Metric
PSI
Jaccard’s
Bray-Curtis
Morisita’s
NMDS
84.5
28.9
74.9
64.8
(91.6)
(53.0)
(89.7)
(78.2)
PSI
Jaccard’s
Bray-Curtis
38.2 (59.4)
85.4 (91.6)
79.8 (85.3)
47.5 (58.8)
58.4 (60.0)
77.7 (84.6)
Note: Numbers in parentheses indicate agreement at 0.5 ⫻
CV .
Morisita’s
ASSESSMENT OF COMMUNITY CHANGE
October 2005
1769
TABLE 3. The percentage of simulated target samples (time step 30) from random-walk simulations that were detected as significantly changed from a reference sample (time step 1)
for four metrics.
Simulated community
Metric
PSI
Jaccard’s
Morisita’s
Bray-Curtis
No change Two changed Six changed 12 changed Six extinct 12 extinct
1
0
0
0
(0)
(0)
(0)
(0)
2
0
6
15
(0)
(0)
(0)
(0)
22
0
42
44
(0)
(0)
(0)
(0)
100
0
100
100
Note: Model sensitivity was adjusted for 1.0 ⫻ (predicted
parentheses) as described in Methods.
transferable across systems. For example, the relationship between abundance and CV in abundance for
Oklahoma stream fish may apply to other midwestern
stream fish communities, thus, allowing a test for community change in any midwestern stream fish community with as little as one reference and one target
sample. The abundance CV in abundance relationships
for other community types could potentially be used
in the same way, making this a useful technique for
assessing change at sites that have not been intensely
studied in the past.
There are two important properties of this approach
that should make it useful to ecologists: (1) it employs
a Monte Carlo approach and (2) the model produces
expected communities that can be analyzed with any
index or metric of community similarity. We chose five
commonly used indices and metrics to represent qualitative (Jaccard’s), quantitative (PSI, Bray-Curtis) and
ordination (NMDS) approaches. It is clear that metric
selection will affect the results of the analyses. For
example, Jaccard’s index was much more sensitive to
change for the NTL-LTER community because it had
a large number of rare species that may not be detected
in a given year. Conversely, PSI and Bray-Curtis will
be much more sensitive to changes in the most abundant species in communities that are not as diverse and
numerically dominated by a few species. These trends
were also observed in analyses of the random-walk
simulations (Table 3). We contend that our approach
provides a framework with which an objective assessment of community change can be made and used with
multiple metrics. Even IBI (Index of Biotic Integrity)
scores can be generated for random communities to
test the null hypothesis of no community change. Because of properties specific to each metric (Boyle et al.
1990), we recommend using our approach with a variety of qualitative and quantitative metrics and using
the combined results to assess change in space or time.
By using multiple metrics (e.g., qualitative vs. quantitative), one can assess what types of change the community has undergone (extinctions vs. significant
change in abundances). At the same time, changing the
expected level of variability (CV) in the model will
yield information about the degree of change compared
to background levels of change in training samples.
(0)
(0)
(0)
(14)
CV )
1
1
0
1
(0)
(0)
(0)
(0)
1
100
1
1
and 2.0 ⫻ (predicted
(0)
(5)
(0)
(0)
CV )
(in
Reference sample accuracy and rare species
The usefulness of this technique relies on the accuracy of the mean abundance estimates in the reference sample. In our analyses we found that averaging
six samples through time provided accurate estimates
of long-term mean abundance with diminishing returns
when averaging more than six samples (Fig. 4). While
it is tempting to average many samples into the reference sample, this will inherently bias the results by
including more rare species than one would expect with
one unit of sampling effort. The addition of more rare
species will tend to bias the qualitative metrics more
than quantitative or other metrics that can be adjusted
to downweight rare species. This problem could be
addressed by random selection of a portion of rare species, essentially standardizing the sampling effort represented in a reference sample. An alternate approach
(one that is common used in community-level analyses;
see Grossman 1985) would be to simply eliminate or
downweight rare species. To examine what potential
effect this would have on the model, we chose one
community with a high proportion of rare species (annually burned KP-LTER community with 49 of 113
species not present in the reference sample) and performed simulations with rare species excluded. The
results of the analysis were similar for the quantitative
metrics (1993 sample not detected as changed by BrayCurtis, and 1995 sample not detected by as changed
by PSI) and identical for the qualitative metrics (even
though the mean Jaccard’s index in simulations increased more than any other, from 0.42 to 0.68). Overall, the presence or absence of rare species had little
effect on metrics that are heavily influenced by abundance data and had limited effect on metrics that are
influenced by presence/absence data.
A second problem with including rare species (zero
abundance in reference sample) is in how variability
over time is calculated. With an abundance of zero in
the reference sample and a predicted CV of 1.0 ⫻ CV,
the SD is undefined. In our simulations, we calculated
SD for these species as SD ⫽ CV ⫻ A where A was an
arbitrarily chosen constant (1.0 for our communities).
Thus, we included a low probability of occurrence and
an abundance estimate for species that were not cap-
1770
JACOB SCHAEFER ET AL.
tured in the reference sample, but were taken in one
or more target samples. Changing this value to something other than 1.0 will have little effect at all on
qualitative metrics but could drastically change results
from quantitative metrics. We chose the arbitrary value
of 1.0 because the abundance distributions generated
with this value fit two of our three communities (KPLTER and NTL-LTER; data not shown). In these communities, raw abundance values were corrected for volume or area and mean abundance over time of 1.0 (as
percent cover or number of organisms per 10 L) was
reasonable for these rare species. This value may not
have been optimal for the stream fishes since raw data
were reported as number of individuals per collection.
Thus, we assumed one individual of these rare species
to be caught over 10 sampling periods. This arbitrary
value is necessary if rare species are included in the
analyses as only rare species need this constant to estimate SD in abundance.
Another consideration is the length of the census
period from which estimates of population variability
are derived. For example, Pimm and Redfearn (1988)
demonstrated that estimates of population variability
increase with the length of the census period. It is therefore imperative that the temporal scale of the training
samples match the temporal scale over which community change is assessed. For example, testing for
community change over a three-year period with an
abundance–CV curve based on 10 years of data might
result in a test that is too conservative. In our data sets
all abundances (or relative cover) were calculated as
annual means and the CV–abundance curves generated
from training samples covering the full length of each
data set. One could therefore argue that our shorterterm comparisons (i.e., all but the last year at each site
in Fig. 3) are overly conservative. This could explain
why we observe more change in later years, but other
studies of the same data sets (e.g., plant communities)
using different techniques noted significant directional
change (Collins 2000).
In conclusion, a species mean abundance in reference
samples can be used to predict how variable that species
abundance should be over time. This relationship along
with a reference sample is used to generate random
communities one would expect in an undisturbed setting. We showed this null model can be used to test
for temporal community change using a variety of metrics and common statistical techniques. We also demonstrated, through the use of simulated data sets, the
sensitivity of different qualitative and quantitative indices of community change. The use of a variety of
indices and parameterizing the model with different
levels of species variability (i.e., 0.5, 1.0, and 2.0 ⫻
CV ) provides a context of community change to which
target communities can be compared to determine the
type and magnitude of change. Thus, with this flexible
framework, ecologists can quantify and statistically test
for community change. Such an assessment is not pos-
Ecological Applications
Vol. 15, No. 5
sible with current techniques. Although our data sets
focused on temporal changes, this approach also can
be used in a similar way to test for community change
in space with a null model based on a relationship
between abundance and variation in abundance in
space. Identifying spatial and temporal changes in community structure is critical for assessing stability of
communities subjected to anthropogenic and natural
disturbances or other drivers of change. Moreover, information on background variability in community
structure should prove useful to those making management decisions concerning disturbed systems that
have not been extensively studied.
ACKNOWLEDGMENTS
We thank Tim Essington, William Matthews, Edie MarshMatthews, Kurt Shulz, Jim Rusak, Don Jackson, and two
anonymous reviewers for assistance with this project at various stages. We thank SIUE Graduate School for funding.
Konza Prairie Long-Term Ecological Research grant and the
U.S. Geological Survey Gap Analysis Program provided support for K. B. Gido. The Knowledge Network for Biocomplexity project (DEB 99–80154) and National Center for Ecological Analysis and Synthesis, a Center funded by NSF
(DEB-0072909), provided post-doctoral support for M. D.
Smith.
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SUPPLEMENT
The program Com Sim: a Monte Carlo community simulator designed to test for community change is available in ESA’s
Electronic Data Archive: Ecological Archives A015-052-S1.