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OIKOS 103: 519–527, 2003
A mechanistic examination of diversity-stability relationships in
annual plant communities
Thomas J. Valone and Catherine D. Hoffman
Valone, T. J. and Hoffman, C. D. 2003. A mechanistic examination of diversitystability relationships in annual plant communities. – Oikos 103: 519– 527.
While recent theoretical work has demonstrated several mechanisms whereby more
diverse communities can exhibit greater temporal stability, empirical examinations
have been few and the subject of much debate. We show that the temporal stability
of natural summer and winter annual plant communities, at spatial scales of 0.25 m2
and 0.25 ha, tends to increase with community richness. Furthermore, more diverse
communities exhibited greater stability because they contained a greater abundance
of individuals (overyielding effect). Statistical averaging (the portfolio effect) and
negative covariances between species (insurance and competition effects) did not
enhance stability. Relationships between diversity and stability tended to be weak
and were significant only at the smaller spatial scale. Because more diverse communities contained higher densities of individuals, the effect of diversity per se on stability
was unclear and likely small. If overyielding is common in other ecological systems,
the loss of individuals and biodiversity may often result in increased variation in
ecological communities.
T. J. Valone and C. D. Hoffman, Dept of Biology, Saint Louis Uni6., St. Louis, MO
63103, USA ([email protected]).
How the number of species affects the stability of
communities has been long-debated in ecology
(MacArthur 1955, Elton 1958, Pimm 1984, Johnson et
al. 1996, Cottingham et al. 2001) and discussion has
intensified recently (Givnish 1994, Grime 1997, Huston
1997, Wardle 1999, McCann 2000) as interest in the
effects of species extinctions on ecosystem function has
heightened (Chapin et al. 2000, Schwartz et al. 2000,
Loreau et al. 2002). One aspect of the debate has
involved definitions because stability has been defined
in a variety of ways (Loreau et al. 2001). Various
workers have measured stability as 1) the degree of
change in an ecosystem following a perturbation (resistance), 2) the rate of recovery of an ecosystem following
a perturbation (resilience), and 3) the inverse of variance of a community property over time (invariability,
Schlapfer and Schmid 1999).
Much recent theoretical work has examined the effect
of diversity on community dynamics and thus has
focused on temporal stability (invariability) (Doak et
al. 1998, Tilman et al. 1998, Tilman 1999, Ives et al.
1999, 2000, Yachi and Loreau 1999, Hughes and
Roughgarden 2000, Lehman and Tilman 2000, Ives and
Hughes 2002). These models predict that the temporal
stability of communities should increase with diversity
and have revealed one statistical and several biological
mechanisms whereby more diverse communities can
exhibit greater temporal stability (see Cottingham et al.
2001 for review).
The statistical mechanism is known as statistical averaging, or the portfolio effect. Here, the variability of
an aggregate community property declines with increased diversity because the temporal fluctuations of
species in a community are not correlated (Doak et al.
1998, Tilman et al. 1998, Ives et al. 1999, 2000).
Several biological mechanisms also may dampen
community fluctuations as diversity increases. First, if
community evenness increases with diversity, the importance of statistical averaging should increase (Cottingham et al. 2001). Second, if many pairs of species
Accepted 23 April 2003
Copyright © OIKOS 2003
ISSN 0030-1299
OIKOS 103:3 (2003)
519
exhibit negative covariances in abundance, this will
reduce the variability in an aggregate community property: in different years, some species will be rare while
others are common and so the total community will
exhibit small fluctuations (Frost et al. 1995, Tilman
1999). This covariance effect can result from two biological mechanisms: species may compete strongly
(competition effect) or they may exhibit different responses to environmental variation (insurance effect,
Doak et al. 1998, Ives et al. 1999, 2000, Tilman 1999,
Yachi and Loreau 1999). And third, a reduction in the
temporal variation of a community property can occur
via an overyielding effect, an increase in the mean
community parameter with increases in diversity
(Tilman 1999, Hughes and Roughgarden 2000). When
overyielding occurs, the abundance of constituent species does not decline as community diversity increases
which tends to stabilize community fluctuations
(Tilman 1999, Hughes and Roughgarden 2000).
While some empirical studies have reported a positive
relationship between community diversity and the temporal stability of various community properties (Dodd
et al. 1994, Naeem et al. 1995, Tilman 1996, McGradyStead et al. 1997, Lehman and Tilman 2000, McGradyStead and Morin 2000), many of these studies have
been brought into question (Cottingham et al. 2001).
Empirical studies of natural communities have been
criticized for containing hidden treatment effects
whereby unmeasured variables covary with diversity
(Givnish 1994, Huston 1997, Loreau et al. 2001) while
studies of artificially created communities may contain
sampling biases in the selection of species and often
result in unnatural assemblages (Huston 1997, Hodgson
et al. 1998, Loreau 1998, Wardle 1998, 1999, Schwartz
et al. 2000, Cottingham et al. 2001). In addition, few
studies have examined explicitly mechanisms that produce greater stability in more diverse communities
(Schlapfer and Schmid 1999). And, while increasing
attention has focused on potential scale effects in biodiveristy-ecosystem function studies (e.g. Loreau et al.
2001), few studies of diversity-stability relationships
have examined the effects of scale.
Using a long-term data set, we examine relationships
between the temporal stability of community abundance (total number of individuals) and community
diversity in two different natural annual plant assemblages at two spatial scales to test the predicted effect of
diversity on community stability. Further, we evaluate
the mechanisms above to determine how more diverse
communities may exhibit greater temporal stability.
Methods
We examined the temporal stability of community
abundances of annual plant communities over an 11520
year period (1989 –1999) from a long-term study site in
southeastern Arizona, United States. The site contains
24 0.25 ha experimental plots subjected to different
experimental treatments that manipulate the number or
kinds of rodents and ants (Brown 1998). Two temporally segregated annual plant assemblages occur at the
site corresponding to the bimodal pattern of precipitation (Samson et al. 1992). The winter plant assemblage
germinates following winter rains and flowers and sets
seed in spring. The summer plant assemblage germinates in early July after the onset of summer rains and
flowers and sets seed in late summer. A total of 37
winter and 45 summer species have been recorded at
the site. On average, 27.6 winter and 21.7 summer
species are observed each year (Guo et al. 2002). Three
bi-seasonal species can occur in both communities.
However, only two of these species may be common in
some years and these species, if present, are common
typically in only one season (Guo et al. 2002).
Each plot contains 16 0.25 m2 permanent quadrats.
Twice each year, all annual plants were counted in each
quadrat, in spring and late summer, corresponding to
peak flowering time for the winter and summer annuals, respectively.
We used species richness as our measure of diversity.
Community abundance, which correlates strongly with
cover and biomass in this system (Ernest et al. 2000,
Guo pers. comm.), was the community property used to
calculate temporal stability. We calculated stability two
ways. First we calculated the coefficient of variation of
community abundance (CV) over the 11-year period.
The CV of aggregate community properties has been
used in other empirical studies and allows comparison
to other systems. Second, to examine more specifically
mechanisms that may affect stability, we used the
method of Lehman and Tilman (2000) to calculate the
temporal stability, ST of the community, where
ST =
'
% Abundance
(% Variances+ % Covariances)
where abundance and variances are summed over all
species in a community and covariances are summed
over all pairs of species.
This measure of temporal stability increases with
diversity if, all else being equal, more diverse communities 1) contain higher abundance (more individuals; the
overyielding effect), 2) have lower summed variances
(portfolio effect) or 3) have lower summed covariances
(competition and insurance effects) than low diversity
communities (Lehman and Tilman 2000, Cottingham et
al. 2001).
We examined the plant communities at the 0.25 ha
plot level by pooling data from the 16 quadrats on each
plot. We calculated mean species richness over the
OIKOS 103:3 (2003)
Table 1. Summary of ANOVA results of the effect of experimental treatments on species richness, temporal stability (ST),
and coefficient of variation of community abundance (CV) for
the summer and winter plant assemblages for the 24 plots.
Assemblage
Variable
F5,18
P
Summer
Richness
ST
CV
Richness
ST
CV
0.83
1.68
0.75
1.90
0.46
0.77
0.55
0.31
0.60
0.14
0.80
0.58
Winter
11-year period in each of the 24 plots, for both summer
and winter plants, as well as summed abundance,
summed variances of each species and summed covariances of all pairs of species using the 35 most common
species in each assemblage. This included all species in
most years.
To eliminate possible effects due to the experimental
treatments, and to investigate potential scale effects, we
also focused on the six unmanipulated plots: four control plots and two plots that remove Dipodomys
spectabilis. The later serve as additional unmanipulated
(control) plots because Dipodomys spectabilis has been
rare at the site since the late 1980s and locally extinct
since the early 1990s (Valone and Brown 1996). First,
we performed all of the above analyses on these six
unmanipulated plots. Second, we examined the local
plant communities on each of the 96 0.25 m2 quadrats
from these six plots. We calculated the mean richness
over the same 11-year period in each quadrat, for
winter and summer plants, as well as the summed
abundance, summed variances of all species and
summed covariances of all pairs of species in each
quadat.
Our use of the quadrats as independent communities
may raise some concerns. In the strictest sense, these
quadrats lack complete statistical independence but we
believe these analyses are warranted for three reasons.
First, they allow examination of the effects of diversity
on temporal stability in the absence of concerns about
possible hidden treatment effects because they come
from unmanipulated plots. Second, they allow examination of potential scale effects via comparison to the
plot-level analyses (Loreau et al. 2001). And third, their
use greatly increases the sample size of the analysis and
thus our power to detect significant relationships. Prior
examinations of diversity-stability relationships have
revealed weak relationships between community diversity and stability (McGrady-Stead et al. 1997). Thus, by
using the quadrat communities, we trade off some
degree of statistical independence for increased power
(Oksanen 2001). Accordingly, we modify our significance criterion to 0.01 for these analyses.
Results
Mean community richness, temporal stability and the
CV of community abundance all varied independently
of the experimental manipulations of the 0.25 ha plots
for both the summer and winter assemblages (Table 1).
Mean richness, stability and CV of community abundance differed significantly between summer and winter
communities. The winter communities were significantly more diverse and exhibited smaller fluctuations
than the summer communities at both spatial scales
examined (Table 2).
Diversity-stability patterns: all plots
Over all plots, the CV of community abundance declined with plot richness for both summer and winter
plant assemblages but neither relationship was significant (Fig. 1). Similarly, temporal stability increased
with diversity for both summer and winter assemblages
but not significantly (Fig. 2).
Because stability tended to increase with diversity, we
examined the mechanisms that generated these relationships. Both plant assemblages exhibited the same patterns: summed abundance tended to increased with
richness consistent with the overyielding effect, but the
relationship was only significant for the winter plants.
Table 2. Mean (SE) and range of species richness, temporal stability (ST) and coefficient of variation of community abundance
(CV) of summer and winter plant assemblages at both plot and quadrat scales. P-values indicate statistical differences using a
paired t-test for N = 24 plots and 96 quadrats.
Summer
Plot scale
Richness
ST
CV
Quadrat scale
Richness
ST
CV
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Winter
Mean (SE)
Range
Mean (SE)
Range
P
11.0 (0.3)
7.3 (0.3)
160.4 (6.1)
8.7–15.4
6.0–10.8
90–200
13.7 (0.3)
9.6 (0.4)
130.9 (3.1)
11.7–15.4
6.7–14.6
90–170
B0.001
B0.001
B0.001
3.0 (0.1)
6.1 (0.2)
190.7 (3.3)
1.1–5.5
4.4–9.6
120–290
4.7 (0.2)
9.2 (0.3)
150.2 (5.9)
1.7–6.9
4.7–14.2
80–260
B0.001
B0.001
B0.001
521
dance of plants increased significantly with mean richness, consistent with the overyielding hypothesis. In
contrast, we found weak positive (destabilizing) relationships between summed variances and summed covariances and quadrat richness (Fig. 7 and 8). Thus, the
overyielding effect alone conferred higher temporal stability on more diverse quadrat communities.
For both plot- and quadrat-scale analyses, we found
no evidence that statistical averaging enhanced the stability of more diverse communities. Recall that the
statistical averaging effect will be enhanced if community evenness increase with diversity. To examine this
relationship, we analyzed data from one high and one
low diversity year for each assemblage. For both assemblages at both scales, evenness was either independent
of, or declined significantly, with diversity (Table 4).
Other years exhibited similar patterns.
Discussion
For both plant assemblages, and at both spatial scales
examined, more diverse communities tended to exhibit
greater temporal stability. However, significant relaFig. 1. Relationships between coefficient of variation of community abundance (CV) and mean community richness for the
(A) summer and (B) winter plant assemblages for the 24 0.25
ha plots. Smaller CV indicates greater stability. Each letter
represents one plot assigned to the following experimental
treatments: A – ant removal; C – control, D – kangaroo rat
(Dipodomys) removal, R – rodent removal, DA – kangaroo
rat and ant removal, RA – rodent and ant removal.
Both summed variances and summed covariances increased weakly with richness and thus acted to destabilize more diverse communities (Fig. 3 and 4).
Diversity-stability patterns: unmanipulated plots
and quadrats
Restricting analyses to the six unmanipulated plots
yielded similar results to those obtained from all 24
plots. For both summer and winter plants, CV of
community abundance declined with richness while
temporal stability, summed abundance, summed variances and summed covariances all increased with richness (Table 3, Fig. 1 –4). Only the relationship between
richness and summed covariances for the summer
plants was significant.
At the smaller quadrat scale, both the CV of community abundance and temporal stability varied significantly with diversity. The CV of community abundance
declined significantly and temporal stability increased
significantly both plant assemblages (Fig. 5 and 6).
And, in both plant assemblages, the summed abun522
Fig. 2. Relationships between temporal stability and mean
community richness for the (A) summer and (B) winter plant
assemblages for the 24 plots. Temporal stability is the calculated ST value of Lehman and Tilman (2000). Larger temporal
stability indicates greater stability. See Fig. 1 for plot symbols.
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found significant variation in community properties
over a small range of diversity (S& paèková and Lepš
2001). Instead, we think the most likely explanation for
the lack of significance at the larger plot scale is the
Fig. 3. Relationships between summed (A) abundance, (B)
variances and (C) covariances of summer plant communities as
a function of mean community richness for the 24 plots. The
overyielding, portfolio and covariance effects would correspond to significant positive, negative and negative relationships, respectively while observed relationships are all positive.
See Fig. 1 for plot symbols.
tionships were restricted to the smaller spatial scale of
the quadrat communities. One explanation for the difference between the plot- and quadrat-level conclusions
is that scale affects diversity-stability relationships.
While spatial scale can strongly affect many ecological
phenomenon (With and Crist 1996, Ludwig et al. 2000,
Whittaker et al. 2001), we think that explanation unlikely in this case because all patterns observed were
consistent between the plot and quadrat analyses (compare Fig. 1 –4 with 5–8). A second explanation is that
the variation in species richness on plots was too small
to detect significant trends. While greater variation in
richness would provide greater statistical power, note
that the range in species richness was similar across
both plots and quadrats and that other studies have
OIKOS 103:3 (2003)
Fig. 4. Relationships between summed (A) abundance, (B)
variances and (C) covariances of winter plant communities as
a function of mean community richness for the 24 plots. The
overyielding, portfolio and covariance effects would correspond to significant positive, negative and negative relationships, respectively while observed relationships are all positive.
See Fig. 1 for plot symbols.
Table 3. Correlation coefficients and associated probabilities
for relationships between richness and coefficient of variation
of community abundance (CV), temporal stability (ST),
SAbundance, SVariances and SCovariances for both plant
assemblages for the n =6 unmanipulated plots.
Variable
Summer
R
CV
ST
SAbundance
SVariances
SCovariances
−0.71
0.66
0.64
0.24
0.88
P
0.12
0.15
0.17
0.62
0.02
Winter
r
−0.27
0.18
0.48
0.10
0.45
P
0.60
0.82
0.33
0.98
0.50
523
Fig. 5. Relationships between coefficient of variation of community abundance (CV) and mean community richness for the
(A) summer and (B) winter plant assemblages for the 96 0.25
m2 quadrats from unmanipulated plots. Smaller CV indicates
greater stability.
weak nature of the relationships between diversity and
stability. The amount of variance explained in our
diversity-stability correlations ranged from 3 to 10%,
values intermediate with respect to other published
relationships (Tilman 1996, McGrady-Stead et al.
1997). Detecting significance of such weak relationships
thus requires the larger sample sizes provided by the
quadrat-level analyses.
Previous empirical studies of the effect of diversity on
temporal stability have been criticized for containing
hidden treatments effects and sampling biases, and for
creating unnatural assemblages (Loreau et al. 2001).
For example, in perennial plant communities, individual species can differ greatly in life history and biomass
such that only a few high-biomass perennial species
may be present in a community. As such, species-rich
communities are more likely to contain species with
high biomass than species-poor communities. Thus,
mean plant biomass will often covary positively with
community richness and therefore increased biomass
rather than increased richness may confer greater temporal stability on more diverse communities (Huston
1997). Experimentally constructed communities can
524
similarly contain hidden treatment effects, because
community construction requires selecting sub-sets of
species to compare communities that differ in richness.
If individual species differ in biomass and high biomass
species are rare, species-poor communities will, on average, contain lower average biomass than species-rich
communities (Givnish 1994, Huston 1997). Furthermore, artificially constructed communities often exhibit
unnatural evenness in the abundances of species
(Schwartz et al. 2000).
While caution is required when interpreting correlations such as ours, the above criticisms are less cause
for concern for three reasons. First, variation in community diversity and evenness resulted from natural
variation across the site and was not influenced significantly by the experimental manipulations. Second, our
communities consisted of natural assemblages of plants
of similar life history and relative biomass; there were
no perennial, high-biomass species in these communities. And third, the positive relationships between community diversity and temporal stability were observed
at two spatial scales, including quadrats within unmanipulated control plots. We acknowledge that in our
study, diversity was not manipulated and so we cannot
examine the effect of diversity, per se, on community
stability because unmeasured variables likely covaried
with diversity. However, our approach does allow testing of the predicted relationship between diversity and
Fig. 6. Relationships between temporal stability and mean
community richness for the (A) summer and (B) winter plant
assemblages for 96 quadrats from unmanipulated plots. Temporal stability is the calculated ST value of Lehman and
Tilman (2000). Larger temporal stability indicates greater stability.
OIKOS 103:3 (2003)
(Lehman and Tilman 2000). Positive covariances suggest that most species responded similarly to environmental fluctuations as might be expected in this system;
in arid environments, increased amounts and more even
distributions of precipitation generally result in increased numbers of individuals and species of annuals
(Ernest et al. 2000). As such, most species were abundant or rare in wet and dry years, respectively, resulting
in positive covariances over the 11-year time period,
regardless of possible competitive interactions.
The importance of competitive interactions in influencing community stability also has been the subject of
much theoretical work (Ives et al. 1999, 2000, Hughes
and Roughgarden 2000, Lehman and Tilman 2000).
While we cannot address this directly, competitive interactions among annual plants can be strong at the
scale of the 0.25 m2 quadrats that we examined (Guo et
al. 1998). Our quadrat-scale analysis therefore would be
more likely to detect the influence of competition, if
present. However, the lack of covariance effects at that
scale suggests that local competitive interactions did not
strongly influence the relationship between diversity
and temporal stability.
Theoretical treatments of the effect of diversity on
community stability have paid the least attention to the
overyielding effect although overyielding is considered
Fig. 7. Relationships between summed (A) abundance, (B)
variances and (C) covariances of summer plant communities
and mean community richness for 96 quadrats from unmanipulated plots. Note the similarity to the patterns in Fig. 3.
community stability in natural systems as well as examination of various theoretical mechanisms that are predicted to enhance stability in more diverse
communities.
Many theoretical treatments have focused on the
portfolio and covariance effects for demonstrating how
greater diversity can confer greater temporal stability
(Doak et al. 1998, Tilman et al. 1998, Tilman 1999, Ives
et al. 1999, 2000, Yachi and Loreau 1999, Hughes and
Roughgarden 2000, McCann 2000, Loreau et al. 2001).
We found no evidence of a decline in summed variances
or covariances with increased community diversity and
so neither effect contributed significantly to the greater
stability observed in higher diversity communities. In
retrospect, this should not be too surprising because
our communities violated an important assumption of
both the portfolio and covariance effects: fixed community abundance (Doak et al. 1998, Lehman and Tilman
2000); in the annual plant communities examined, more
diverse communities contained a greater number of
individuals. In addition, community evenness declined
significantly with diversity, further weakening the
strength of the portfolio effect (Cottingham et al. 2001).
In fact, summed covariances in our system tended to
be positive rather than negative as is typically assumed
OIKOS 103:3 (2003)
Fig. 8. Relationships between summed (A) abundance, (B)
variances and (C) covariances of winter plant communities and
mean community richness for 96 quadrats from unmanipulated plots. Note the similarity to the patterns in Fig. 4.
525
Table 4. Summary of relationships between evenness and community richness for both plant assemblages in one low and one
high diversity year. Slope characterizes the nature of the relationship between evenness and diversity. In low diversity years,
sample size for quadrats is less than 96 because some quadrats contained no plants.
Assemblage
Year
Scale
Mean Richness
Slope
P
N
Summer
1990
Plot
Quadrat
Plot
Quadrat
Plot
Quadrat
Plot
Quadrat
17.7
7.0
7.4
2.2
16.0
4.2
19.9
7.9
−0.02
−0.59
−0.58
−0.70
−0.26
−0.47
0.01
−0.54
0.93
B0.001
0.003
B0.001
0.22
B0.001
0.95
B0.001
24
96
24
72
24
90
24
96
1996
Winter
1991
1993
to be an important component of relationships between
diversity and productivity (Hector et al. 1999, S& paèková
and Lepš 2001). In our communities, overyielding was
the sole mechanism that led to greater stability in more
diverse communities. In fact, overyielding was sufficiently strong to overcome the destabilizing effect of the
positive summed covariances observed.
Our results suggest that overyielding may be an
important mechanism that affects the stability of natural communities. The generality of this mechanism,
however, remains to be determined. It may be the case
that overyielding occurs mostly in annual communities
and is rare in communities of perennial species. In our
arid system, seasonal precipitation strongly affects the
number and diversity of individuals in communities and
this resulted in a strong overyielding effect. However,
we suspect that in nature, community diversity in many
systems likely will often covary with factors such as
productivity and disturbance that are known to influence the abundance of species (Sankaran and McNaughton 1999). The abundance of individuals in a
community tends to increase with productivity (Wright
1983, Rosenzweig 1995, Kaspari et al. 2000, Valone and
Hoffman 2003) suggesting that more productive habitats will often have greater densities of individuals and
higher diversity of species, and these communities may
also exhibit greater temporal stability as a result of
overyielding. As such, the greater temporal stability of
species-rich communities may result because of increased abundance rather than increased diversity. Future work should focus on disentangling the causal
relationship between community abundance and community richness (Kaspari et al. 2000, Hubbell 2001) to
understand more fully the effects of abundance, as well
as diversity, on temporal stability.
The accelerating extinction rate has raised concern
among ecologists about the effects of species losses on
ecosystem properties (Chapin et al. 1997, Grime 1997).
Our work suggests that species-poor communities will
often exhibit greater fluctuations in abundance than
species-rich communities, owing to a lower number of
individuals. In such systems, maintaining a high total
abundance of individuals as well as a large number of
species will stabilize fluctuations in ecological
communities.
526
Acknowledgements – Thanks to J. H. Brown, S. K. M. Ernest
and M. Kaspari for helpful comments. Data collection was
supported by NSF grants, most recently by DEB-0211069.
C.D.H. was supported by a SLU 2000 research assistantship.
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