Folia Geobot. Phytotax., Praha, 30: 231-242, 1995
QUANTIFYING THE COMMUNITY-LEVEL CONSEQUENCES
OF COMPETITION
Deborah E. Goidberg 1), Roy Turkington 2) & Linda Olsvig-Whittaker 3)
1) Department of Life Sciences, Ben Gurion University, PO.B. 653, Beer Sheva 84105, Israel;
Current address: Department of Biology, University of Michigan, Ann Arbor, M148109, USA;
E-mail DEGOLD@ UMICH.EDU
2) Department of Botany, University of British Columbia, Vancouver, B.C., V6T lZ4, Canada;
E-mail RO YT@ UNIXG. UBC. CA
3) Mitrani Center for Desert Ecology, Blaustein Institute for Desert Research, Sede Boqer Campus 84990,
Israel; Current address: Nature Reserves Authority, 78 Yirmiahu Street, Jerusalem, Israel;
E-mail LINDA @BG UMAIL BGU.A C.IL
Keywords: Community-density experiments, Competition, Perennial grasslands, Plant communities,
Productivity gradients. Species composition, Species diversity, Yield-density experinaents
Abstract: Changes in plant community structure after changes in some aspect of the environment such as
nutrients or grazing is often ascribed to changes in competitive relationships among the plants. However, very
rarely is competition measured directly in such experiments. To distinguish between the direct effects of
environmental treatments and changes in competitive relationships, it is necessary to quantify the influence of
competition on community structure and compare the magnitude and direction of this influence between
environments. We describe an experimental approach to accomplish this that is based on the classic yield-density
experiment of agronomy. The approach is called the community-density experiment and requires experimental
establishment of a gradient in total initial community density such that absolute densities of each species
increase but initial relative abundances of each species stay constant along the gradient. We define various
indices of the magnitude of community-level consequences of increasing density that can be compared among
environments such as different fertilizer or grazing treatments. We also discuss various practical ways of
achieving the experimental density gradient that are suitable for different kinds of communities.
INTRODUCTION
Numerous studies have measured the impact of various environmental treatments on plant
community structure, including many of the papers in this symposium. Such studies often
attribute changes in species composition or diversity among environments to changes in
competitive interactions (WILSON 1978, FRENCH 1979). A large literature documenting the
occurrence of competition in plant communities in general and in grasslands in particular is
certainly consistent with this assumption (RaSSER 1969, FOWLER 1986, AARSSEN & EPP 1990,
TURKINGTON & MEHRHOFF 1990, GOLDBERG & BARTON 1992). However, almost no studies
have actually distinguished between the effects of competition and the direct effects of the
environmental treatments on COmmunity structure. One or both of two necessary components
for such tests are usually lacking: (a) quantification of the effects of competition alone on
the entire community rather than on one or a few selected target species (see CONN'ELL1983,
232
D,E. Gotdberg et al.
SCHOENER 1983, GUREVrrCH& UNNASCH1989, GOLDBERG& BARTON1992), and (b) direct
assessment of the difference in magnitude of the effects of competition among environments,
i.e., tests of a competition x environment interaction (GOLDBERG& BARTON1992, GOLDBERG
t~r SCHEINER 1993).
The lack of direct tests of community-level consequences of competition may be due to
the lack of appropriate experimental designs or analytical approaches. The relatively few
existing experiments on community-level consequences of competition all use a similar
approach: removal of a single species at a time (usually a dominant) and measurements of
abundance or diversity of the remaining species (review in GUREVITCH& UNNASCH 1989,
GOLDBERG& BARTON 1992). While a very useful method for assessing the influence of the
dominant on the rest of the community, this approach does not assess interactions among all
the species in the community. GOLDBERG(1994) suggested an alternative approach that requires
experimental low-density monocultures of all species that occur within the community as
well as an additive mixture of all species; this approach is obviously feasible only for relatively
simple communities (see also JOLn~FE et al. 1984 for a related technique for pairwise
interactions). In this paper, we describe a very different experimental approach called the
community-density series that is suitable even for highly diverse communities because it does
not require separate monoculture experiments for all species in the community. We then
discuss how the method can be used to distinguish between alternative hypotheses about
patterns in the magnitude of competition over gradients such as predation, disturbance, and
productivity (e.g. CONNELL 1975, GRrME 1973, 1988, MENGE & SUTHERLAND 1976, 1987,
NEWMAN 1973, OKSANENet al. 1981, SOUTHWOOD 1977, 1988, TILMAN 1988). Finally, we
will discuss specific application of the design to perennial grassland systems.
THE COMMUNITY-DENSITY SERIES
The basic experimental approach is a simple extension of the single species yield-density
experiment to multi-species assemblages. In a typical yield-density experiment, seeds of a
single species are sown over a wide range of densities and yield is measured at some point,
in time (usually the end of a growing season) (HARPER1977, chapter 6). Typical results for
total biomass yield exhibit three phases along a gradient of planting density (Fig. 1). At low
planting densities, the final biomass yield is strictly proportional to initial planting density,
indicating no effects of competition in this linear phase. Above some threshold density (DD,
the slope changes from linear to positive but with a negative second derivative, i.e., biomass
continues to increase but the amount of increase with each added individual declines with
increasing density, indicating some competition. Finally, above a second threshold density
(Din), further increases in initial planting density do not result in any further increase in
biomass, i.e., a biomass carrying capacity (Brn) is reached. All these changes in total biomass
yield as a function of initial planting density could be either a function of mortality (final
density < initial density) and/or differential growth (smaller individuals at higher density, i.e.,
plasticity).
An experiment using the community-density series is analogous to a yield-density
experiment, except that the initial density of the entire community rather than the density of
a single species is manipulated. The absolute density of the entire community and of each
species changes along the community density gradient, but the relative initial density of each
Community-level consequences of competition
233
species stays constant. One can then plot
total community yield along the initial
community density (ICD) gradient to
determine the threshold density at which
competition
starts
to
influence
community biomass or other measures of
total yield (Dc), as well as the asymptotic
IT.
total community yield or carrying
capacity (Bin; Fig. 2a). More complex
community parameters can then be
related to the experimentally-extended
gradient of initial community densities
Initial dens~
(Fig. 2b). Of primary interest are
parameters
describing
species
or
functional group composition such as Fig. 1. Typical results from a yield-density experiment,
indices from multivariate ordinations where yield is measured as total biomass. In a yield-density
experiment, seeds of a single species are planted at different
(e.g. canonical correspondence analysis; densities and a measure of final yield is plotted as a function
TER BRAAK 1987-1992). However many of initial planting density. The results show 3 phases defined
other parameters could be used ranging by the two threshold densities Dc and Din. At densities less
from relatively simple ones such as than Do yield is a linear function of planting density,
diversity or dominance indices to more indicating no competition. At densities between Dc and Din,
yield still increases with planting density, but at an
complex indices of spatial patchiness in
ever-decreasing rate, indicating some competition. The
species composition.
addition of a single individual adds a smaller increment to
The basic assumption
of the total biomass at high density than at lower densities. At Din,
community-density series is that the total yield reaches an asymptotic value (Bin) where
potential
for
interactions
among increasing density has no further effect on yield. Bm is a
individuals increases with increasing biomass carrying capacity.
density. If this assumption is correct, the
value of the community parameters at low ICD (below Dc) characterize the "null community"
(ZOI3EL 1992), i.e., what the community would look like in the absence of competitive
interactions among individuals. As initial community density increases above De, deviations
of the community parameters from these null values indicate the consequences of interactions
among individuals at the community level (Fig. 2b). As with any experiment manipulating
density, these interactions can be positive (facilitative) or negative (competition) and results
only indicate the net outcome of all such interactions. However, because this net effect is
typically negative and, for convenience, we will simply refer to competition or the effects of
competition.
For any particular community parameter, several indices from these graphs can be used to
quantify the magnitude of the effects of competition on a single community in a single
environment, and to compare these magnitudes among communities or environments:
The threshold density at which competition begins, De
Dc is the density at which a deviation from strict linearity becomes apparent in yield-lCD
relationships (Fig. 2a) or at which a deviation from a flat line (slope = 0) becomes apparent
in relationships between other community parameters and ICD (Fig. 2b). For example, we
234
D.E. Goldberg et al.
(a)
Bm
De
Dn
Dm
initial oommunity density
(b)
could hypothesize that Dc for biomass
yield will be lower in more productive
environments because individuals are
larger and therefore will begin to overlap
in zones of influence at a lower density
than in less productive environments.
Alternatively, we could argue, perhaps
less convincingly, that the threshold
density will be higher in more productive
environments because resources are more
available and thus it takes more
individuals to reach a point where the
resources are depleted and become
limiting.
The slope of the relationship between
some community parameter and initial
community density, for ICD > Dc
r
Larger absolute values of this slope
indicate
bigger effects of competition. For
E
simplicity, Fig. 2b depicts the curve as
linear once ICD is greater than Dc but
there is no reason to expect such strict
13
Dn
Dm
linearity. In addition, depending on the
Initial community density
community
parameter
under
Fig. 2. Hypothetical results from a community density series consideration, competition could be
experiment for (a) final biomass yield and (b) other indicated by positive or negative slopes.
community parameters such as diversity or dominance. Dc
is the competition threshold density: i.e., the density at For diversity measures, we usually expect
which we first detect deviation from linearity in increasing density to increase competitive
biomass-initial density relationships or deviation from exclusion, thereby reducing diversity.
slope = 0 (flat lines) in other community parameter-initial Thus, a negative slope is predicted (but
density relationships. Dn is the mean naturally-occurring see below for special problems in testing
density of the community. Dm is the density at which the species richness). However, for indices of
asymptotic total community bioma.ss is reached. En is the
difference in the community parameter between no community composition, species or
competition (ICD < Dc) and natural density (Dn); i.e., the groups of species that are good
magnitude of the effect of competition at natural density. competitors will, by definition, increase
in relative abundance with ICD, and
therefore exhibit a positive slope with
ICD, while poor competitors will exhibit a negative slope.
The deviation of the community parameter between the null community and natural density, En
Comparisons of threshold densities or slopes only assess the potential for competition to
affect the community at a given ICD. To assess whether competition actually influences the
community in the field, it is necessary to locate the position of the natural range of ICD values
(Dn in Fig. 2) on the full ICD gradient and then calculate En, the difference in the value of
various community parameters between Dn and any ICD < De. Qualitatively, we can also ask
Community-level consequences of competition
235
if the typical range of Dn values for a given
community falls above or below Dc for that
environment? Or, because density is
typically very patchy in real plant
communities, what proportion of patches in
the field have ICD values above or below
~B
the threshold competition value?
" "-.
The community-density series can yield
A
a wide diversity of results from even a
simple comparison of the effects of
Dn(A)
On(B)
competition among only two different
Initmlr
density
environments or community types. First, it
is possible that these three indices (Dc,
Fig. 3. A hypothetical example of different results of a slope, En) can give very different results
comparison between two environments (A and B) when when compared among communities or
two different indices of community-level effects of
competition are compared. In this example, the environments. For example, Fig. 3 shows a
per-individual effect on diversity (slope) is higher in case where environment A has a steeper
environment A, but the effect at natural density (En) is slope of species diversity vs. ICD than does
higher in environment B because the naturally-occurring environment B once past the threshold
density is so low in environment A (e.g., because of density, which is similar for both
herbivory or disturbance).
environments. However, the naturally-occurring ICD in environment A (Dn (A))
is so low that competition barely occurs at all, reflected in the very small value for En (A).
Such a low/9,, could be due to low productivity or high rates of disturbance or herbivory.
Second. a single index such as Dc or En could differ among community parameters when
compared among the same set of environments or communities. Fig. 4a shows an example
where total community biomass is first affected by competition at lower densities in
environment B[Dc (B) < Dc (A)], while species composition (Fig 4b) is first affected at lower
densities in environment A [De (A) < Dc (B)]. Such a scenario might arise if species were
more similar in competitive ability for the limiting resource in environment B so that, although
individual growth is strongly reduced at even relatively low densities in environment B, this
reduction is similar enough among species that no species have strong advantages over others
that would result in a change in their relative abundances. At high enough density, however,
even small differences among species will have an impact on their relative competitive ability
and species composition will be affected even in environment B.
Third, comparisons among communities or environments are straightforward when they
have similar values of the community parameter in the null communities (no competition) as
in Figs. 3 and 4. However, if values are not similar, comparisons could be made in two ways:
(a) the absolute difference between no competition and a higher ICD for both communities
[D,~ (A,B); Fig. 5a] or, (b) a relative difference, where values at high competition are
standardized to values at low competition (Fig. 5b). This standardization could have a big
impact on patterns of community-level effects of competition (GOLDBERG 8s SCHEINER 1993,
GRACE 1993). For example, in Fig. 5, community A has a lower diversity than community
B even at the lowest ICD, although they have similar natural densities. When compared in
i V~Bi
.
.
.
.
.
.
.
.
.
.
236
(a)
D.E. Goldberg et al.
absolute terms, En is similar between the two
communities (Fig. 5a). However, in relative
terms, the effect is much larger in community
.,'-'"" .................................................. B
A (Fig. 5b).
The examples in Figs. 3-5 of differences
in interpretation among different parameters
or indices of the magnitude of the effects of
competition in communities suggest that
o~)
oc(A)
extreme caution must be used in testing
hypotheses
about
patterns
among
InJt~ oomn~n~
environments
or
community types.
(b)
Empirical tests of an hypothesis must use
indices and parameters that match those on
which the hypothesis is based. For example,
depending on whether an absolute or relative
index was used, both CAMPBELL& GRIME
(1992) and TURrdNGTONet al. (1993) found
contrasting results for patterns in the effects
of competition at the population level along
nutrient
and
disturbance
gradients.
tO(A)
De(a)
CAMPBELL
&
GRIME
(1992)
argued
that
Inllialcommunitydensity
GRIME'S (1977) prediction of smaller effects
Fig, 4. A hypothetical example of different results of a of competition at high disturbance or low
comparison between two environments when different nutrients (high stress) is based on having less
community parameters (but the same index) are
absolute biomass of competing plants and
compared. In this example, the competition threshold
density (De) is higher in environment A for final yield therefore only the absolute index was
(a) but higher in environment B for a species appropriate. WILSON 8z TILMAN (1991),
composition index (b).
however, used a relative index to test the
same hypothesis. While this may be
inappropriate in terms of testing GRIME'shypothesis, the absolute index will usually necessarily
be higher in more productive environments (GRACE 1993) and so the hypothesis may itself
be trivially true.
For most community parameters, the above analyses are straightforward in principle, even
when the parameters themselves are the result of a complex analysis such as a multivariate
ordination to characterize species composition. However, quantifying the effect of density on
the number of species and other measures of diversity presents a special problem in analysis
because increasing density effectively increases sample size. Therefore, all else being equal,
the number of species should increase with density (up to some value) simply because more
individuals are sampled. This sampling effect may well overwhelm or at least partially
counteract the negative effect of density on species diversity that is expected because of
increa,~ing competitive exclusion or at least increasing dominance.
The problem of comparing species richness between samples with different numbers of
individuals may be solved by using the rarefaction technique, first introduced by SANDERS
(1968) and later corrected by HURLBERT(1971) and SIMBERI-.OFF(1972). The technique
estimates the number of species expected in a random sample of individuals taken from some
Community-level consequences of competition
(a)
|
i
D n (A,B)
Ir~aJcomnu~ den~
(b)
J
o n ~,~
Jnit~ ~
~
237
larger pool, thus making it possible to
generate an entire curve of species richness
estimates as a function of sample size. This
expected curve of purely sampling effects
can then be compared to the observed
curve of richness versus ICD. If increasing
density increases the potential for
competitive exclusion, the difference
between the expected and observed curves
of richness vs. density should increase with
ICD. KREBS (1989) summarizes the
rarefaction method and provides a
FORTRAN computer program for doing
the calculations. The major potential
problem in applying the method is deciding
what constitutes the larger pool that is used
to generate the expected curve of richness
vs. ICD. Ideally, the species composition
of the initial community should be pooled
along the ICD gradient, because this is
measured before any interactions occur.
One additional problem is that if species
are aggregated due to noncompetitive
interactions, the actual number of species
per unit area may be less than the expected
number, even in the absence of any
competitive effects (J. LEPL pers. comm.).
Fig. 5. A hypothetical example of different results of a
comparison between two environments (A and B) when
absolute (a) vs. relative (b) values of a community
parameterare compared. In this example,speciesdiversity C A R R Y I N G O U T T H E DESIGN
is lower in environment A at all initial communitydensity
There are two main practical issues
(ICD) values, although the threshold competition density
associated
with using the community(Dc), natural density (Dn), and diversity-lCD slope are
-density
series:
(a) defining initial densities
identical in the two environments. However, if the
and
(b)
manipulating
initial community
diversity values are standardized to a percentage of the
value in no competition, the diversity-ICDslope is steeper density while keeping initial relative
in environment A. Consequently the magnitude of the abundances constant. In this section, we
relative effect at natural density (En) is also greater in
suggest methods for both of these, with a
environment A.
special emphasis on perennial grassland
communities.
Defming initial density. It is important to use a gradient of initial, rather than final, density
to define the gradient in potential interactions because competition can cause mortality and
this mortality is often differential among species. Therefore relative abundances of species
are unlikely to be the same along a gradient in final community density. However, when
establishing an initial community density gradient, "initial" can mean a variety of things,
depending on life histories of the organisms and the time scale of observation. For an annual
238
D.E. Goldberg et al.
plant community, seed density will generally be the most appropriate stage so that any
density-dependent germination can be taken into account. For conununities of long-lived
perennials, "initial" can mean the beginning of a given growing season (e.g., density of all
ramets) or it could be the density at the initiation of succession after some major disturbance,
in which case seed density is again the relevant stage. Regardless of life history stage, it is
not necessary that "initial community density" be an actual density count of individuals; other
measures of abundance such as initial cover, initial biomass, or initial number of ramets could
also be used. It is also not necessary that the measure used for initial abundance be independent
of past effects of competition because the community-density series only quantifies subsequent
effects of competition in any case. However, it is necessary that any past effects of competition
are constant along the current competition gradient (i.e. constant with experimental ICD).
Generating an ICD gradient. The critical aspect of generating an ICD gradient is that
initial relative abundances of each species are constant along a gradient where their absolute
abundances are increasing. This allows any subsequent differences in relative abundances or
diversity to be ascribed to the effects of density. Natural gradients in total community density
are not satisfactory because the differences in ICD among locations may be due to some
environmental factor that could directly influence the magnitude of the effects of competition
or initial relative abundances, Therefore it is necessary to manipulate total community density
in common conditions. There are a number of ways this could be done, each with different
advantages and limitations and suitable in different types of communities and/or for different
questions.
(I) Using mixtures of propagules (usually seeds) and adding different amounts of this
"concentrated community" to achieve a range of densities from below to above natural density.
These propagule mixtures can be obtained in several ways:
(a) Extract the seedbank from soil and litter. We have been successfully using this technique
to manipulate initial community density in experiments with sand dune annuals in Israel.
Sand is a particularly easy matrix to work with because it can be removed or added and so
used to concentrate or dilute the seedbank but KROPA(2(1966) and ROBERTS(1981) describe
techniques for separating the seedbank from other soil types. NEILL (pers. comm.) has used
a similar technique with plankton communities from freshwater lakes. The seedbank extraction
technique is most appropriate for annual communities that start from seed every year or for
studying the succession of perennial grasslands or other communities after a soil disturbance.
(b) Collect current year's seed production by harvesting seed heads before seed release.
This would ensure that only species represented as mature adults in the local community are
included and so probably exclude many ruderal species that have either dormant seed in the
soil or widely dispersed seed. This would be appropriate for examining the potential of
seedling-seedling interactions within a perennial community to influence the adult community
structure (does differential success in seedling interactions correspond to patterns in adult
relative abundance?).
(c) In managed pastures, use the recommended mixture from seed suppliers.
Regardless of seed collection method, starting the community from seed measures the
effect of competition on community development and therefore is most suitable for questions
about competition and succession or the influence of initial conditions. Across generations,
we would expect initially low density plots to have high per-capita reproduction and therefore
catch up in density relatively rapidly. However, do the different initial densities give different
Community-level consequences of competition
239
species an initial advantage, which carries through subsequent generations? I.e., are there
persistent effects of initial density on successional patterns and how long do these effects
last? The mixed propagule approach is obviously not appropriate if the question concerns the
effect of competition on an already existing community because relative competitive abilities
among species (and therefore the community-level consequences of competition) may differ
depending on whether adult-adult, adult-seedling, or seedling-seedling competition is
considered (GOLDBERG1990). For such questions, manipulation of density of established
plants as described in the next section will be more appropriate.
(2) Removing/adding established individuals. Alternatively, a protocol for removing or
adding individuals can be established that would maintain relative abundances while
decreasing or increasing total density; the latter would be more limited especially in
communities which are visually quite saturated with few openings. For example, to achieve
a density half that of natural, remove every second individual encountered of each species.
Such removal experiments would have all the problems attendant on any removal experiment,
such as potential artifacts of roots left in the ground that may either release or immobilize
nutrients during decomposition [e.g., TURKINGI"ON1989, although MCLELLAN et al. (1995)
found these effects to be fairly minor in a recent study]. A removal experiment is particularly
difficult to interpret in communities with highly clonal organisms for two reasons: (a) it is
sometimes difficult to know whether one is removing competitors that are preempting resources
from some target individual or removing ramets still connected to the target that may be
donating resources to the target, and (b) it is difficult to remove individuals completely because
of clonal connections or underground perennating tissues and therefore regrowth of"removed"
competitors often occurs. If species differ in amount of regrowth, this is particularly
problematical for the community density series where it is critical to control relative species
abundances. Species with such potential for regrowth will have a biased representation in the
developing manipulated community and their abundance will be less a reflection of competitive
ability than a result of poor experimental protocol.
An addition experiment could be tractable in a community with gaps in the vegetation, i.e.
where the individual plants are spaced. There may be some difficulties, however, in
communities with continuous vegetation cover. Firstly, the actual act of transplanting may
damage existing individuals. Secondly, it may not be feasible to appreciably increase the
density above natural levels. Nevertheless, even in communities which have apparently
continuous cover such as pastures or temperate grasslands, upon close inspection it is common
to find numerous small spaces at ground level. These may be adequate to increase densities,
and to do it without damaging existing individuals. Thirdly, in patchy field plots there is the
potential for integration effects from parts of a plant living in poor patches to parts growing
in good patches. This may cause the response of the plant to its local density conditions to
be obscured (SLADE& HUTCHINGS 1987, TURKINGTON&KLEtN 1991).
Despite all these problems of both addition and removal experiments, they are the most
common types of field experiment on competition and have a long history of use for studying
the individual-level consequences of competition in perennial grasslands and other
communities (AARSSEN & EPr' 1990, GOLDBERG& BARTON 1992, GUREVIXCHet al. 1992).
They seem to be the primary options (other than the logistically difficult (3) below) currently
available lbr studying the individual or community-level interactions among
already-established adults in perennial communities and therefore we reluctantly recommend
240
D.E. Goldberg et al.
their use, with all the caveats discussed above. Some of the problems can be dealt with by
careful experimental technique.
(3) Reconstruction of the community by transplanting established plants. This would involve
quantifying the relative abundances of the species in the natural community, collecting
transplants of the appropriate age/size distributions from all the species in the community,
and then planting predetermined numbers of individuals of each species in experimental plots
such that total density varies but relative abundances of each species are constant along the
total density gradient. This would be a logistic nightmare for plant communities of even
moderate diversity and introduce many potential artifacts due to transplant effects, soil
disturbance, etc. This may, however, be an option for less diverse communities with organisms
less likely to be affected by handling/transplanting.
Finally, we note that for any of these techniques, many of the questions of interest to plant
ecologists and to pasture managers will require comparing the effects of competition on
community structure among environments-either sites that differ in some environmental
characteristic such productivity or herbivory or experimental treatments such as fertilizer or
grazer manipulation (GOLDBERG & BARTON 1992). Therefore experimental designs will
typically be factorials involving several levels of an environmental factor (site or treatment)
fully crossed with several levels of initial community density (at least 2 levels are required:
natural density and a single very low density, although more levels are strongly preferred so
that all the parameters in Fig. 2, including slope, can be calculated). For example, to test
whether the effects of competition at natural densities are stronger in fertilized plots, a minimal
design is a two way factorial of competition treatments (natural community density, very low
community density) x fertilizer treatments (fertilized, unfertilized). If natural densities are
very different between fertilized and unfertilized plots, this design is inadequate to separate
per-plant effects of competition from total density effects, For management-related questions,
this may not be an important distinction. Where the distinction is important, it is necessary
to have an entire density gradient so that slopes can be estimated and then compared. For
generalizing results, it is also useful to have a wide range of densities, including some higher
than natural, because densities vary between years.
CONCLUSIONS
The community-density series potentially allows us to fill a big empirical gap by testing
a wide variety of hypotheses about patterns in the influence of competition on entire
communities. In addition, simply describing the design by itself opens up a series of important
questions because it is immediately clear that different ways of quantifying the "influence"
of competition at the community level may well give different patterns along productivity
gradients, herbivory gradients, or any other type of gradient (Figs. 3-5). Therefore, even
without using the design empirically, it can be helpful by forcing us to define exactly what
we mean by "influence of competition" in the context of any particular hypothesis. As with
the example of changes in the importance of competition along productivity gradients, to a
large extent, some controversies may be a simple consequence of different definitions of
"influence".
Acknowledgments: We are grateful to the participants in the Bedrichovworkshopfor stimulating discussions
on the community-densityseries experimentalapproach, and especiallyfor discussions on how to apply it in
Community-level consequences of competition
241
perennial grasslands. We also thank the Binational Science Foundation (US-Israel), the Keren Kayemet
LeYisroel, and the University of Michigan for supporting ongoing empirical tests of the method.
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