Journal of Ecology 2009, 97, 379–384
doi: 10.1111/j.1365-2745.2009.01497.x
FORUM
Blackwell Publishing Ltd
Measuring the importance of competition in plant
communities
Robert P. Freckleton1*, Andrew R. Watkinson2 and Mark Rees1
1
Department of Animal and Plant Sciences, University of Sheffield, Sheffield S10 2TN, UK; and 2School of Environmental
Sciences, University of East Anglia, Norwich NR4 7TJ, UK
Summary
1. Plant ecologists have developed numerous ways to measure competition and to rank the effects
of competition relative to other factors. According to one line of logic, there is an important
distinction between competitive intensity (broadly, the absolute, proximate effects on individuals) and
the importance of competition (loosely, the relative effects on ecological or evolutionary processes).
2. It has been argued recently that there is a great deal of confusion in the literature regarding these
concepts. We agree and suggest that this arose because of loose logic in the initial formulation, and
that this has been perpetuated and exacerbated in recent critiques.
3. Using a simple example, we argue that recent analyses have generated new problems because of
a failure to measure importance in terms of individual fitness (defined in an evolutionary sense) or
per capita rates of population change. Only when calculated in this way can importance be measured
relative to all other processes in the life cycle.
4. It is not possible to directly measure the importance of competition from short-term experiments that last less than one generation, using data from artificial conditions, or using data from
glasshouse experiments.
5. Too often researchers use the term ‘importance’ without stating clearly what this is measured
with respect to. We highlight, for example, that importance could be measured for population
growth rate, community composition or community invasibility and that the appropriate measure
would differ in each case.
6. Synthesis. We ask whether a single index of importance is really useful in plant ecology. The
concept focuses on index-based measures of competition using experimental data, narrowly concentrating on comparing two theories of plant competition. In the rest of the ecological world,
researchers are using model-based analyses of field data and increasingly sophisticated fitting
techniques to dissect out the various processes determining the dynamics of single and interacting
populations and making a great deal of progress. It is obviously very useful to disentangle the
effects of competition at different stages in the life cycle and to determine how these vary along
environmental gradients. However, the measure of competition and the measure of importance
should be tailored to the question being addressed.
Key-words: competition, competition coefficient, population dynamics, population growth rate,
stochastic model
Introduction
One of the key aims of plant population and community ecology
is to measure the effects of biotic interactions, especially
competition, and then understand and predict how these
translate into consequences at the level of the whole community (Grime 1979; Tilman 1988; Hubbell 2000). In a recent
*Correspondence author. E-mail: [email protected]
critique of other studies on competition in plant communities,
Brooker & Kikvidze (2008) argue that researchers are confusing
the issue by conflating two key measures of competitive interactions. Following Welden & Slauson (1986), they argue for
the distinction between competitive intensity (a measure of
absolute, proximate strength) and importance (broadly, a
long-term, relative outcome). Citing two studies, one of which
did not use either term in this framework, they argue that
‘widespread confusion produces continued debate’. Here we
© 2009 The Authors. Journal compilation © 2009 British Ecological Society
380
R. P. Freckleton, A. R. Watkinson & M. Rees
argue that Brooker and Kikvidze do not provide a resolution
because they do not make the distinction between studies that
focus on the outcome of competition on, say population
growth rate, and those that focus on components of competition, and by accepting the arguments presented by Welden
& Slauson (1986) too uncritically. Moreover, they only consider ‘importance’ in one context, that is, competition along
environmental gradients, whereas the fundamental distinction
between proximate effects of competition and fitness consequences can be applied more generally.
In this article we argue that the inconsistencies in the work
by Welden & Slauson (1986) preclude a meaningful interpretation of either the importance or intensity of competition,
and caution against reading their definitions and concepts
too uncritically. We emphasize that studies that do not take a
population or community dynamic perspective, can, necessarily, say little about the importance of competition to
population or community ecology. Finally we question whether a single concept or measure termed ‘importance’ is really
useful, especially in the light of the developments in the
theoretical and statistical literature over the past 20 or so years.
Importance and intensity
SIMPLE CONCEPTS
The ideas of importance and intensity are put deceptively simply by Welden & Slauson (1986) in the abstract to their article:
‘The intensity of competition is a physiological concept,
related directly to the well-being of individual organisms
but only indirectly and conditionally to their fitness ...’
and
‘The importance of competition is primarily an ecological
and evolutionary concept, related directly to the ecology and
fitness of individuals but only indirectly to their ecological
states.’
The subsequent discussion in that article elaborates on this
idea, but unfortunately does not keep to these key concepts.
The basis of the idea is, however, that the importance of
competition should be measured relative to other processes
and should summarize the impact of competitive interactions
on, say, fitness (i.e. per capita rate of increase) relative to these
other processes, whereas intensity is a measure of the proximate effects of competition on individuals.
EXAMPLE WITH ANNUALS
This initial distinction may be illustrated simply using annual
plants as an example, and here we outline a hypothetical
example of how we might use the basic notions of intensity
and importance in an application. We use this example not to
suggest or promote a new or particular index of competition.
Rather, we use the model to explore how simple measures of
competitive intensity and importance with respect to popu-
lation growth behave in a simple model, and to contrast that
with the generic index proposed by Brooker & Kikvidze (2008).
Annual plants frequently compete for resources (e.g. water,
light and nutrients). In the absence of competition a plant will
grow to a size wm, but in the presence of competitors at density
N (it does not matter whether N is the density of con- or
heterospecifics) will grow to a smaller size w(N). The ratio of
wm and w(N) or the difference between them – the distinction
is immaterial, we do not wish to relive here the protracted
debates on relative vs. absolute measures of competition – is a
measure of competitive intensity according to the definition
of Welden & Slauson (1986) ‘the amount by which the
competition-induced component of the sub-optimal state
differs from the optimal’:
Intensity =
w( N )
wm
eqn 1
This ratio ranges from 0 (relative performance is zero and
intensity is maximal) to 1 (relative performance is 1 and no
effect of competition).
In this example, we can measure the importance of competition for population dynamics by relating w(N) to population
growth rate: this is because the ultimate aim is to measure the
effects of competition with other processes in the life cycle,
and to summarize an effect on net fitness. In our example of
annuals this is easily done as there is usually a linear relationship between biomass and seed production (Watkinson 1980;
Rees & Crawley 1989; Thomson et al. 1991). If S is the production of seeds per unit biomass and g is the proportion of
seeds that survive to become plants the following year (i.e.
includes all mortality in the life cycle), then population
dynamics are given by:
N t+1
= gSw( N t )
Nt
eqn 2
Eqn 2 integrates all the effects of competition and other processes (reproduction, mortality and seed germination) on the
life cycle. At a given density, the importance of competition
for population growth rate is calculated from the ratio
between this quantity and the maximal per capita population
growth rate, Nt+1/Nt = gSwm. Most usefully, this is calculated
at the equilibrium density:
Importance =
gSw( N eq )
gSwm
=
w( N eq )
wm
eqn 3
Similarly this ratio varies from 0 (no population growth
and maximal effect of competition) to 1 (maximal growth and
no effect). From eqn 2 we note that at equilibrium, w(Neq)
equals 1/gS so that:
Importance =
1
gSwm
eqn 4
It may appear that quantities (1) and (3 or 4) are the same;
however, two important points need to be made. First, eqn 1
is derived solely from measures on performance within a
growing season and with no reference to population growth;
specifically, the density N is arbitrary. Thus, if the density N is
© 2009 The Authors. Journal compilation © 2009 British Ecological Society, Journal of Ecology, 97, 379–384
Importance of importance? 381
held constant, the intensity of competition will also remain
constant, and if density is varied, then the intensity will vary
(Freckleton & Watkinson 1997a). However, in eqn 4 the
importance of competition will vary with factors that affect g
or S, because they influence Neq, but do not affect the intensity
of competition at a given density. Thus, in this example,
increasing g , S or w m will decrease the importance of competition for population growth rate.
Competition need not only affect biomass; for example, if g
could be affected by density (e.g. through density-dependent
emergence or predation of seed). If this were the case, a study
on the effects of competition that estimated biomass effects
via eqn 1 would not be relevant to understanding the net
effects of competition through its combined effects on germination and biomass and consequent impact on population
growth rate. For example, Lintell Smith et al. (1999) showed
that in the annual weed Anisantha sterilis the intensity of
competition measured on biomass alone was approximately
10 times lower than the combined effects of germination and
biomass. In this example, information on competition
between individual plants would yield no information on how
populations are regulated by competition in the wider sense,
and this can only be achieved by considering the whole life
cycle and population growth rate.
INTENSITY AND IMPORTANCE OVER GRADIENTS
So far we have considered measures of the intensity and
importance of competition within a site. One frequently
explored issue is how competition varies along experimental
environmental gradients. For comparisons along a gradient,
Brooker & Kikvidze (2008) suggest using an index of the
form:
C imp =
wm − w( N )
wm
⋅
wm
wMAX − W ( N )
wm − w( N )
wMAX − w( N )
C imp ≈
wm
wMAX
Importance (environment 1) =
1
g1S1wm,1
and Importance (environment 2) =
Importance (environment 1 vs. 2) =
The assumption that wm >> w(N) can always be justified by
increasing the sowing density (N), as this is usually fixed by
the experimenter (e.g. see examples analysed in Brooker &
Kikvidze 2008). From eqn 6, we conclude that the importance of competition increases as productivity (measured by
maximum rates of individual growth) increases. However, this
is a consequence of the way the index is constructed rather
than of any deep biological significance, because the values
estimated are not generated with respect to the whole life cycle
or population growth.
g2 S2 wm, 2
g1S1wm,1
eqn 7
The key point about eqn 7 is that any of the parameters
might vary between the two environments. For instance, if
environment 1 were a drier environment, individual productivity (wm) would decline as might seed germination and
subsequent survival (decreasing g), or facilitation in such an
environment could increase g. An alternative scenario is
that in more productive environments, predation of seeds
or seedlings might increase because higher-productivity
environments harbour more natural enemies, and consequently
g or S could decline with increasing wm. Many outcomes are
possible and the relative measure in eqn 7 can encompass a
range of behaviour that the restricted index (eqn 5) cannot.
We note that if we assume that g and S are constant between
environments, then eqn 7 reduces to:
Importance (environment 1 vs. 2) =
eqn 6
1
g2 S2 wm, 2
We can calculate how important competition is in environment 1 relative to environment 2, and ask how the importance
of competition for population growth changes along the
gradient by looking at the ratio of these:
eqn 5
where wMAX is the maximum weight mass of an isolated plant
along the gradient, and wm and w(N) are as defined above.
This index varies between 0 (no competition) and 1 (maximal
effect of competition). Simplifying and assuming wm >> w(N)
we find:
C imp =
In our example of annuals, what would the measure of
importance that we used for population growth tell us about
the importance of competition for population growth rates in
contrasting environments? Consider the case when we measure competition in two environments, denoted 1 and 2. Hence
we can estimate the importance of competition for population growth rate in both:
wm, 2
wm,1
eqn 8
At first glance, this might seem to be the same as eqn 6.
However, eqn 8 is arrived at by considering population
growth rates and has a population dynamic interpretation: if
productivity were twice as high in environment 2 compared
with 1, then eqn (8) says that competition will reduce population
growth rates by twice as much in environment 2 compared to
1. Furthermore, eqn (8) is a null prediction under the simple
expectation that g and S are constant, and this may or may
not be the case in reality. In contrast, the result in eqn (6) simply
follows from the way the index is constructed.
CONCLUSIONS
What do we learn from this example? First, to measure the
effects of competition it is necessary to include the proximate
effects of competition on individuals, as well as the effects on
the population growth rate from other sources of flux in the life
cycle. Second, an index that is based solely on measurements
of plant performance is not adequate to characterize competition as this fails to integrate other sources of mortality,
© 2009 The Authors. Journal compilation © 2009 British Ecological Society, Journal of Ecology, 97, 379–384
382
R. P. Freckleton, A. R. Watkinson & M. Rees
variability or competition. This can only be achieved by
measuring population growth rate. Third, the question of
how competition scales along gradients or within habitats
requires that competition is characterized fully in this way
within each habitat. Finally, the difference between eqns 6 and
7 is that the latter allows all factors operating on population
growth within each habitat to be accounted for, whereas the
former only focuses on the effects of competition on vegetative
growth. Although we have framed this example in terms of
annual plants for simplicity of presentation, the same conclusions apply to perennials: all processes in the life cycle need to
be measured and integrated into a single relevant measure of
fitness or population growth.
Critique
WHAT IS MEANT BY
‘POPULATION-LEVEL
EFFECTS’?
Brooker & Kikvidze (2008) claim that there is ‘widespread confusion’ in the literature. In sole support of this contention they
argue that Freckleton & Watkinson (2001) in particular employed
a confusing definition of importance. They argue that Freckleton
& Watkinson (2001) define importance at the ‘population level’
and intensity at the ‘individual level’. And indeed, Weldon and
Slauson also do this, or at least in some parts of their article.
More specifically, Brooker & Kikvidze (2008) say in critique
of Freckleton & Watkinson (2001): ‘even if you can demonstrate a population-level effect of competition, it remains a
measure of competition intensity if you fail to place that effect
within the context of population-level effects from other
sources’. It is clear from both of our original definition
(explicitly given in terms of population growth rate), from the
equations given by Freckleton & Watkinson (2001), and the
foregoing expanded rationale that this criticism is quite
unjustified. If examining the dynamics of a species within a
community, the population growth rate is the only measure
that allows this integration to be achieved, and we specifically
defined importance with reference to population growth rate.
Although not defined explicitly, it appears that what Brooker
& Kikvidze (2008) mean by ‘population-level effects from other
sources’ are differences in population growth rate or performance with respect to other environments, basically with
respect to WMAX in eqn 5. Thus, if a population in an ‘optimal’
habitat can achieve a maximum mean mass per individual of
10 g per plant, and in a suboptimal one achieves 5 g per plant,
this twofold difference in growth is a ‘population-level’ effect
of ‘stress’ on the population in the sub-optimal environment.
In the sub-optimal environment it is argued that plants experience this stress in addition to the effects of competition
and the importance of competition has to account for this.
Brooker & Kikvidze (2008) are therefore asking about
importance in only one respect, that is, how the effects of
competition vary along environmental gradients. This is only
one context in which the effects of competition might be
explored, and can by no means be used to ascribe a general
index of ‘importance’ to competition. The issue is that,
although performance with respect to WMAX could be used to
analyse relative performance in a series of populations, it cannot
be used to predict performance within a focal population or
community, is irrelevant to population persistence, and,
within multispecies communities, is irrelevant to the outcome
of competition. The question of how competition scales with
the effects of competition along gradients is of course potentially interesting, but is not directly relevant to understanding
the long-term effects of competition within communities,
what determines whether species are able to coexist or not, or
whether communities can be invaded by new species.
T H E I M P O R T A N C E O F C O M P E T I T I O N I S 42
What does this mean? Symptomatic of much of the literature
on the importance of competition is the failure to state to
what competition is important and what this is measured
relative to. Without stating this explicitly, any statement, such
as ‘evidence for the decline in importance of competition for
resources in unproductive vegetation’ (Grime (1979, p. 20)
becomes open to misinterpretation. Brooker & Kikvidze (2008)
discuss Grime’s theories and present an analysis of two field
experiments quantifying the within-season effects of competition on plant performance, and a pot study looking at the effects
of competition on relative growth rate. They then use their
measure of importance measured on gradients to interpret these.
However, Grime (2001), when discussing the importance of
competition, seems to be primarily interested in controls on
community membership. He writes:
‘However, it has never been the contention in CSR theory
that competition disappears completely under conditions
of low productivity or intense disturbance. It does seem
logical, however, to use terminology which reminds us of
the circumstances where competition for resources is the
dominant (but not exclusive) influence on the membership of
plant communities’
and later on page 37 he says
‘As Welden and Slauson (1986) recognised, there is an obvious
and continuing conceptual gulf dividing those ecologists
who are measuring the role of competition in modulating
the relative abundance of species co-existing in plant communities and those pursuing the larger predictive framework
that identifies the circumstances where competition determines the kind of plant species admitted to communities.’
Particular confusion can arise here as competitive intensity or importance (i.e. effects on performance, population
growth or abundance) is not a direct predictor of invasibility
(i.e. whether a species can enter a community from which it is
absent; see Lonsdale 1999). Measuring invasibility (i.e. whether
a population can exhibit positive population growth under
given conditions) is a different matter from measuring
competitive intensity or importance and there is no simple
way to predict one from the other. In summary, without
clearly spelling out what competition is important to and
relative to what, statements about the importance of competition are largely devoid of meaning.
© 2009 The Authors. Journal compilation © 2009 British Ecological Society, Journal of Ecology, 97, 379–384
Importance of importance? 383
The way forward?
more progress could be made by doing so (e.g. Sears &
Chesson 2007).
THE QUANTITATIVE BASIS
An uncritical reading of Welden & Slauson (1986) could
result in a focus on an inappropriate measure with which to
estimate ‘importance’. For example, if competition experiments focus only on the growth phase, failure to measure survival or reproduction would yield incomplete and potentially
faulty estimates of the net effects of competition. If there is
confusion in the literature regarding the ideas of importance
and intensity, this in part arises because the examples used by
Weldon and Slauson are unhelpful and even contradict the
broad aims of the distinction between importance and
intensity that they propose at the outset of their article. For
instance, in their fig. 1, Weldon and Slauson attempt to
distinguish the importance and intensity of competition by
reference to survival of individuals. However, survival is only
one component of fitness and the fitness of an individual (or
equivalently the population growth rate) may be sensitive to
other factors (e.g. reproduction, growth). Thus, despite
proposing an apparently appealing idea, the examples given
are unclear and even contradictory and we would caution
against reading this article uncritically.
This contradiction is pointed out by Brooker & Kikvidze
(2008), but they do not attempt a resolution. To us the only
logical way to resolve this contradiction is to regard withingeneration competitive effects as being incapable of providing
information about the importance of competition in broader
terms. For instance, the information in fig. 1 of Welden &
Slauson (1986) (or fig. 1 of Brooker et al. 2005) can only be
used to measure the intensity of competition as it does not
integrate processes operating across the whole life cycle via
estimating population growth rate or fitness.
A general issue is that the article by Weldon and Slauson
was written over 20 years ago before many of the considerable
developments in theoretical population ecology and the
recent closer integration of theoretical and statistical ecology.
Brooker & Kikvidze (2008) do not (by necessity) incorporate
the ideas that have been developed in this time, such as
quantitative measures of invasibility (Geritz et al. 1997,
1998), population persistence in the face of stochasticity
(Lande 1998; Lande et al. 2003), community dynamics and
invasibility (Chesson 2000) or measurements of evolutionary
fitness (Metz et al. 1992; Metz & Gyllenberg 2001). Moreover,
an increasing number of studies have dissected population and
community dynamics from first principles, especially in the
zoological and epidemiological literatures (e.g. Rees et al.
1996; Pacala & Rees 1998; Fromentin et al. 2000; Lande et al.
2003; Clark & Bjornstad 2004; Grenfell et al. 2004; Morris
et al. 2004; Cornell et al. 2008). In plant community ecology
there has been a shift towards looking at the fundamental
factors determining life-histories and the trade-offs between
traits to understand how plants evolve to fit into their
environment (Rees et al. 2001). The analytical tools exist
with which to analyse population and community dynamics
from a purely quantitative basis and it seems that far
MEASURING COMPETITION IN THE SHORT-TERM
By focussing on gradients and not examining long-term outcomes of competition within communities it is possible to be
misled into believing that the underlying determinants of
competition have been isolated. In particular, the long-term
impacts of competition relative to stochastic factors such as
climate or herbivory could be missed. The examples by
Brooker & Kikvidze (2008), together with those given in an
earlier article (Brooker et al. 2005) would seem to contradict
the call by Brooker and Kikvidze to evaluate the effects of
competition relative to other factors: Brooker et al. (2005)
attempt to calculate the ‘importance’ of competition based on
a 10–12 week field trial with the perennial grass Poa pratensis
and using data from a 1-month glasshouse experiment with
seedlings of a perennial shrub.
To calculate ‘importance’ using such data is clearly inconsistent
with a broad reading of the recommendations by Brooker &
Kikvidze (2008). Our simple example with annuals makes it
clear why this is not correct. Even if asking a simple question
such as ‘what is the importance of competition for population
growth in an annual plant?’, a short-term experiment would
only be able to measure the effects of competition on part of
the whole generation. Thus, it would only be possible to estimate eqn 1, and not to estimate the quantity in eqn 4. Even if
this were done across a gradient, such that the importance
index of Brooker & Kikvidze (2008) could be measured, it
would be an incomplete measure, particularly if the gradient
is an experimental one at fixed density.
It is, almost by definition, not possible to estimate the
importance of competition relative to other processes operating on a population unless all components of the whole
population growth cycle have been estimated. In a long-lived
perennial, a short-term experiment involving only one life
stage, for example, will tell us nothing about the effects of
competition or other process operating at other stages of the
life cycle. At the least, all stages of the life cycle need to be
measured, preferably via multi-generational studies.
Of course that does not mean that short-term studies have
no place in research on competition. These are of considerable
value in testing hypotheses and in elucidating mechanisms.
There are many types of experiment and manipulation that
are impossible to carry out in the field or under uncontrolled
conditions and that can only be performed in the short-term
under controlled conditions. However, at the same time it
needs to be realized that there are limitations in using data
from highly controlled conditions to infer the strength of
competition under field conditions.
DEFINING IMPORTANCE
We would question whether the concept of ‘importance’ as a
single concept or measure is of any value in plant population or community ecology. The idea behind calculating
© 2009 The Authors. Journal compilation © 2009 British Ecological Society, Journal of Ecology, 97, 379–384
384
R. P. Freckleton, A. R. Watkinson & M. Rees
‘importance’ is to estimate the effect of competition relative
to other processes as a single index. In many circumstances
this seems to be of questionable value for several reasons.
First, as an example, consider the case of single-species
dynamics (such as the general model in eqn 2), where the
product of g, S and wm is (when appropriately averaged)
greater than one, then the population will grow exponentially.
Density-dependence via competition will serve to reduce
population growth so that an equilibrium is achieved. In
one sense it is immaterial whether the density-independent
population growth rate is 1.1, 10 or 100 in three different
environments, that is whether the required net reduction
in population growth rate via competition to achieve equilibrium is 1%, 90% or 99%, because in all three cases competition is ‘important’ in preventing unlimited population
growth. That is, as we emphasize above, specifying the ‘important
to’ is critical.
A second reason why general measures of the importance
of competition are of questionable value is that such indices
are often not related to the fundamental parameters generating
population dynamics. This is true whether one is considering
one, two or many species. For instance, in eqn 1 or 4 point
estimates of either the intensity or importance values are not
sufficient to fully characterize population dynamics. This is
because the function w(N) is a nonlinear function of density
and measuring this requires data on performance that was
measured at a range of densities. In two species mixtures the
problem of trying to infer the nature of competition from
indices becomes worse (see Freckleton & Watkinson 1997a,b,
1999) and, despite claims to the contrary, the situation
becomes hopeless if there are more than two species. This is
because in an n-species mixture there are at least n2 pairwise
interaction coefficients (ignoring higher order effects) as well
as variance in n densities, all of which combine in a nonlinear
way to determine proximate effects of competition and their
net effects on populations. A single estimate of ‘importance’ is
averaging across at least n2 + n unknown variables, and is
therefore unlikely to yield any useful information on the
underlying community dynamics.
Concluding remarks
In short, we would advocate less reliance on ad hoc and questionable index-based measures of competition from artificial
conditions as they have to date not thrown much light on
how natural population and communities function and are
unlikely to do so in the future. We urge plant ecologists to
study real populations and communities using model-based
approaches. At present, semantic debates about terminology,
indices and measuring competition are hindering plant ecology.
What is needed is a mechanistic, model-based approach to
measuring competition and the other factors determining
population dynamics.
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Acknowledgements
RPF is funded by a Royal Society University Research fellowship.
Received 29 September 2008; accepted 16 February 2009
Handling Editor: David Gibson
© 2009 The Authors. Journal compilation © 2009 British Ecological Society, Journal of Ecology, 97, 379–384