The concept of competition has a strong explanatory power in plant ecology and is central to most hypotheses on the structure and dynamics of plant communities (e.g. Grime 1979; Tilman 1988; Huston 1994). In the light of the huge variability of life histories and ecosystems, this explanatory power and the apparent success of generating fairly general hypotheses is to some degree a result of a rather loose definition of the term ‘competition’. However, a loose definition is also dangerous and may lead to unfruitful dialogues due to differences in semantics, especially if the use of mathematical models in the scientific tradition has been downplayed. A systematic experimental approach has led to an amazing amount of evidence that competition exists in natural communities [for example, Goldberg & Barton (1992) reviewed 101 experiments]. However, the role of competition in the structure and dynamics of plant communities is still poorly understood (Suding, Goldberg & Hartman 2003; Agrawal et al. 2007; Lamb & Cahill 2008), even though the key questions have already been addressed, as exemplified by the quotations below.
Documenting that competition occurs does not necessarily imply that this competition has important consequences for ecological communities (Goldberg & Barton 1992).
The first part of any analysis of competition is to determine whether it occurs and then what its form is. Having done this, we may ask, does it matter? (Rees, Grubb & Kelly 1996).
The distinction between importance and intensity of competition
A central refinement in the theory of plant competition is the distinction between the intensity and the importance of competition. This distinction was first introduced by Welden & Slauson (1986) and later explored by several authors (e.g. Grace 1991; Brooker et al. 2005; Brooker & Kikvidze 2008; but criticized by Freckleton, Watkinson & Rees 2009). The intensity of competition refers to the degree to which a plant population is reduced by the presence of neighbours, whereas the importance of competition refers to the relative reduction of a plant population by competition compared to the reduction due to other forces, such as herbivory or unfavourable abiotic conditions (both definitions due to Grace 1991). To illustrate the distinction between intensity and importance of competition, imagine a plant community where neighbouring individuals have strong negative effects on each other (intense competition), but where the interspecific competitive interactions do not play an important role in the structuring of the plant community compared to the filtering effect of an abiotic factor on species composition. Both the intensity and the importance of competition have been investigated experimentally; but where the intensity of competition has been examined in numerous studies, only relatively few studies have made empirical investigations of the importance of competition (e.g. Greiner La Peyre et al. 2001; Gaucherand, Liancourt & Lavorel 2006).
The significance of the distinction between intensity and importance of competition cannot be downplayed. Indeed, it is at the heart of the prolonged and painful ‘Grime-Tilman-debate’ in plant ecology on the role of competition in structuring plant communities along productivity gradients (Grace 1991). It is now recognized that the two authors employed different definitions of competition and competitive success or ability (Goldberg, Grace & Tilman 1990; Grace 1991; Brooker et al. 2005; Brooker & Kikvidze 2008): Grime’s theory postulates that the importance of competition in structuring plant communities increases along a productivity gradient. In his view, competition corresponds to the mechanism whereby a plant suppresses the fitness of a neighbour, and competitive ability is linked to resource acquisition. Tilman’s theory, on the other hand, postulates that the intensity of competition is constant along a productivity gradient. In his view, competition corresponds to the mechanism whereby a plant tolerates a low level of resource, i.e. if a species has a high competitive ability at low levels of a specific limiting resource; this is because the plant is able to grow at low levels of that resource.
The need for an integrated approach
To date, plant ecological literature has mainly focused on how to measure the intensity and importance of competition (Freckleton, Watkinson & Rees 2009). Indices are calculated from transplant or replacement experiments, comparing a set of interacting species and/or community position along an environmental gradient. The indices originally suggested by Welden & Slauson (1986) measure intensity of competition as O−C, where O is the state of a plant in the absence of competition and under optimal growing conditions, and C is the state of the plant when competition is taking place again under optimal growing conditions. The importance of competition is measured by (O−C)/(O−A), where A is the state of a plant when both competition is taking place and the plant is growing in a stressful environment. Except in the case of facilitation (Bruno, Stachowicz & Bertness 2003; Brooker et al. 2008), we expect that O > C > A, and, consequently, that the index of importance of competition takes values between 0 and 1 and may be interpreted as the decrease in the state of a plant due to competition relative to the decrease in the state of a plant due to both competition and a stressful growing environment.
Some of the other indices used in the literature generalize the above index by Welden & Slauson (1986) to include the effect of facilitation, but all measures of the intensity and importance of competition have in common that they are not functions of either density or the level of the environmental gradient (see Weigelt & Jolliffe 2003 for a review of indices measuring competition intensity). This is unfortunate, as we know that competition, generally, depends on plant density and the level of the environmental gradient (e.g. Goldberg et al. 2001; van Andel & Aronson 2005; Turkington et al. 2005; Freckleton, Watkinson & Rees 2009).
Here, we present a generalization of the indices of importance and intensity of competition that causes them to be functions of density and the level of an environmental gradient in such a way that (i) the competition intensity and importance indices can be calculated on any measure of ecological success at the population or individual level; (ii) the functions contain the same ecological information as the indices, but for general densities and levels of an environmental gradient and (iii) in the case of a simple experimental design, e.g. if only one density is used in a competition experiment (a replacement design), the functions will degenerate to the indices used presently.