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 ...’
‘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 population 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’:
- (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:
- (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:
- (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:
- (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 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 wm 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:
- (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:
- (eqn 6)
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.
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:
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 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:
- (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.
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, 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.