The measurement of competition (and other interactions)

The previous chapter on defining competition leads to questions about how it should be described and measured. A definition based on resources means that there is a large body of theory about consumer-resource interactions more generally that can be applied to competition.

Measuring the effect of one consumer (competitor) on another requires an appro­priate experiment, whether it is carried out using the real system or a mathematical model. The ‘experiment' using a model may be a simulation or an analytical calcu­lation. Measuring the ‘effect' of one species on a second requires a description of the perturbation to the first species and the temporal responses of both species following that perturbation.

Competition Theory in Ecology. Peter A. Abrams, Oxford University Press. © Peter A. Abrams (2022).

DOI: 10.1093∕oso∕9780192895523.003.0003 the short-term effects of a perturbed initiator population on other ‘receiver’ popula­tions is useful because they can often identify quantities that need to be considered in constructing a dynamic model of the interaction.

The long-term effect on the abundance of a second species must be established using what Bender et al. (1984) called a ‘press’ perturbation. This involves a sustained change in some property of the initiator species. For example, instead of the one­time introduction of individuals in a pulse perturbation, the input of individuals is sustained over time in the corresponding press perturbation. The parameter that is changed in such a press experiment is ideally one that causes a unidirectional change in the per capita population growth rate of the initiator species, but that does not directly affect any other species in the system (Yodzis 1988, 1989; Schoener 1989, 1993; Abrams et al. 1996). Because of their lack of an immediate effect on the per capita growth rate of any other species, such parameters will be referred to as ‘neutral’ parameters here.

In a competitive interaction, the resources used by consumer species 1 will usual­ly change following any alteration in the input of individuals of consumer species 1; these changes would eventually alter the abundances of other consumers that share at least some of the same resources. However, there might be fluctuations in all of the abundances as they approach the new equilibrium (dynamic attractor), as illustrated in Figure 2.1 in the previous chapter.

If the perturbation is small enough, different neutral parameters will produce sim­ilar relative effects on the sizes of the two populations involved. However, this is not true of larger perturbations, or of non-neutral parameters. The neutral perturba­tion used to define interspecific effects in most previous theory is usually either the immigration or per capita mortality rate of the initiating species (Yodzis 1989). Both immigration and per capita mortality are quantities that can usually be manipulated in laboratory experimental systems. The same is true for at least some field scenarios as well. However, larger magnitude perturbations usually produce different effects per unit of parameter change than do small perturbations. In real experiments, very small perturbations do not produce large enough effects on populations to distinguish them from measurement error. For the two traditional neutral perturbations, greater immigration is usually a stabilizing factor, while lower mortality is often destabiliz­ing. This may need to be taken into account in experimental measurements. If the system is nonlinear, the cycle amplitude often has a large impact on mean population size and is sensitive to neutral parameters. In this case, neutral perturbation size can have a particularly large impact on the measured effect.

In most food web models the majority of parameters are non-neutral; they directly affect the dynamics of two or more species.

Measuring competition: a consumer-resource framework • 35 consumption rate of one or more resources. Such a parameter in one consumer will produce immediate effects on both the consumers and the affected resource(s), and will usually alter the magnitude of any interspecific effect because of this. The fact that two species have their growth rates affected simultaneously makes such non-neutral parameters inappropriate for assigning a sign to the effect of one species on another. This, in turn, means that a greater variety of effect signs are associated with non­neutral parameter change. For example increased consumption of a resource used by one consumer species may actually increase the equilibrium population sizes of both the resource and a competing consumer species, even in simple all-linear models (Abrams 2002, 2003). The direction of the response of another species after perturb­ing any parameter in the focal species may depend on the magnitude of the change. Thus, a complete picture of the interaction should consider the full range of potential magnitudes and parameter identities.

Nevertheless, if one wants to characterize an interaction by a single figure, it is reasonable to use a neutral parameter and consider a small magnitude change. A small magnitude parameter change is particularly useful from a theoretical per­spective because analytical methods of determining the effect are possible when the equilibrium is stable (Yodzis 1988, 1996). Unfortunately, the standard approach in experimentation is to use a large magnitude change in order to obtain a statistically significant measurement of the response. This requirement has limited the applica­tion of the theoretical results. If the per capita dynamics are close enough to linear and the perturbation is not too large, a linear extrapolation of the ‘small pertur­bation' outcome may provide a reasonable approximation to the actual change in abundance of the competitor.

In some cases, behavioural changes in resource species may produce a large part of the effects of a neutral parameter change in one consumer species on other con­sumers. Models and a large number of experiments have explored the possibility of such behaviourally transmitted effects in food chains (Abrams 1984b, 1995; Matsuda et al. 1993, 1994, 1996; Werner and Peacor 2003). Depending on the spatial loca­tions of different consumer species and/or their foraging behaviours, it is possible that defending against one consumer entails greater risk from the others. Alterna­tively, defences may be generally applicable to both (or all) consumers, in which case the behaviour mobilized against one predator will reduce the capture rates of other predators. Both behavioural pathways imply rapid effects of altered preda­tor abundance on the per capita capture rates. Changes in population growth rate due to such behavioural shifts are often referred to as trait-mediated effects, and are important, but largely ignored, components of consumer functional responses. They

occur in plants as well as animals. For example, Ohgushi (2005) reviewed the effects of trait-mediated changes in plant defences against herbivores and finds that these usually cause positive rather than negative indirect effects between their consumers. This occurs because defences tend to be consumer-specific, so the initial effect of greater defence against consumer A is usually an increased intake rate by consumer B.

Models have shown that defensive behavioural/phenotypic changes in the resource species may enhance or reverse the effect that would have occurred with fixed behaviours (Matsuda et al. 1993, 1994, 1996; Sommers and Chesson 2019). Even in cases with large trait-mediated effects, there is likely to be some population-level com­ponent, so press perturbations to mortality or immigration can provide a measure of inter-consumer effects. However, behavioural change usually increases the non­linearity of interactions (Abrams 1984b, 1992c, 1995), so the ability to predict the effects of large-magnitude neutral perturbations is even more limited in these sys­tems. The effects of both consumer and resource behaviours on the functional forms of consumer-resource models are discussed in more detail later in this chapter.

3.2