Implications of the definition

A few of the advantages of going back to such a strictly resource-based definition are:

1. It makes competition theory more consistent with general theory on indirect effects.

2. It provides a basis for describing and measuring the full range of factors that influ­ence the effect that one consumer may have on another. These include changes in any of a consumer's traits that affect its interaction with its various resources, changes in the interaction between the resources, and changes in the abundance of one or both consumers.

3. It establishes a more productive approach to understanding the evolution of the traits that define the competition within and between species, as many of these traits affect both relative and absolute uptake rates of different resources.

Predicting the effects of environmental and evolutionary changes on species' abundances represents two of the main goals of ecology. In addition, the science of ecology should be useful in explaining some of the properties of existing eco­logical communities and how they and their component species have changed over time. All these goals require a quantitative description of the interactions between dynamic components of the system. If we accept that competition always involves effects on resources, then it seems that a minimal model would need to contain: (1) some description of resource dynamics in the context of the community in which they occur; (2) descriptions of rates of consumption of the various resources by the consumers; and (3) the effects of those consumption rates on the demographic rates (birth, death, growth) of the consumers.

Models of interspecific competition from the period 1973-1980 that included resources often had results that differed from those of the most comparable mod­els that lacked resources (e.g., Schoener 1973,1974c, 1976,1978; Abrams 1975,1977, 1980a). Calls for representing competition using resource-based models continued in the 1980s (e.g., Abrams 1983a, b; Schoener 1982, 1986; Tilman 1982, 1987), and have been repeated more recently (McPeek 2019a, among others). Even if a model is developed by assuming that resources are at quasi-equilibrium with respect to cur­rent consumer densities, deciding on the form of that model requires knowledge of the dynamics of the resources. Once a resource-based model is constructed it makes little sense to replace it with an approximation to it that leaves out resources (Abrams 1975). Letten and Stouffer (2019) is a recent analysis that nevertheless does so. They show that consumer-only models with fitted nonlinear terms can better approximate resource-based models than can the LV model. However, except as part of a critique of the LV model, it is unclear why one would need or want to replace a model with explicit resources by an approximation that lacked them. Chapter 6 will show that simple models with explicit resources often predict that the interspecific effect of one consumer species on another is positive rather than negative, at least for some ranges of population sizes. Chapters 8 and 9 demonstrate that explicit representa­tion of resource dynamics is particularly important for understanding competition in variable environments.

At this point, a brief digression regarding the three component functions of consumer-resource interactions identified above is called for. It turns out that our current understanding of each of these is at best inadequate. This theme is devel­oped in more detail in Chapter 3.

The numerical response has been the subject of surprisingly little research, which has led to the assumption that it is linear in the vast majority of models.

Box 2.1 Functional responses and their role in competition

One of the key elements of any consumer-resource system involving foods or nutrients as resources is the set of ‘functional responses’ of the consumers to the resources. A func­tional response is the relationship between the abundance of the resource and the amount ‘consumed’. That relationship may depend on the abundances of other resources and on the abundances of a variety of other interacting species. Functional responses have been a key element of consumer-resource systems from the time that C. S. Holling (1959, 1965) proposed a set of four (later often reduced to three) common shapes for systems having a single type of resource. These relationships implicitly assumed no effect of abundance of other resources, predators, or any species other than the one resource in question, a problem discussed in Chapter 3. MacArthur (1970,1972) assumed linear (Hollingtype I) functional responses for the consumers in his exploration of the connections between one particular consumer-resource model and the LV model. Type I responses imply no upper limit on the intake rate of the resource, a biological impossibility that is not present in Holling’s types II, III, or the seldom-mentioned type IV. Oaten and Murdoch (1975) extended the type II response to systems with multiple resources, but did not discuss this in connection with competition. A type II response to resource 1 in a system with two resources (R₁, R₂) is rep­resented by C₁R₁∕(1 + C₁h₁R₁ +C₂h₂R₂). Here C_i is a per capita attack rate while searching and h_i is the handling time for resource i.

Box 2.1 Continued

1-predator-1-prey systems. Later, Armstrong and McGehee (1976a, 1980) showed that a type II response in one consumer species could allow coexistence of two consumer species on a single self-reproducing (‘biotic’) resource. Abrams (1980a) investigated systems with two consumers and two resources, and showed that similar type II consumer functional responses in both species made the strength of competition very sensitive to the absolute and relative abundances of the two consumer species; i.e., competition was a highly nonlin­ear function of abundances. Abrams’ (1980a) analysis was confined to systems that did not cycle, but the dependence of measures of competition on the parameter values of the model is also nearly universal in cycling systems, as well as being significantly different from the corresponding measures in analogous systems having type I responses (Abrams et al. 2003; Abrams 2004b). Subsequent empirical work on competition has largely ignored functional responses, except for some studies of phytoplankton competing for abiotic resources; these have largely assumed the simplest form of the Holling type II response (see Abrams 1990c for other forms). The form of resource dynamics could be equally important in determin­ing the strength of competition and the linearity of competitive effects (Abrams 1980b). Functional responses are the central topic of the following chapter, where more details are given. However, the simple early results reviewed in this box illustrate why considering these responses, and the resource dynamics they produce, are essential for understanding competition. This argues strongly for including resources in the definition of competition.

Ecologists should not be (and generally are not) only interested in the change in population size in one competitor that is caused by adding or subtracting some particular number of individuals of a single competing species (or adding or sub­tracting them at some specific rate).

An understanding of interactions with resources is also needed to determine the relative fitness of individuals with different traits; this, in turn, is required to under­stand the evolutionary trajectory of that species and many of those that interact with it. By leaving resources out of a model, it becomes difficult to do any of this, and the lack of resources has already been a source of misunderstanding. This is true for intra- as well as interspecific competition. Leaving out resources in models of single­species growth has led to the idea that adaptive evolution will not decrease population size. This traditional view was buttressed by early models of r- and K-selection based evolution of the parameters of logistic growth, the traditional model of intraspe­cific competition. However, this evolutionary result was shown to be inconsistent with consumer-resource models by Matessi and Gato (1984). Evolution of the rate of resource consumption reduces population size in a large range of systems with self­reproducing resources. Nevertheless, the popularity of the logistic model of intraspe­cific competition (density dependence) has led to the persistence of the incorrect view that adaptation always increases population size, and maladaptation decreases it (see Abrams 2019). Similarly, the persistent belief that evolution favours divergence in the relative use of different resources when two competing species come into sympatry is inconsistent with many resource-based models (Abrams 1986a, 1987a, b; Vasseur and Fox 2011). More details on evolutionary responses to competition are provided in Chapter 11.

Even if we put aside the issue of resource dynamics, the definition of competition based on mutually negative changes in population size is inconsistent with the out­comes of many models having three or more competitors (even for models as simple as the Lotka-Volterra model). Most ecologists in 1970 would have admitted that com­petition between species was not confined to species pairs. Yet the bulk of theory on competition is still based on the two-species case. Levine's (1976) demonstration that an increase in one competitor's population could increase that of a second competitor by causing large changes in the abundance of a third competitor should have changed this narrow focus. This was followed by a more detailed analysis of sets of three-or- more species interacting according to the LV model (Gilpin and Case 1976; Lawlor 1979), which again demonstrated that net positive effects were possible in many cases. These results showed that mutually negative changes in population size cannot be the defining feature of competition, unless one places restrictions on the range of admis­sible systems. Allowing only two competitors would reduce, but not eliminate this problem, as shown by Levine's (1976) example with competing resources. In addi­tion, there is the well-known example of rock-scissors-paper types of interaction in 3-species competitive systems (e.g., May and Leonard 1975; Laird and Schamp 2006; Soliveres et al. 2015). These involve intransitive competition in which, for example, species 1 would exclude species 2 in a strictly two-species system; 2 would exclude 3, and 3 would exclude 1. Long-term coexistence of all three can occur in many such systems. Such systems also are characterized by the fact that mortality applied to one competitor can increase its abundance (Cortez and Abrams 2016), a result that affects some sign-based definitions of interspecific interactions. A variety of views have been expressed on whether such intransitive competitive systems are common. Soliveres et al. (2015) make the case that they occur frequently. Even if this assessment is not correct, there is no doubt that intransitive competition does occur, and interactions in such systems cannot be described as mutually negative effects on abundance.

The above discussion does not imply that models lacking explicit representation of resource dynamics are always inadequate for answering all questions regarding the population-level effects of competition. Competition for space is one example, since the resource can reappear immediately when an occupying individual dies. However, even here, death may not immediately produce usable space; it may be necessary for most of the remains of the dead individual to decay or be otherwise removed before the space is again suitable for occupancy. Similarly, in a more-or-less closed aquatic system with competition for nutrients, the nutrients contained in dead or consumed individuals may be rapidly recycled, potentially allowing the approximation that the amount of resources in the system is functionally determined by the current num­ber of consumers (e.g. Miller and Klausmeier 2017; Kremer and Klausmeier 2017). However, most recycling takes time, so the dynamics of space regeneration may be important. In any event, having a definition of competition based on shared use of resources makes it far more likely that such assumptions are assessed before mak­ing predictions using a simpler model. And the proper form of the consumer-only approximation should be determined using a reasonable model of the dynamics of the resource.

2.5