Choosing articles to represent current competition theory

To what extent has competition theory embraced the use of consumer-resource mod­els, included more than two competitors, addressed questions other than coexistence, and dealt with the other issues raised above? I examine a set of the most influential recent works on ecological competition to shed light on this question.

There have been many other prominent recent works published during the years since 2017. Most of these are discussed more briefly here or in later chapters. They include Germain et al. (2018), Hart et al. (2018), Chesson (2018), Letten and Stouf­fer (2019), Song et al.

All the articles in Table 4.1 and almost all listed in the previous paragraph refer extensively to Peter Chesson’s (2000a) review article. This is by far the most cited paper dealing with competition from the past 120 years. Chesson’s paper received roughly twice the number of citations during the past year alone than the most cited recent article (Levine et al. 2017) received during the past four years. Treated in more detail later in the book (see summary in Chapter 12), this single work by Chesson seems to have been a major factor in the current focus on coexistence, a focus that has apparently come at the expense of studying the nature of the competitive interaction.

Five of the six articles in Table 4.1 have the word ‘coexistence’ in the title, but none mention ‘competition’ in the title. Mayfield and Stouffer (2017) do not have either word in their title, but their work is the only one that focuses more on the interaction (competition) than on the outcome (coexistence or exclusion). Several of the above, as well as many other recent articles, have proclaimed the existence of a ‘modern’ form of competition/coexistence theory, usually citing Chesson (2000a), who introduced

Table 4.1 Top cited recent papers from 2017 through 2020

*Thisisbasedon a Web of Science search in December 2020. Short summaries of some problematic features of each of these articles are provided in the chapter appendix (section 4.7). Amore recent Web of Science search, just prior to submitting the final manuscript of this book in late February 2022 identified the same set of five top articles, although the relative ranks of the third through fifth had changed. McPeek (2019a) had only approximately 1/6 the number of citations of the currently lowest ranked of the top five in the later search. Holt and Bonsall (2017) was actually ranked second in the recent search, but would not have been included here because it deals almost exclusively with apparent competition.

the idea of separating coexistence into ‘stabilizing’ and ‘equalizing’ factors (but did not use the term ‘modern’). Later articles by Chesson (2018,2020b) updated this idea.

The large number of recent theoretical articles dealing with competition and the frequent claim that they are ‘modern’ seems to suggest major new advances in our understanding of competition, and particularly the theory underlying that under­standing. However, this is contradicted by the fact that the approaches used and recommendations in the recent articles identified in Table 4.1 are inconsistent or contradictory regarding several important issues. One of these is the importance of explicit resource dynamics. Saavedra et al. (2017) base all, and both Levine et al. (2017) and Barabas et al. (2018) base most, of their treatments on models that lack explicit descriptions of resources. In a later influential article on quantifying compet­itive ability, Hart et al. (2018) use a Beverton-Holt model, which also leaves out any explicit resources. Mayfield and Stouffer (2017) argue for modelling competition as a direct effect, but one that includes both linear and quadratic terms in the expressions for per capita population growth rates.

Saavedra et al. (2017) is based on multi-species models, and both they and Levine et al. (2017) stress the need for more multi-species models. However, Saavedra et al. (2017) is strictly based on the LV model, and it is worth noting that a number of arti­cles from the 1970s had analysed 3-or-more species LV models and stressed the need for more work on them (Gilpin 1975; Gilpin and Case 1976; Levine 1976; Lawlor 1979). Moreover, it had been shown that the case of logistic resources was unique among density-dependent growth models in predicting that the per capita impact of one consumer species on another was independent of the resource abundances (Abrams 1983a). Because addition of a third species changes abundances of at least some of the resources used by the original two, the results of Abrams (1983a) imply that the competitive effects between those first two will change in any nonlinear model.

Most of the multi-species works cited by Levine et al. (2017) are cases in which the indirect effects are transmitted via other competitors rather than via changes in resource abundance. The exception is the work of Huisman and Weissing (1999,2001) who explored a set of conditions for a rock-scissors-paper type interaction to arise among three competing consumers, each requiring and using three abiotic resources. The resulting chaotic dynamics can allow coexistence of even more consumers. How­ever, these unusual conditions for three-species coexistence arose only when the consumer species each had their most rapid intake of the resource they required in intermediate amounts (Huisman and Weissing 2001). This scenario seems unlike­ly on evolutionary grounds, since species would be expected to evolve the highest intake rates for the resources required in greatest amounts. Even if we ignore this, the parameter range required for multi-species coexistence is quite narrow (Schip- pers et al. 2001). The argument that interspecific effects between a pair of species are altered by a third species is valid for more probable reasons than the scenario described in Huisman and Weissing (1999).

The six works in Table 4.1 also differ on other issues. Letten et al. (2017) suggest that the division of forces promoting coexistence into ‘stabilizing’ and ‘equalizing’ factors proposed by Chesson (2000a) is a major advance, while Barabas et al. (2018) make the opposite point. The latter work (2018, p. 277) states that ‘these concepts [equalizing and stabilizing factors as components of invasion growth rates] are use­ful when used judiciously, but have often been employed in an overly simplified way to justify false claims’. Barabas et al. (2018) point out limitations of invasion analy­sis in determining the outcome of competition, but other articles in the list make it a prerequisite for coexistence (Letten et al. 2017; McPeek 2019a; Levine et al. 2017). More recently Grainger et al. (2019) published a review in which they argue that inva­sion analysis is, ‘a common currency for ecological research’. This book will point out numerous cases where invasion analysis cannot be used to assess coexistence. Both articles in Table 4.1 that focus on consumer-resource models, (Letten et al. (2017) and McPeek (2019a)), restrict their analysis to systems having equal numbers of con­sumers and resources. Graphical analysis of the dynamics of models was a central feature of Letten et al. (2017) and McPeek (2019a), but was (in my opinion, properly) ignored in other works (Saavedraet al. 2017; Barabas et al. 2018). Manyofthe features of isocline analysis, such as insight into the stability of equilibria cannot be extended to systems with more than two variables; this includes essentially all real competitive communities.

The second most cited paper in Table 4.1, Mayfield and Stouffer (2017, p. 1), states that studying communities ‘often requires some simplification, such as the widespread assumption that direct additive competition captures the important details about how interactions between species impact community diversity’. How­ever, both this article and the related later work by Letten and Stouffer (2019) fail to provide a good reason why the simplification of direct effects (no resource dynamics) is or should be required.

The article by Barabas et al. (2018) is restricted to competition in temporal­ly variable systems, and understanding such systems is incompatible with some of the assumptions and methods advocated in other articles. Temporal varia­tion prohibits graphical analysis using isoclines, and it creates additional mech­anisms by which coexistence can occur when mutual invasion is impossible (see e.g., Chapters 8 and 9). While there is some reference to models with resources, the potentially large effect of the resource dynamics on the nature of variable competition is not explored. The focus of Barabas et al. (2018) is purely on coexis­tence, and they do note some limitations of using invasion analysis in this context. However, they refer to few of the previous works that had earlier made this case.

A surprising aspect of these differences in approach and outright disagreements is that some of the underlying issues had seemed to be close to resolution decades earlier. For example, the need to represent resource dynamics in competition theo­ry was the subject of many works during the decade following MacArthur’s seminal (1970) article (e.g., Schoener 1974a, c, 1976, 1978; Leon and Tumpson 1975; Levine 1976; Abrams 1975, 1977, 1980a; Vandermeer 1980; Tilman 1980). The importance of resources in understanding both the evolutionary and ecological consequences of competition was reinforced in the following decade (e.g., Lundberg and Stenseth 1985; Schoener 1986; Tilman 1987; Abrams 1986a, 1987f, g). Abrams (1987b, 1988a), and Abrams and Shen (1989) pointed out problematic features of the graphical analy­sis introduced by Leon and Tumpson (1975) and later popularized by Tilman (1982). The limitations of such graphical shortcuts were implicit, if not explicit, in all analy­ses of competition invariable environments (e.g., Chesson and Warner 1981; Abrams 1984a; Chesson 1994,2000b, 2003). The fact that dynamics near an equilibrium point could not be extrapolated to competitive systems with sustained large amplitude fluc­tuations was the subject of several works on the limiting similarity of competing species during the 1970s (Abrams 1976; Turelli 1978). The fact that the effect on equilibrium population size of one ‘competitor’ species on a second could become positive when a third competitor was added was a central topic of Levine (1976), Gilpin and Case (1976), Lawlor (1979), Mayand Leonard (1975), and Gilpin (1975), among others. Three-competitor systems were central to MacArthur and Levins’ (1967) introduction and analysis of the concept of the ‘limiting similarity’ of com­petitors. Thus, the need to extend competition theory beyond two species and/or Lotka-Volterra models seemed to be widely accepted well before 1980, and many of the consequences of that extension had already been documented at that point. One of these was the dependence of community composition on the order of inva­sion (Gilpin and Case 1976). This work implied that the ability of a focal species to coexist with others is not identical to its ability to invade from near-zero densities into an existing equilibrium community.

4.4