A brief history of work on the evolutionary responses to competition
ll.2.l Empirical studies of competitive coevolution
Empirical work preceded theory dealing with competitive coevolution. Brown and Wilson (1956) coined the term ‘character displacement' for what they thought to be the primary evolutionary response to competition; two competing species evolve greater differences in the values of traits determining their use of one or a set of limiting resources.
This ‘displacement' or ‘divergence' was thought to reduce the negative impact of competition on fitness. Divergence was supported by anecdotal observations in Hutchinson (1959) who found some cases where character differences were greater in sympatry than in allopatry. Schoener (1965) presented an extensive analysis of intraspecific variation in bill size in 46 families of bird species and concluded that some of the patterns were consistent with character displacement. Bill dimensions associated with food use diverged in possibly competing species in a number of cases. Grant (1972) argued for the possibility of character convergence of competitors in some cases, but the evidence for such responses was weak, and some convergence could be predicted as a common response to being in a new and different environment. In another review article Schoener (1970) found a significant number of studies that indicated convergence in head and body size measures of pairs of Anolis lizard species in the Greater Antilles. The convergence, particularly of larger species towards smaller ones, appeared to be at least partially an effect of different habitat structure rather than the change in competition. In any case, subsequent general theory concentrated on divergence.The evolutionary responses that have most often been studied using multiple field sites or semi-natural constructed communities are those involving consumption rates of different resources by two or occasionally three species.
Studies of communities of two or three Galapagos finches on a variety of islands by Peter and Rosemary Grant (Grant and Grant 2008) and of two stickleback fish subspecies by Schluter and collaborators (Schluter 2000, McKinnon et al. 2004) are probably the best-known examples. Both systems exhibited divergence in response to competition, and a variety of evidence from other systems has strongly suggested that divergence has occurred.Schluter (2000) provided a summary of the evidence for character displacement at the turn of the millennium; by that time, this set of studies included a larger number of strongly supported examples of character displacement, but most had some caveats. There were 71 cases with 61 of those involving a pair of congeneric species. However, only 14 of the congeneric cases met all six of Schluter's criteria for strong evidentiary support. Most of the 10 additional (not congeneric species) cases had relatively weak evidence. Nevertheless, given the high prevalence of effects of interspecific competition on abundance, the number of strongly supported examples of character divergence in sympatry seems to be rather small (Schluter 2000; Pfennig and Pfennig 2010). Is this because evolutionary responses are rare, or small in magnitude, or because the responses have forms other than mutual divergence? This question is still unanswered.
11.2.2 A history of theoretical models of competitive coevolution
A proper study of the evolutionary consequences of competitive interactions requires knowledge of the relationship between demographic parameters and the evolving traits. This in turn depends on having some knowledge of the functional and numerical responses of the competing species. Similar requirements apply for studying intraspecific competition and apparent competition. In all of these cases, the evolving parameters and changing population size(s) necessarily influence each other's dynamics via functional and numerical responses. This would seem to make consumer-resource models the logical choice for studying evolution in any of these scenarios.
Despite this, most models have been based on modified LV models, in which consumers have direct effects on each other. A problematic aspect (beyond the limited possibility of getting LV dynamics from resource-based models) is that the parameters of the LV model can have a wide variety of relationships to measurable quantities, such as maximum consumption rates of resources. Nevertheless, most models of competitive coevolution continue to be based on a Lotka-Volterra framework, usually assuming MacArthur's proposed formula for the competition coefficient.The first published model of character displacement was that of Bulmer (1974), although an unpublished Ph.D. thesis treated the topic a decade earlier (Bossert 1963). Bulmer used a one-locus-two-allele model of displacement and focused mainly on intraspecific competition. His underlying ecological model assumed discrete generations of the consumers and used linear effects as an approximation that should be valid near equilibrium. Bulmer's work has not been cited much in the subsequent literature on character displacement, perhaps because his discrete framework was inconsistent with the more popular differential equation models of ecological theory.
A short time later, Lawlor and Maynard Smith (1976) published the first consumer-resource model of character displacement. This study looked at 2- consumer-2-resource models, but adopted MacArthur's assumptions of linear consumer functional and numerical responses. It assumed that a trade-off function specified per capita capture rates of each resource as a function of the trait. This tradeoff meant that an evolutionary increase in one capture rate would decrease the other. Depending on whether the trade-off was convex or concave, a single consumer could evolve to be either one of two specialists (concave) or a generalist (convex). This study did not include explicit trait dynamics, but assumed that the system would evolve to an evolutionarily stable state. It predicted that divergence of two competitors would occur, so that they would have a greater difference in trait values in sympatry (living together) than in allopatry (living apart).
The most influential early study was Slatkin’s (1980) analysis, which adopted a Lotka-Volterra framework. Some elements of his analysis were present in slightly earlier works by Roughgarden (1976) and Fenchel and Christiansen (1977). Slatkin assumed a continuous trait, with dynamics governed by the ‘breeder’s equation’ of quantitative genetics. This assumes that the mean value of the trait changes at a rate proportional to the fitness gradient (i.e., the slope of the relationship between the trait and fitness). The competition between two consumers having different values of a single trait related to resource use was a decreasing function of their difference in phenotypic values as in MacArthur and Levins (1967). This basic ecological assumption was combined with the breeder’s equation model for the evolution of the mean value of the trait determining resource use. Although Slatkin (1980) stated that Lawlor and Maynard Smith’s (1976) consumer-resource model produced predictions similar to his, subsequent extensions of the Lawlor and Maynard Smith models (Abrams 1986a; 1987f, g; 1990a, b; Abrams et al. 2008b; Abrams and Cortez 2015b) made predictions that often differ significantly from both Slatkins work and that of Lawlor and Maynard Smith.
Taper and Case (1985) extended Slatkin (1980) in several ways; one was to numerically study some versions of MacArthur’s (1970) consumer-resource model with many explicit resources. However, it appears that their parameter range did not involve resource exclusion, so their results were largely consistent with those derived from the Lotka-Volterra model. Slatkins (1980) work predicted that convergence of competitors was possible, but this convergence did not represent a difference between sympatric and allopatric traits; it was a case in which the original trait values were not at their allopatric equilibrium values, and both species had their maximum resource capture rate at the same phenotypic value. Taper and Case (1992) and Case and Taper (2000) extended the same coevolutionary model to examine the role of asymmetry and degree of trait variation and to consider the effect of coevolution on species range limits.
Taper and Case (1992) stressed the limited real-world applicability of their assumptions of fixed carrying capacity curves, Gaussian utilization curves, and Lotka-Volterra dynamics. Nevertheless, these have remained as the default assumptions in most of the subsequent literature.The definition of convergence depends on whether it is being applied to the process of character displacement, or just the direction of evolution from some arbitrary starting character value. Character displacement compares the evolutionary equilibrium with and without a competitor. In contrast, invasion by a competitor from another location, potentially having different resources and conditions, can involve evolution that is driven more by the new environment than by the competitor. Both Slatkin (1980) and McPeek (2019b) have described the latter as evolutionary convergence. However, it is not convergent character displacement. It is not surprising that a sufficient inequality in productivities of different resources within a habitat can favour two species evolving to have their resource use concentrated on the most abundant or productive type.
There appeared to be rough consistency of the qualitative predictions of the continuous resource spectrum models growing out of Slatkins (1980) study and the early 2-consumer-2-resource models of Lawlor and Maynard Smith (1976). Both predicted divergent character displacement (when the sympatric equilibrium is compared to the allopatric one). However, several later studies of resource-based models have examined evolution of characters determining resource capture rates and that produced outcomes other than divergent character displacement (Abrams 1986a, 1987f, g, 1990a, b; Vasseur and Fox 2011). Some of these studies examined non-substitutable resources and/or asymmetric patterns of resource use. Others included the possibility of negative effects of consumer abundance on mortality that were independent of resource consumption rates (i.e., interference).
The evolutionary responses in systems with non-substitutable resources are considered further in Section 11.4, and interference is considered in Section 11.6.Returning to the substitutable resources assumed by all of the earliest theory, both of the early models (Lawlor and Maynard Smith 1976; Slatkin 1980) assumed linear functional responses. Type II responses can give rise to population cycles. Abrams (2006a, b, 2007b) studied evolution in a 2-resource model with type II consumer functional responses. This led to the possibility of up to four coexisting consumers in systems with cycles, even though only two could coexist in the comparable linear functional response models of Lawlor and Maynard Smith (1976). Cases in which addition of the second consumer gave rise to cycles could result in different directions of character response in the original species than in cases without cycles.
Evolutionaryresponses to purely intraspecific competition are important for both speciation and the regulation of variation within a species. Very early studies examined evolution based on the logistic growth model with two parameters, maximum per capita growth rate, r, and equilibrium population size, K (e.g., Charlesworth 1971). This suggested that populations at equilibrium should maximize population size as a result of evolution of intraspecific competition. This was shown to be inconsistent with consumer resource dynamics by Matessi and Gatto (1984). Most subsequent work has focused on situations that produce disruptive selection, which has the potential to produce two species with distinctly different character states. Understanding disruptive selection almost always requires a resource-based approach. This is because traits determining the relative consumption rates of different resources are usually the characteristics involved in disruptive selection (Abrams et al. 1993; Geritz et al. 1998; Dieckmann et al. 2004). Most work on the evolution of traits involved in intraspecific competition from the past two decades has in fact included explicit resource dynamics (Dieckmann et al. 2004; Rueffler et al. 2006a,b).
Returning to interspecific competition, an important but neglected point is that an evolutionary response to shared resource use with another consumer is likely, even when the shared resource use does not affect the equilibrium population size of a focal consumer (Abrams 2012, Abrams and Cortez 2015b). Consider two consumers, either one or both having a specialist, food-limited predator. In this case, the specialist predator determines the equilibrium abundance of the consumer species it eats. Changing a neutral parameter in this consumer will not change its equilibrium abundance. However, the neutral parameter will generally produce an evolutionary response in a second consumer, because it will result in altered relative abundances of different resources. Figure 11.1 is a food web diagram of such a system with a predator on one of two competing consumers. Assuming a standard 3-level model like that in Chapter 7, a change in the mortality rate of the generalist consumer species 2 (d2) will not alter the population size of consumer 1 (population N1), unless the change is a sufficiently large decrease to exclude consumer 2. However, any increase in d2 decreases N2, and therefore changes the relative abundances of the two resources at equilibrium. If species 1 has a trait that determines its relative capture rates of the two resources, this trait will change in response to those altered resource abundances, even though species 1's own equilibrium population is unchanged. Whether this response represents convergence or divergence depends upon the consumption rates of the consumers and the trade-off relationship between those rates within each species. The higher-level predator in this example has an impact similar to that of an independent limiting factor, such as nesting sites, for consumer 1.
A question related to the above example is the issue of how evolution of one or both competitors changes their own population size. The usual assumption is that adaptive evolution will increase population size. In fact, simple consumer-resource models suggest that the adaptive evolutionary response to competition may often reduce the population size of the evolving species (Abrams 2012, Abrams and Cortez 2015b). This possibility had not been noted in the earlier theoretical or empirical literature (Schluter 2000). This is primarily because most of the earlier theory lacked explicit resources, and most of the empirical work had not (and still has not) quantified population responses to evolutionary change. Similarly, when two consumers have positive effects on each other's population density (e.g., when there is competition between resources), the divergence brought about by adaptive evolution will frequently reduce the population size(s) of the diverging species (Abrams and Cortez 2015b).
11.3