AbstractThis book explores how mathematical models can illuminate the interaction known as interspecific competition. Competition occurs whenever two or more species share at least some of the same limiting resources. It is likely to affect all species, as well as many higher-level aspects of community and ecosystem dynamics. Interspecific competition shares many of the same features as density dependence (intraspecific competition) and evolution (competition between genotypes). In spite of this, a robust theoretical framework for understanding its outcomes and many potential effects on ecological communities is lacking. Despite its prominence in the ecological literature, the theory seems to have lost direction in recent decades, with many synthetic papers promoting outdated ideas, failing to use resource-based models, and having little utility in applied fields such as conservation and environmental management. The book examines how theory that began to be developed half a century ago can be extended to illuminate the effects of environmental change on the abundances of competing species. Current competition theory needs to incorporate findings regarding consumer–resource interactions in the context of larger food webs containing behaviourally or evolutionarily adapting components. Overly simple models and methods of analysis have led to past theory contributing less than it should have to practical applications. The book also discusses the related interactions of intraspecific competition and apparent competition, and examines the evolutionary as well as the ecological effects of this important process.

Abstract Chapter 2 discusses the definitions of interspecific competition used from the middle of the twentieth century until today. It shows that definitions based on mutual resource use or mutually negative effects on population growth have both been used in the past, and both are still being used. The chapter shows that these definitions identify different, although overlapping sets of systems. The chapter then argues for a definition based on use of shared resources. Mutual resource use can result in positive effects of each species on the other, or one positive and one negative effect. Some of the circumstances producing these outcomes are identified. The mechanism-based definition has the advantage of making competition theory more consistent with theory dealing with other indirect effects. This category of definition also leads to better descriptions of the interaction, and a better ability to understand coevolution of the interacting species. Descriptions of competitive interactions must include descriptions of resource growth, and both consumer functional and numerical responses. The chapter discusses the need for a more consistent basis of classifying and understanding all indirect interactions in food webs.

This article reviews the nature of functional responses that have commonly been used to represent feeding relationships in the ecological literature. It compares these with the range of functional response forms that are likely to characterize species in natural communities. The latter set of responses involves many more variables. The article reviews the history of functional response models, and examines previous work that has allowed the functional response of a predator to a single type of prey to depend on additional variables beyond the abundance of that prey type. While a number of more complex functional responses have been discussed over the years, many variables affecting feeding rates are still typically omitted from models of food webs. The influences on functional responses from trophic levels above that of the predator or below that of the prey are particularly likely to be ignored, although models and data have suggested that they can have large effects on the functional response. The influences of adaptive behavior and of the time-scale of response measurement are also too often ignored. Some of the known and unknown consequences of these omissions are discussed.

AbstractChapter 4 analyses six recent, high-profile articles to determine to what extent they have adopted a consumer–resource approach, and have advanced our understanding of interspecific competition. Five were chosen because they were the most highly cited articles (as of 2020) published in 2017 or later. The sixth was published most recently, so has had less time to accumulate citations; it appeared in the same journal as the majority of the top five articles, and had an approach that was more consistent to that recommended here. Several other recent articles are discussed more briefly. The results show that many articles are based on models that either ignore resources, or adopt extremely simplified component functions to describe the dynamics of the consumers and resources. Others use simplified analyses that may not reveal the true outcome of competition; this is the case for the one article that argues strongly for a consumer–resource approach.

This chapter analyses a version of simple models of competition for a single resource between two species with different seasonal variation in their resource capture rates. This scenario had been shown to promote coexistence in earlier studies. The chapter shows that, for different parameters, the ability of species to coexist often decreases with greater differences in their season resource uptake patterns. In addition, a given pair species often has alternative outcomes, which may be two different coexistence outcomes, two exclusion outcomes, or coexistence and exclusion. This is related to the fact that a single consumer may also have several alternative attractors, due to interaction of the inherent consumer–resource cycle and the seasonality in capture rate. Most of the models assume a single resource type with logistic growth, but the qualitative results can also be found in systems with abiotic resource growth and systems with multiple resources. Longer period lengths for the cycle in capture rates favours coexistence over exclusion outcomes, and coexistence of multiple species at long period lengths is possible. Coexistence of seasonal and aseasonal species on a single resource can occur, and the same mechanism operates in systems with type II functional responses. The results have several general messages about seasonal systems: (1) increasing similarity can make coexistence more or less likely; (2) invasion ability often does not imply persistence in cases with multiple attractors, which includes many seasonal systems; (3) differences in seasonal responses often produce qualitatively different outcomes than do other types of resource segregation.

AbstractInterspecific competition shares the same dependence on consumer–resource interactions as intraspecific competition and apparent competition. These two related interactions are the subject of this chapter. Both interactions are present in most, if not all, systems in which interspecific competition occurs. Intraspecific competition is usually discussed in the context of models that lack resources, while models of apparent competition always involve explicit dynamics for consumers and resources. The chapter examines whether these differences are justified, and concludes that both interactions should be studied using a consumer–resource framework. The ‘theta-logistic’ is a popular model that extends the logistic by allowing for density dependence under which per capita growth rate decreases as abundance raised to a positive power other than unity. This, however, is shown not to correspond to popular consumer–resource models. In addition, it lacks the time lag in consumer response that follows from resource dynamics. Traditional measures of density dependence are complicated by the possibility that adverse changes in a neutral parameter can cause the equilibrium or mean abundance of a consumer to increase (i.e., a ‘hydra effect’). The forms of density dependence for several simple consumer–resource models are analysed and compared. Although apparent competition is always based on consumer–resource models, the vast majority of the literature only considers a single consumer, and usually assumes the systems are stable. The consequences of having instability and/or two or more consumer species are analysed.

AbstractThis chapter uses relatively simple consumer–resource models to show that several phenomena that are impossible under the Lotka–Volterra model are common in models with resources. For the vast majority of models, all common measures of competitive effect differ depending on the size of the initial change used to make the measurement. Adding, removing, or changing the growth rate of a second consumer can produce, alter, or eliminate population cycles, and thereby alter the interaction. Changes in stability are almost always associated with large magnitude changes in competitive effects. If the experimental change used to measure the interspecific effect causes resource extinction, this often causes a discontinuous jump in the magnitude of the competitive effect. In two-resource systems, the possibility of resource extinction in the presence of a single consumer can lead to exclusion of a second consumer. In this case, the later arriving of two competitors always excludes the earlier one, producing a ‘posteriority’ effect. Such effects have never been observed. In systems where resource immigration prevents exclusion, posteriority does not occur. Systems in which each species has an exclusive resource are particularly likely to have very nonlinear competitive effects, and coexistence may be guaranteed in spite of high overlap in consumption rate curves.

AbstractThis chapter examines the relationship between similarity in the relative abilities of two consumers to capture available resources and the amount of competition between them. From a theoretical perspective, this question was regarded as having a simple and universal answer in the early 1970s. However, the proposed Gaussian shape of resource utilization curves was shown to be rare in empirical systems. The resulting form of the similarity–competition relationship also was shown to depend on linear functional and numerical responses plus independent logistic growth of all resources. Theory suggests that a wide range of similarity–competition relationships occur in natural systems. Empirical studies of the actual relationships have been limited by lack of knowledge of resource dynamics, and most studies have limited spatial extent with a bias towards studying strong competition. Hermit crab competition for shells is one of the systems in which the process can be easily studied in the field. Work on such systems from 40 years ago suggested that interspecific competition in cases was weak relative to intraspecific in most communities. The chapter concludes with an analysis of a 6-species model to examine the relative effects of a competiting consumer vs species on higher or lower trophic levels on coexistence of the two consumer species. In a wide range of systems, the competitor is not expected to have the largest effect on existence.

AbstractThis chapter shows that many of the consumer–resource interactions that underlie competition in natural systems are likely to be quite different from those considered by Robert MacArthur’s model. In addition, most of the wide variety of potential forms for models have still have not been analysed. The chapter introduces two measures of the strength of competition, the second of which is equivalent to the competition coefficient in the Lotka–Volterra model. The chapter presents replies to two arguments that explicit representation of resources is unnecessary in models of competition. MacArthur’s consumer–resource model is presented and his analysis of this model is summarized and critiqued. MacArthur ignored the potential for resource exclusion or invasion to occur when one of the competing species experiences positive or negative environmental change. A second failing of this model is its inability to produce population cycles in the two-competitor version. An example shows that such cycles can greatly alter average abundances and competitive effects. The effects are highly nonlinear, and can change sign and magnitude with small changes in the mortality rate of either of the consumer species. The important roles of resource growth and consumer functional response in determining the nature of competition are discussed. Recent work on the role of adaptive behaviour in determining the shape of functional responses has yet to be incorporated into models of competition. The use of some simplified methods of analysing consumer–resource models is criticized.

AbstractThis chapter continues the analysis of seasonal competition, begun in Chapter 8. It examines cases in which there are differences in the shapes of two consumer species’ demographic responses (functional and/or numerical response) to resource abundance. Temporal variation affects parameters other than the consumer’s per capita resource capture rate, including variation in the resource growth rate or in a neutral parameter of one or both consumers. As in Chapter 8, temporal variation can make exclusion either more or less likely depending on the details of the mechanism(s) driving that variation. Mutual invasibility of single consumer systems is often not required for coexistence. Alternative attractors are a frequent occurrence in these systems, and different period lengths of temporal environmental variation can result in qualitatively different effects on coexistence. The complicated outcomes are largely due to interaction of the environmental seasonality with the inherent periodicity of one or both consumer–resource interactions.

Abstract This chapter examines the effects of competition on the evolution of the competing species. Like most of the scientific work on this topic, it concentrates on systems having two competitors. The chapter begins by pointing out the focus of previous work on the evolution of traits affecting resource capture rates, which are not the only consumer characteristics that may evolve due to the addition of another consumer. Previous work has concentrated on divergence of traits, which is not the only outcome that competition may produce. The differences in predictions of models that include explicit representation of resources and those that do not are discussed. Convergence or parallel change are also expected to occur in response to the addition of a competing species, with these outcomes often associated with nutritional or other interactions between resources, and with interference components of competition in the consumers. Most previous work has ignored the role of resource evolution in response to the addition of a consumer; this can alter the direction of trait change in the consumer. Theory shows that evolutionary responses to competition should often reduce the population size of the evolving species, but this has yet to be studied in natural systems. Apparent competition is also expected to produce evolutionary responses, but it remains largely unstudied.

AbstractCompetition always has some spatial component, and this chapter explores the main effects that spatial subdivision has on competitive interactions. After a brief general description of various ways in which spatial issues can be modelled, the chapter explores a metacommunity approach, in which interactions occur within discrete patches, and movement can occur between any pair of patches. This means that competition and coexistence can be measured locally or globally, with the latter measurement being more appropriate for comparison with homogeneous systems. Measuring the shape of competitive interactions in the whole system is affected by the different effects of a neutral parameter in those patches, and by extinctions within patches. In systems having logistic resources where one consumer experiences environmental change, extinctions occur first in patches that have larger contributions to the total competitive effect. This produces a concave relationship between total population size and mortality. Random movement of resources must occur at quite high rates to make a metacommunity approximate a homogeneous system. Random movement of two consumer species at different rates in a metacommunity can lead to coexistence or produce exclusion of the superior consumer. Adaptive consumer movement often makes the abundances of two consumers less sensitive to changes in a neutral parameter of one of them. Adaptive movement may increase or decrease the synchrony of consumers in systems with cycles. More work on mathematical descriptions of adaptive movement is required to better understand competition in metacommunities.

Maximum Sustainable Yield (MSY) theory, based on a single species dynamics model, has been considered to rule out both no-take rules and overfishing. It is thought to recommend moderate catch rates that do not lead to exhaustion of the fish population. However, ecosystems are complex systems, and they usually have uncertain observations and nonstationary dynamics even in the absence of fisheries or interspecific interactions. There is a need to build a new management theory that takes these aspects of an “ecosystem approach” into consideration.One example, where single species approaches are clearly inappropriate is the case of sardine, anchovy, and chub mackerel. It is known that these small pelagic fish repeatedly alternate outbreaks every several decades, and this phenomenon is called “fish species replacement”. The mechanism of species change has not been clarified, and it is difficult to predict its dynamics.Adaptive management is attracting attention as a strategy for sustainable resource use based on feedback control and adaptive learning with uncertain information (Walters ). Adaptive management is a measure to understand resource dynamics through continuous monitoring and to flexibly respond to fluctuations of resource abundance. Rather than predicting resource fluctuations, we aim for human beings to respond appropriately ex post facto. Adaptive management can cope with resources that are difficult to predict and have large fluctuations.In previous work, we also considered how to design fishery regulations in systems having various prey/predator types. This work assumed that the amount of effort towards catching each fish species could be adjusted independently. The fishing effort for each species together with their abundances and relative values defined the total fisheries yield, denoted by Y, which is called the “multispecies MSY” or the maximum sustainable revenue. We selected 1000 virtual food webs with random variables of community structure parameters and calculated the multispecies MSY for a system with coexistence equilibrium points in the absence of catch. We also asked for MSY (called conservation MSY) under the constraint that all species persist.

Antarctic toothfish Dissostichus mawsoni and Weddell seals Leptonychotes weddellii are important mesopredators in the waters of the Antarctic continental shelf. They compete with each other for prey, yet the seals also prey upon toothfish. Such intraguild predation means that prevalence and respective demographic rates may be negatively correlated, but quantification is lacking. Following a review of their natural histories, we initiate an approach to address this deficiency by analysing scientific fishing catch per unit effort (CPUE; 1975-2011 plus sporadic effort to 2018) in conjunction with an annual index of seal abundance in McMurdo Sound, Ross Sea. We correlated annual variation in scientific CPUE to seal numbers over a 43 year period (1975-2018), complementing an earlier study in the same locality showing CPUE to be negatively correlated with spatial proximity to abundant seals. The observed relationship (more seals with lower CPUE, while controlling for annual trends in each) indicates the importance of toothfish as a dietary item to Weddell seals and highlights the probable importance of intra- and inter-specific competition as well as intraguild predation in seal-toothfish dynamics. Ultimately, it may be necessary to supplement fishery management with targeted ecosystem monitoring to prevent the fishery from having adverse effects on dependent species.

In 1957, George Williams [ 1. Williams G.C. Pleiotropy, natural selection, and the evolution of senescence. Evolution. 1957; 11: 398-411 Crossref Google Scholar ] argued that higher, age-independent, adult mortality should be correlated with more rapid senescence. Charlesworth [ 2. Charlesworth B. Evolution in Age-Structured Populations. Cambridge University Press, 1980 Google Scholar ] and most subsequent studies have added the adjective 'extrinsic' to mean that the age-independent mortality was due to sources 'external' to the organism. We now know that neither age- nor condition-independent increases in extrinsic mortality are necessary for more rapid senescence to evolve, and analyses have also shown that higher mortality can lead to the evolution of slower senescence [ 3. Abrams P.A. Does increased mortality favor the evolution of more rapid senescence?. Evolution. 1993; 47: 877-887 Crossref PubMed Google Scholar , 4. Williams P.D. Day T. Antagonistic pleiotropy, mortality source interactions, and the evolutionary theory of senescence. Evolution. 2003; 57: 1478-1488 Crossref PubMed Scopus (198) Google Scholar ]. Indeed, there are empirical examples where an added source of mortality seems to have extended lifespan [ 5. Reznick D.N. et al. The effect of extrinsic mortality on the evolution of senescence in guppies. Nature. 2004; 431: 1095-1099 Crossref PubMed Scopus (334) Google Scholar ]. Nevertheless, Williams' hypothesis remains popular [ 6. Gaillard J.-M. Lemaitre J.-F. The Williams' legacy: a critical reappraisal of his nine predictions about the evolution of senescence. Evolution. 2017; 71: 2768-2785 Crossref PubMed Scopus (68) Google Scholar ].

This article argues that adaptive evolutionary change in a consumer species should frequently decrease (and maladaptive change should increase) population size, producing adaptive decline. This conclusion is based on analysis of multiple consumer-resource models that examine evolutionary change in consumer traits affecting the universal ecological parameters of attack rate, conversion efficiency, and mortality. Two scenarios are investigated. In one, evolutionary equilibrium is initially maintained by opposing effects on the attack rate and other growth rate parameters; the environment or trait is perturbed, and the trait then evolves to a new (or back to a previous) equilibrium. Here evolution exhibits adaptive decline in up to one-half of all cases. The other scenario assumes a genetic perturbation having purely fitness-increasing effects. Here adaptive decline in the consumer requires that the resource be self-reproducing and overexploited and requires a sufficient increase in the attack rate. However, if the resource exhibits adaptive defense via behavior or evolution, adaptive decline may characterize consumer traits affecting all parameters. Favorable environmental change producing parameter shifts similar to those produced by adaptive evolution has similar counterintuitive effects on consumer population size. Many different food web models have already been shown to exhibit such counterintuitive changes in some species.