The nature of spatial competition
Space itself is a resource for many sessile organisms. However, this chapter focuses on space as a ‘container’ for both resources and consumers. What does spatial variation in physical and chemical conditions mean for competition between consumer species? Answering such a question for any real system requires some understanding of the theoretically possible effects.
This in turn requires a family of mathematical models with a range of levels of simplification. The importance of space for interspecific competition was recognized early in the 1970s. Simon Levin (1974, p. 207) stated that, ‘The distribution of a species over its range of habitats is a fundamental and inseparable aspect of its interaction with its environment, and no complete study of population dynamics can afford to ignore it’.Constructing and analysing the simplest consumer-resource models of competition for systems with a small number of patches is a first step in developing an understanding of the range of spatial effects. Surprisingly, this task is still quite incomplete. As a result, many questions remain unanswered. Is a resource item that is present at one spatial location part of the same resource population as a second, physically or biologically identical, resource item at a different location? What amount of spatial separation is sufficient to ensure that two consumer individuals or two resource items belong to distinct populations? These questions cannot be answered in the context of most models of competition discussed thus far in the book, as they do not include space, except as a source of a fixed amount of immigration. In addition, most of the models have assumed that each population is well mixed within the area that is described.
Yet space in reality is a continuous variable, and the level of resolution applied to understand it is always an issue.
Both consumer and resource items/individuals are characterized in part by their current location. Even within an area that has uniform physical, chemical, and biological conditions, a consumption event will have its greatest impact on consumers that are located nearby. These close individuals are most likely to have encountered the resource item subsequently if it had not been consumed. Thus, not having an exact and continuous description of space always involves at least some degree of simplification.Another complication is that most habitats in which species occur are characterized by spatial variation in conditions. These conditions are usually defined as
Competition Theory in Ecology. Peter A. Abrams, Oxford University Press. © Peter A. Abrams (2022).
DOI: 10.1093∕oso∕9780192895523.003.0010 physical and chemical properties, but they may also be defined to include the presence or abundance of species other than the focal set of competitors. Unfortunately (from a modelling standpoint), different variables and/or different conditions usually do not have identical patterns of spatial variation. This fact may require a high level of spatial resolution to accurately describe the interaction between species. This again causes problems, as representing multiple quantities in continuous space in a tractable mathematical model is generally impossible. Even if the model could be formulated, spatially local parameter values could only be approximated, and the model would be impossible to analyse fully.
As a consequence of these features of space, all ecological analyses have greatly simplified space in one way or another. The approach to spatial structure used here is the most common one, which represents space as a number of discrete ‘patches' that are separated by areas that cannot support populations of the species of interest, but that permit travel by one or more of these focal species. This ‘metapopulation' (Levins 1969,1970) or 'metacommunity' (Leibold et al.
2004) approach has been used in studies of interspecific competition since the 1970s (Levins and Culver 1971, Horn and MacArthur 1972, Levin 1974). It is still the approach most often used to study groups of interacting species in spatially subdivided populations. It has the advantage of being a simple extension of non-spatial models. It is also an increasingly accurate representation of space for many species as human modification of the environment continues to fragment areas of semi-natural habitat.Much of the earliest work on such patch-structured systems followed the framework of Levins (1969,1970), which does not explicitly model the processes occurring within a patch. This family of models just accounts for extinction and colonization events; abundances within the patch are ignored. Interspecific competition is reflected in a higher extinction probability for a given species within patches that it shares with one or more other competing species. The status of a population is measured by the proportion of patches in which it occurs, rather than the number of individuals or biomass. This leaves out essentially all the details of interactions between species. Hanski (1999) provided a comprehensive summary of this method, which has mostly been used to study the dynamics of single species. This chapter will use a different approach; it will focus on models in which the patches are sufficiently large that stochastic extinction can be ignored on the timescale of interest. The ‘within patch' components of these models are provided by the simple resource-based models described in previous chapters.
Adopting a metacommunity framework requires recognition of the differences between patches in conditions that affect the population growth rates of their inhabitants and the nature of movement by the component species/entities between those patches. The definition of coexistence also changes within a metacommunity framework, as has been noted before. Coexistence may be local or global, and local coexistence usually requires that a threshold density be defined, below which the species does not qualify as coexisting in that patch.
A metacommunity framework also complicates the issue of invasion, as invasion may occur in a single patch or in many patches more-or-less simultaneously. The framework used here is to consider systems in which all resource types are capable of existing in all patches in the absence of consumers. This simple case makes it possible to attribute differences between spatially subdivided and well-mixed systems to the spatial structure of the former system. In most of this chapter's examples, simultaneous introduction of a small number of individuals into all patches will be assumed when invasion is analysed.The majority of the analysis here will be based on systems with only two patches. This very simple case is sufficient to illustrate many of the qualitative characteristics that differ between spatially heterogeneous and homogeneous systems. It allows the minimal elements of a spatial model to be identified. The two patches may differ in properties that affect the demographic and/or ecological parameters of either consumer or resource or both. For example, the patches may have different mean temperatures, and this difference is likely to affect a range of processes in both consumer and resource. Regardless of cause, if some property of a patch creates different local dynamics of one or more consumers, this qualifies the resource population in that patch as being a distinct entity from the standpoint of consumer coexistence; this was initially discussed by Haigh and Maynard Smith (1972).
The question whether coexistence at a global scale in a metacommunity qualifies as ‘true' coexistence does not have a universally accepted answer. When coexistence is defined locally for a patch that is open to immigration, there is usually some arbitrariness in the decision of what abundance of a locally rare species allows a classification of exclusion. Because consumers and resources can have very different movement abilities, the most general approach would seem to be to define coexistence at a global scale; i.e., species coexist if each is present somewhere in the metacommunity.
This allows comparison of spatial resource segregation to other types of resource partitioning. Under this global definition, the quantitative measure of an interaction using the population responses to changes in a neutral parameter should logically assume that the parameter changes in identical ways across all patches. This convention means that, if patches differ in their initial population dynamical parameters, ‘quasi-extinction' of a focal consumer population will occur at a different value of an imposed mortality rate for different patches. ‘Quasi-extinction' implies that, if the patch were isolated, its consumer population would drop to zero; however, it may have a low abundance sustained by immigration. If each patch is characterized by unique parameter values or species compositions, the proportional rate of decrease of the global equilibrium population size will often change rapidly at a mortality rate that implies quasi-extinction within any one patch. These quasi-extinction events of the resource will generally produce a significant change in the global measures of both inter- and intraspecific competition between consumers.Each resource/patch combination acts as a resource in that the effect of a consumption event on the consumer's per capita growth rate is dependent on the properties of the space where it occurs. The resources in different patches may also be connected via movement. The nature of movement in both consumers and resources plays a key role in the competitive process. Interest in movement has increased rapidly in recent years (see Lewis et al. 2021), and there is now a journal devoted exclusively to this subject. However, it is fair to say that there is still no consensus on the proper approach to describing movement quantitatively (Gross et al. 2020). This chapter will focus on the different effects of random and adaptive forms of movement.
A more complete account of spatial competition would include an exploration of models using continuous space, and those cases (appropriate for stationary individuals) where adults interact only with a small set of nearest neighbours.
Unfortunately, both cases involve more complex mathematics or very large numbers of simulations. Existing results for these interactions cover a much narrower range of biological scenarios than do those for discrete patches, embodied in metacommunity models. See Snyder and Chesson (2004) or Cantrell et al. (2012) for examples of approaches to competition in continuous space.A major theme of Chapters 8 and 9 was that temporal variation affecting consumers differently could either enable or prevent the coexistence of competitors. The same is true of spatial variation, although this result has been more widely accepted than the corresponding temporal result. Rather than focusing exclusively on coexistence, the present chapter takes a somewhat broader approach and examines how various aspects of movement in both consumer and resource affect the competitive interaction between consumers, measured at the level of the whole metacommunity. The descriptions of within-patch dynamics explored here assume the simple ‘continuous time-homogenous population' consumer-resource models used in previous chapters.
The movements of any given consumer or resource type may be independent of the conditions in the occupied patch. However, for biological species that are capable of directed movement, it seems more likely that the movement will be influenced by conditions in the currently occupied patch, and possibly by conditions in other patches. The resource population size and the values of the consumer's own demographic parameters in its current patch are likely to be better known than are those of other patches. As a result, conditions in the currently occupied patch are expected to have a larger effect on consumer movement in most circumstances. If information on resource abundance and patch properties affecting fitness in other patches is available, that information should also affect movement. The local consumer density affects the rate of change of local resource abundance in the near future. Thus, consumer density as well as resource abundance and non-resource related physical/chemical conditions in the currently occupied patch may affect movement, although such purely densitydependent effects are not treated here. It is possible that consumers make exploratory trips to nearby patches that provide information. If such visits are sufficiently short in duration, they can be assumed to be roughly equivalent to remote detection of conditions in other patches. The various possibilities for remote detection and short-term visits suggest that a general approach to consumer (or resource) movement should include the possibility that conditions in both the origin and the destination influence consumer movement rates.
Temporal and spatial variation may interact; for example, the environmental fluctuations experienced in one spatial location may differ from those experienced in another location. A given patch with a temporally constant environment may experience cycles because of consumer-resource interactions within that patch. If so, it may influence the dynamics of other patches by producing temporally varying numbers of emigrants. Even in cases with identical conditions in each of two patches, the interaction of consumer-resource cycles with movement between patches can result in cycles that differ between the two patches.
The rest of this chapter begins (Section 10.2) with a short history of theory regarding competition in subdivided populations. This is followed in Section 10.3 by an analysis of how spatial subdivision affects the nature of intraspecific competition, as described by the relationship between a ‘neutral’ parameter (here, per capita mortality) and population size. Section 10.4 then examines the impact of random movement by both resources and consumers on their ability to coexist and on the functional form of their interaction. Adaptive movement by consumers and/or resources is treated in Section 10.5, which uses the simplest possible representation of dynamics within a patch (MacArthur’s consumer-resource model). Section 10.6 broadens this to consider adaptive movement in the context of consumer-resource models involving some nonlinear components. Possible pathways for advancing our understanding of competition in metacommunities are treated in Section 10.7.
10.2