What do coexistence and exclusion mean?
The definition of coexistence may seem obvious. For example, in his book on resource competition, Grover (1997, p. 11) simply states that ‘two or more populations may persist, in which case we speak of coexistence’.
One problem is that nothing on Earth persists indefinitely; the vast majority of species that have ever existed on this planet are now extinct. Chesson (2020b) is one of the few accounts of competition theory that acknowledges this fact. Thus, coexistence needs to be defined as long-term persistence by all the species concerned, given the existence of some regime of environmental conditions (which may include constantly present variation). The other problem is that continued persistence of one species in a spatially distinct community may be terminated by large environmental perturbations such as exceptional weather, diseases, evolution of other species, or changes in the reproduction or input of some subset of resources. All these types of perturbation are possible in almost all naturally occurring sets of competitors. Is it necessary that each species is able to grow back from extreme rarity, and what constitutes that ‘extreme rarity’? ‘Exclusion’ of a species has analogous definitional issues; is it a total inability to achieve a continued positive abundance, or an inability to increase when rare enough when the remaining species are at equilibrium?A large body of theory now defines coexistence as the ability of each species to increase from near-zero abundance when the rest of the consumer species have reached their limiting dynamics (usually, but not always assumed to be a stable equilibrium point); e.g., Grainger et al. (2019) and Chesson (2020b). This is termed ‘invasion analysis’ Invasion, however, need not imply continued coexistence (Abrams and Shen 1989; Mylius and Diekmann 2001; see examples in Chapters 8 and 9).
And long-term persistence is possible even when neither species can increase when very rare (Gilpin and Case 1976; Barabas et al. 2018). These cases either require a large number of individuals in the initial propagule or some large perturbation awayfrom the original equilibrium of the original community at the time of invasion. Pimm's (1991) review had already shown that most communities experience frequent large perturbations. Given the temporary nature of all biological communities, it seems more reasonable to adopt the less restrictive definition of coexistence as the possibility of continued persistence without directional change over many generations. For the typical differential equation model of competing species, this implies the existence of an attractor with all species present and bounded away from zero. The attractor should have a large enough basin of attraction that multi-generational persistence of all species is likely over such a time frame. Meszena et al. (2006) give a similar definition of coexistence as the existence of ‘...a fixed point of the community dynamics with no population having zero population size’.
The definition of coexistence becomes more complicated in the context of a metacommunity, consisting of two or more spatially distinct ‘patches' connected by migration of some or all of the species. As early as 1974, Simon Levin had pointed out that, for the LV model with contingent outcomes (species 1 excludes species 2, or 2 excludes 1, depending on initial abundances), a two-patch environment has a stable equilibrium with both species persisting. This is the equilibrium with only species 1 in one patch and only species 2 in the other (actually there are two such outcomes, the dominant species having reversed locations). There are also two additional potential outcomes with species 1 in both patches or species 2 in both patches. To apply the ‘invasion criterion' to this case, one has to decide whether the resident species is present in one or both patches; only systems with an empty patch can be invaded.
Ifboth are initially empty and small groups of colonist individuals arrive randomly with long inter-arrival intervals and with an equal probability of an invasion by either species, then the end result is likely to be coexistence (always with a different species in each patch) about half the time. In any case, exclusion and coexistence are both possible in the system as a whole. Given a large number of identical patches, with some movement between most of them, and occasional extinction events, it is likely that the two consumers in this scenario will persist for a long time when the single patch model says that they cannot.This case of alternative exclusion outcomes in a spatial context also presents a challenge to the belief that stronger competition (as measured by the product of the two competition coefficients at the equilibrium point in a spatially homogeneous system without temporal variation) makes coexistence less likely to occur. Competition coefficients whose product is greater than one usually involve some form of interference competition. For initially identical exploitative competitors with competition coefficients both equal to one, coexistence would not occur given some change in system-wide conditions that favoured one species or the other. Such a change, slightly favouring one species, would not cause system-wide exclusion in the multi-patch, alternative-exclusion case.
Defining coexistence also requires a definition of exclusion. This is usually taken to mean that the excluded species is completely absent. However, most communities come into existence by receiving immigrants from other communities, and it is illogical to think that this immigration ends at a point where that species becomes very rare. The same is true of biotic resources. In a more realistic metacommunity context, exclusion is more appropriately considered to include situations in which a species has a very low abundance that is maintained only by immigration. Even if the topic of interest is the interaction between consumers in one patch, it is important to include a low level of resource immigration. This will only affect the interaction between two consumers in cases where some subset of the potential consumer species results in near-zero abundance of one or more resources. With resource immigration these resources maybe able to return from near-zero abundance following introduction of one or more new consumer species (see Chapter 5 on apparent competition). In the absence of resource immigration, those resources would be permanently lost. The question of how to deal with immigration in real-world competitive communities has been avoided by the concentration on laboratory systems, in which immigration can often be prevented.
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