Inherently unstable consumer-resource interactions
Earlier chapters have already shown that the shapes of consumer species' functional responses have a major effect on the relationship between their overlap in use of different resources and several measures of competition between them, even when both species have the same response shapes.
However, most species differ in response shapes. Armstrong and McGehee (1976a) showed that such differences could lead to coexistence. They examined competition for a single biotic resource between a consumer with a linear functional response and a similar one with a type II response. This did not affect coexistence unless there were sustained population cycles, driven by the consumer-resource interaction involving the type II response. Armstrong and McGehee (1976b, 1980) later extended this analysis to systems with more resources and included the possibility of abiotic resource growth. At the time of their original work, the main issue of interest to ecologists was whether two or more consumers could coexist while limited by a single resource. The presence of a saturating functional response (one having a negative second derivative for a significant range of resource abundances) had been shown to produce population cycles in a simple predator-prey model by Rosenzweig and MacArthur (1963). The mechanism driving coexistence in the Armstrong-McGehee model is that a species with a less saturating response (including linear or accelerating responses) has a higher mean resource intake requirement for positive population growth. The species with the more strongly saturating response is characterized by a lower intake requirement for zero population growth. However, the population cycles that the saturating species generates when it is numerically dominant increase the mean abundance of the resource. This larger mean abundance can be sufficient that the less efficient but less saturating consumer is able to persist in the system. The two consumer species then coexist in a system involving resource cycles that are smaller in amplitude than those generated when the saturating species is the only consumer present.The above results were widely known when Armstrong and McGehee (1980) published their then-comprehensive review of coexistence. However, the likelihood that this mechanism explained many cases of coexistence was not assessed, empirically or theoretically for many years. Abrams and Holt (2002) used extensive numerical results to determine the range of potential parameter space over which coexistence occurred in several models. They concentrated on the simplest scenario exhibiting this mechanism (logistic resource growth; two consumers, one with a linear, and the other with a Holling type II functional response). The range of a neutral parameter (the per capita mortality rate) allowing coexistence in the 2-species system was compared to the range of that parameter allowing existence in a single-species system. Armstrong (1976) was the first to use this approach; he called the measure a ‘coexistence bandwidth’. The bandwidth in the single-resource system could then be compared to similar systems in which species used two resources and exhibited various amounts of resource partitioning.
The main results of the Abrams and Holt (2002) analysis were:
(1) Coexistence bandwidth for two consumers can be substantial when one consumer has a linear functional response and the other has a type II response that reaches one half of its maximum value when the prey abundance is a relatively small fraction (on the order of 1/5 or less) of its carrying capacity (see Fig. 2, p. 285 in Abrams and Holt (2002)). The coexistence bandwidth could be increased substantially if the species with a linear functional response also had an accelerating numerical response (per capita growth rate increases at faster than linearly as the rate of consumption increases).
(2) It is possible, but difficult (very narrow bandwidth) to get coexistence of more than two consumer species on a single resource in this model.
(3) If each consumer utilizes two or more resources, the mechanism driven by different functional response shapes is less likely to operate. This is because the high efficiency that leads to cycles in the single-resource model frequently causes extinction or quasi-extinction of the most vulnerable resource species in a 2-or- more resource system with a single consumer (see Fig. 5 in Abrams and Holt 2002). This reduces that system to one having a single resource, and one that is likely to be stable because of its lower vulnerability to the consumer. Thus, the mechanism is less likely in part because the required interaction-generated population cycles are less likely. The lower probability of limit cycle dynamics in multi-prey systems was also made in connection with purely intraspecific competition (Abrams 2009b). Even if both resources persist, the amplitude of cycles is usually reduced by the difference in their vulnerabilities, which reduces the impact of the cycles on coexistence (Abrams and Holt 2002). In addition, substantial partitioning of resources alone produces a large coexistence bandwidth, and thereby reduces the maximum extent to which the bandwidth can be increased by any additional mechanism.
If we move beyond the issue of coexistence, the interaction-driven cycles of the Armstrong-McGehee system provide an example of how the quantitative form of competition between two coexisting consumers is changed when their dynamics are characterized by interaction-driven instability. The standard description of interspecific effects used in previous chapters has been to determine how a neutral parameter in one species affects the mean abundance of a competitor, relative to the effect on its own abundance. Abrams et al. (2003) examined this issue for the Armstrong- McGehee model, as well as examining the nature of population dynamics over the complete parameter space over which two consumers could coexist. Figures 6 and 7 in that work show a variety of complicated responses of both species to the per capita death rate of one of them.
One phenomenon shown was non-monotonic responses of each consumer’s abundance to the per capita mortality rate of the other consumer, meaning that interactions could not always be classified as (-, -). Another possibility in this system was that the mean density of a species could increase with an increase in its own mortality (later termed a ‘hydra effect’). Abrams et al. (2003) also showed that it was possible for an increased death rate of the nonlinear consumer to change coexistence to exclusion of the linear species by stabilizing the system. Alternative dynamical attractors characterized by the opposite direction of response to a given species’ mortality also exist over some ranges of mortality rates. Cases with two attractors are associated with abrupt changes in abundances with a very small parameter change when one attractor disappears. While there is still little evidence that that the simple model considered in Abrams et al. (2003) is a good description of many pairs of species in natural communities, it would be surprising if differences in the linearity of per capita growth rate functions did not occur in, and contribute to coexistence of, many sets of competing species. The non-traditional responses to neutral parameters predicted by the simple model are also likely to occur in some of these.The Armstrong-McGehee scenario, based on consumption-driven cycles with no variability in the physical environment, is narrower than Chesson’s (1994, 2018) concept of relative nonlinearity. However, it has been the subject of the majority of theoretical work on the relative nonlinearity mechanism of coexistence. The rest of
this chapter shows how differences in the linearity of the consumers’ functional or numerical responses affect coexistence and other aspects of competition when cycles are driven by qualitatively different mechanisms. These two other sources of cycles are: (1) periodic variation in the resource per capita growth rate; and (2) periodic variation in consumer mortality rates or other parameters that are not directly involved in their uptake or conversion of resources. These two additional drivers of consumerresource cycles may operate alone, or in systems with interaction-caused instability. How combinations of different drivers of instability affect the likelihood of coexistence and the nature of interactions is only treated briefly, as there has been little previous work on this topic, and there are many different scenarios for combining different sources of instability. The chapter concentrates on the case of two consumers utilizing a single resource.
9.3