Interdependence of competitive effects with more consumers
Another phenomenon first noted in the 1970s was that the 3-species Lotka-Volterra model allowed a wide range of outcomes that had not been observed in similar 2-species models. Two of the first studies of unusual dynamics in 3-species competition systems were May and Leonard (1975) and Gilpin (1975), who noted cyclic outcomes.
An earlier analysis by Strobeck (1973) had wrongly suggested that cases with unstable equilibria having positive abundances of all three species necessarily implied competitive exclusion. Additional outcomes of 3-species LV competition were explored by Hallam et al. (1979). Such systems were later shown to be capable of exhibiting several different limit cycles for a given set of parameters (Gyllenberg et al. 2006, Gyllenberg and Yan 2009). However, these and most subsequent studies of multi-species systems treated the interaction of a given pair as being independent of the presence of other competitors, and have used the LV model, thus ignoring resources. This tendency to ignore resources when there are three or more competitors has continued through the past decade (e.g., Saavedra et al. 2017; Levine et al. 2017; Hart et al. 2018; and many others).The type of intransitive ordering of competitive abilities that is best known for producing cyclical dynamics in 3-species systems (Laird and Schamp 2006, 2015) requires a large interference component in the pairwise interactions. The pairwise exclusion that underlies the competitive ordering requires some interference competition, but most models of this phenomenon have not included a separate exploitative component. Exploitation is usually required for interference to be evolutionarily favoured. Huisman and Weissing (1999, 2001) is an exception to this, and they provide an additional example where having three competitor species and three nutritionally essential resources allows a wide range of non-equilibrium dynamics.
No interference competition is required for this outcome. However the complex unstable outcomes require that every consumer species be best at consuming an essentialnutrient that is needed in intermediate amounts, something that is evolutionarily unlikely.
A resource-based approach suggests that in almost all cases, adding a third consumer will alter the interaction of the original pair. In general, both the scaled (eq. (3.2)) and unscaled (eq. (3.1)) responses of one consumer species to change in a neutral parameter of the second species are changed by the presence of additional consumer species. In most cases this dependence will occur even if the added consumer only affects resources used by just one of the original consumer species. This comes about because a change in the abundance of one of the original consumers implies altered resource densities, which, as detailed above, usually changes the per capita competitive effect transmitted via each of the resources. This interdependence of competition coefficients has been shown to affect arguments about the limiting similarity in sets of three competitors that have exclusively exploitative competition, even in the MacArthur model (Abrams and Rueffler 2009). The dynamics of multispecies consumer-resource systems with both exploitative and interference effects remain largely unexplored.
Golubski and Abrams (2011) examined the effect of multiple species in changing pairwise interactions in a variety of food webs. Recent work by Letten and Stouffer (2019) also supports the presence of effects from other consumers on the competition coefficients between a given pair. Even cases with nutritionally substitutable, noninteracting, logistically growing resources that are consumed with linear functional responses by all consumer species can have pairwise interaction coefficients that are affected by the presence or absence of an additional consumer species.
A simple way to determine whether a third consumer species could alter the interaction between two other consumers in the models presented above is to examine the effects of different fixed abundances of the third consumer.
(Fixed abundance could come about because of limitation of that third consumer by a specialist food-limited predator, combined with consumption of other substitutable resources not explicit in the model.) In the 3-resource model used here, the effect of such a competitor at a stable equilibrium is equivalent to reductions in the intrinsic growth rates, r, of the resource(s) it consumes. It is easy to show that, if such a species consumes the shared resource in the system considered above, it would lead to exclusion of the resource over a much wider range of other parameter values; this eliminates competition between the original two species. Of course, elimination of the resource is not necessary to produce large changes in the competition coefficients that characterize the original two consumers when the resources have non-logistic growth.6.6