Nearly every community on earth contains more than two species. Yet classic models of species competition include only pairwise interactions. These models may fail when applied to multi-species communities if there are higher order interactions (HOIs). HOIs are defined as changes in pairwise competitive interactions in the presence of a third competitor. While the possibility of HOIs has long been recognized, ecologists have rarely investigated how these emerge either in nature or in simulation. To investigate the possibility of HOIs among competitors, we built a simple model of resource competition among annual plants. In our model, plants germinate simultaneously early in the growing season when resource availability is high, grow until resource availability is exhausted and then produce seeds and die. We studied a system of three competitors differing in only two parameters: their maximum resource uptake rate and a their low resource tolerance. Using this mechanistic model, we simulated the fecundity of each species in communities of one, two and three competitors. We then fit two phenomenological models of annual plant competition to the simulated data: one that included only pairwise interactions and another that included pairwise interactions and HOIs.
Results/Conclusions
In our model, three species can coexist when there is a strict trade-off between maximum resource uptake rate and low resource tolerance. An early season species grows rapidly and senesces early, a mid season species grows slower and senesces later, while a late season species grows most slowly and senesces last. A phenomenological competition model including HOIs fit the simulated data better than a model that included only pairwise interactions. The model with HOIs also more accurately reproduced the equilibrium abundances observed in the mechanistic model but the magnitude of HOIs was greater for the early and late season species than the mid season species. The magnitude of HOIs depended greatly on the range of simulated densities used to fit the phenomenological model: when a narrow range of densities near the three species equilibrium was used to fit the model a pairwise model often performed as well as a model with HOIs. Our work suggests that HOIs may be commonly encountered when fitting phenomenological competition models to multi-species communities, however, their importance may depend on the type of model used and the range of experimental densities considered.