When Do Trait-Based Higher Order Interactions and Individual Variation Promote Robust Species Coexistence?

Models on the effects of individual variation often focus on pairwise interactions, but communities could harbor both pairwise and higher order interactions (HOIs). Theoretical studies on HOIs, where a third species modulates pairwise species competition, tend to assign them at random, even though they could be mediated and structured by one-dimensional traits. Here, we consider two different classes of models of both pairwise and higher order trait-mediated interactions: competition alleviated by increasing trait distance, and hierarchical competition where species higher in the hierarchy exert more competition on those lower and vice versa. Combining these models with evolutionary dynamics based on quantitative genetics, we compare their impact on species diversity, community pattern, and robustness of coexistence. Regardless of individual variation, trait-mediated HOIs generally do not promote and often hinder species coexistence, but there are some notable exceptions to this. We present an analytical argument to make sense of these results and argue that while the effects of trait-based HOIs on diversity may appear confusing on the surface, we can understand what outcome to expect in any given scenario by looking at the shape of the effective interaction kernel that arises from the joint action of pairwise and HOI terms. In addition, we find that (i) communities structured by competitive trait hierarchies are highly vulnerable to external perturbations, regardless of HOIs, and (ii) trait-based HOIs with distance-dependent competition create the most robust communities, with minimal impact from individual variation, and (iii) both individual variation and HOIs consistently lead to a more even distribution of species traits than would occur by chance. These findings suggest that trait-mediated HOIs foster coexistence only under special conditions, raising the question of whether HOIs must involve multiple traits to positively affect coexistence in competitive communities.