All in all, HOIs hardly promote species diversity/coexistence, and trait variation further disrupts it. This goes in saying that maybe for HOI to promote diversity, it should be high-dimensional or have multiple traits mediate it to positively affect coexistence in competitive communities.

If pairwise competition width is very wide in contrast to the very narrow range at which HOIs come into play, trait-based HOIs can promote diversity than its pairwise counterpart. However, if width of HOI kernel and pairwise are even comparable, HOIs will always reduce species diversity -fig above-

When does trait-based HOI promote species coexistence? The answer lies in the relative widths of pairwise and HOIs competition, i.e., the width at which pairwise effects dominate versus trait-based HOIs dominate.

We searched in extensive ways to understand if it is ever possible for trait-based higher order interactions (HOIs) to promote robust coexistence more so than only pairwise competition. The answer is: mostly not, BUT, it is possible under certain scenarios--

Unreal and unbelievable

We show that a reduced 2-D model of complex tri trophic food webs can very well capture the recovery dynamics of complete food webs from a collapse state.