Detecting and interpreting higher-order interactions in ecological communities.

When species simultaneously compete with two or more species of competitor, higher-order interactions (HOIs) can lead to emergent properties not present when species interact in isolated pairs. To extend ecological theory to multi-competitor communities, ecologists must confront the challenges of measuring and interpreting HOIs in models of competition fit to data from nature. Such efforts are hindered by the fact that different studies use different definitions, and these definitions have unclear relationships to one another. Here, we propose a distinction between 'soft' HOIs, which identify possible interaction modification by competitors, and 'hard' HOIs, which identify interactions uniquely emerging in systems with three or more competitors. We show how these two classes of HOI differ in their motivation and interpretation, as well as the tests one uses to identify them in models fit to data. We then show how to operationalise this structure of definitions by analysing the results of a simulated competition experiment underlain by a consumer resource model. In the course of doing so, we clarify the challenges of interpreting HOIs in nature, and suggest a more precise framing of this research endeavour to catalyse further investigations.