Intuitive and broadly applicable definitions of niche and fitness differences

Explaining natures biodiversity is a key challenge for science. To persist, populations must be able to grow faster when rare, a feature called negative frequency dependence and quantified as niche differences ([N]) in coexistence theory. Here, we first show that available definitions of [N] differ in how [N] link to species interactions, are difficult to interpret, and often apply to specific community types only. We then present a new definition of [N] that is intuitive and applicable to a broader set of (modelled and empirical) communities than is currently the case, filling a main gap in the literature. Given [N], we also re-define fitness differences ([F]) and illustrate how [N] and [F] determine coexistence. Finally, we demonstrate how to apply our definitions to theoretical models and experimental data, and provide ideas on how they can facilitate comparison and synthesis in community ecology.