Intuitive and broadly applicable definitions of niche and fitness differences.

Explaining nature's 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' ( ) in modern coexistence theory. Here, we first show that available definitions of differ in how link to species interactions, are difficult to interpret and often apply to specific community types only. We then present a new definition of 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 , we also redefine fitness differences ( ) and illustrate how and 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.