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.