To be able to persist, populations must be able to grow faster when rare, a feature called negative frequency dependence. Coexistence theory quantifies negative frequency dependence as niche differences. To avoid exclusion, niche differences must be strong enough to overcome fitness differences: competitive differences between species in absence of niche differences. While these concepts are intuitively appealing, proper quantification is challenging. In the past 20 years, ten different definitions have been proposed to quantify niche and fitness differences (N and F). However, the available definitions differ greatly in how N and F should vary with the type and strength of species interactions, and are often applicable to specific community types only. In particular, there are no robust methods to measure N and F in multi-species communities or communities with positive interspecific interactions.
Results/Conclusions
Here we review and highlight the limitations of the ten existing definitions for N and F . We show that seven of these definitions do not align with biological intuition and the other three can only be applied to one specific model. Then, we present a new definition of N that is consistent with biological intuition and can be applied to communities driven by both negative and positive species interactions, filling a main gap in the literature. We also derive a definition for the corresponding F, and illustrate how the new N and F jointly determine coexistence for various community types, given the new definitions. We demonstrate that our definitions can be applied based on model equations and on experimental data with unknown underlying mathematics. Our definition is the first to quantify N and F in a standardized way across theoretical and empirical communities, facilitating comparison and fostering synthesis in community ecology. Finally, we apply our definition to multi-species communities with negative and positive interspecific interactions, i.e. community types where coexistence is least understood. We show that species richness does not affect N and increases F using simulations.