Density dependence promotes species coexistence and provides a unifying explanation for distinct productivity-diversity relationships

Understanding complex communities, such as microbial consortia, requires a mechanistic framework appropriate for large numbers of species. Negative density dependence is often included in population models, typically as a density-dependent mortality term, but its full impact on community structure remains unclear. Here we use mechanistic population models of resource consumption to examine the effects of negative density dependence and develop a tractable framework for understanding diversity patterns in complex systems. Using graphical analysis, we show that density-dependent mortality expands coexistence zones along resource gradients. We then derive a simple formula predicting species abundances in subsets (guilds) of a complex ecosystem, in which many species compete for a resource or share a predator, modulated by density-dependent mortality and other factors. Finally, we use our formula to explain how qualitatively distinct relationships between productivity and diversity can emerge from a generalized ecosystem description, providing new insights into previously unreconciled observed patterns.