Adam T Clark , Lauren Glenny Shoemaker, Jean-François Arnoldi, György Barabás, Rachel Germain, Oscar Godoy, Lauren Hallett, Canan Karakoç, Serguei Saavedra, Sebastian Schreiber

Coexistence is simultaneously one of the most fundamental concepts of ecology, and one of the most difficult to define and quantify. A particular challenge is that, despite a well-developed body of research on the subject, several different schools of thought have developed over the past century, leading to multiple independent, and largely isolated, branches of literature with distinct methodologies. Here, we provide a broad overview of the most common concepts and metrics currently used to detect and quantify ecological coexistence. We first introduce four classes of behaviour that describe different aspects of community dynamics: (i) the existence of a feasible steady state, i.e. where all coexisting species retain positive abundances in the long-term in the absence of interference by external forces; (ii) the existence of a local attractor that draws the community towards a feasible steady state from within a restricted set of starting conditions; (iii): the existence of a global attractor that draws the community towards feasible steady states from any non-zero starting condition; and (o) a null transient state, where species abundances vary over time irrespective of steady states and attractors. Next, we explain how these classes of behaviour relate to commonly used metrics for classifying and quantifying coexistence, including analyses of parameter sensitivity, asymptotic return rates, invasion growth rates, and time to extinction. We then discuss the scope and limitations of each of these behavioural classes and corresponding metrics, with a particular focus on applications in empirical systems. Finally, we provide a potential workflow for matching empirical questions to theoretical tools, and present a brief prospectus looking forward to opportunities to better advance and integrate research on quantifying coexistence.