Chesson's coexistence theory

We give a comprehensive review of Chesson's coexistence theory, summarizing, for the first time, all its fundamental details in one single document. Our goal is for both theoretical and empirical ecologists to be able to use the theory to interpret their findings, and to get a precise sense of the limits of its applicability. To this end, we introduce an explicit handling of limiting factors, and a new way of defining the scaling factors that partition invasion growth rates into the different mechanisms contributing to coexistence. We explain terminology such as relative nonlinearity, storage effect, and growth-density covariance, both in a formal setting and through their biological interpretation. We review the theory's applications and contributions to our current understanding of species coexistence. While the theory is very general, it is not well suited to all problems, so we carefully point out its limitations. Finally, we critique the paradigm of decomposing invasion growth rates into stabilizing and equalizing components: we argue that these concepts are useful when used judiciously, but have often been employed in an overly simplified way to justify false claims.