Abstract
Sensitivity analysis, the study of how ecological variables of interest respond to changes in external conditions, is a theoretically well‐developed and widely applied approach in population ecology. Though the application of sensitivity analysis to predicting the response of species‐rich communities to disturbances also has a long history, derivation of a mathematical framework for understanding the factors leading to robust coexistence has only been a recent undertaking. Here we suggest that this development opens up a new perspective, providing advances ranging from the applied to the theoretical. First, it yields a framework to be applied in specific cases for assessing the extinction risk of community modules in the face of environmental change. Second, it can be used to determine trait combinations allowing for coexistence that is robust to environmental variation, and limits to diversity in the presence of environmental variation, for specific community types. Third, it offers general insights into the nature of communities that are robust to environmental variation. We apply recent community‐level extensions of mathematical sensitivity analysis to example models for illustration. We discuss the advantages and limitations of the method, and some of the empirical questions the theoretical framework could help answer.