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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.