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Nature's variability plays a major role in maintenance of biodiversity. As global change is altering variability, understanding how key food web structures maintain stability in the face of variation becomes critical. Surprisingly, little research has been undertaken to mechanistically understand how key food web structures are expected to operate in a noisy world and what this means for stability. Omnivory, for example, has been historically well studied but largely from a static perspective. Recent empirical evidence suggests that the strength of omnivory varies in response to changing conditions in ways that may be fundamental to stability. In the present article, we extend existing omnivory theory to predict how omnivory responds to variation and to show that dynamic omnivory responses are indeed a potent stabilizing structure in the face of variation. We end by synthesizing empirical examples within this framework, demonstrating the ubiquity of the theoretical mechanisms proposed across ecosystem types, spatial scales, and taxa.