Omnivory does not preclude strong trophic cascades
Omnivory has been cited as an explanation for why trophic cascades are weak in many ecosystems, but empirical support for this prediction is equivocal. Compared to predators that feed only on herbivores, top omnivores -- species that feed on both herbivores and primary producers -- have been observed generating cascades ranging from strong, to moderate, null, and negative. To gain intuition about the sensitivity of cascades to omnivory, we analyzed models describing systems with top omnivores that display either fixed or flexible diets, two foraging strategies that are supported by empirical observations. We identified regions of parameter space wherein omnivores following a fixed foraging strategy, with herbivores and producers comprising a constant proportion of the diet, non-intuitively generate stronger cascades than predators that are otherwise demographically identical: (i) high productivity relative to herbivore mortality, and (ii) small discrepancies in producer versus herbivore reward create conditions in which cascades are stronger with moderate omnivory. In contrast, flexible omnivores that attempt to optimize per capita growth rates during search never induce cascades that are stronger than the case of predators. Although we focus on simple models, the consistency of these general patterns together with prior empirical evidence suggests that omnivores should not be uniformly ruled out as agents of strong trophic cascades.