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: (1) high productivity relative to herbivore mortality and (2) small discrepancies in producer vs. 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. Trophic cascades occur when top predators indirectly effect change in primary producer biomass by directly reducing populations of intermediate herbivores (Paine 1980, Strong 1992, Terborgh and Estes 2013). A growing number of factors that control the strength of trophic cascades continue to surface from model‐based and experimental studies, and their identification has improved our understanding of processes that dampen or enhance indirect effects between species in ecological networks and ecosystem responses to disturbance (Pace et al. 1999, Shurin et al. 2002, 2010, Borer et al. 2005, Estes et al. 2011, Heath et al. 2014, Fahimipour et al. 2017, Piovia‐Scott et al. 2017). Theories for cascades have traditionally focused on top‐down effects in tritrophic food chain models comprising predators that do not directly interact with primary producers (Oksanen et al. 1981, Schmitz et al. 2000, Heath et al. 2014). In many communities however, omnivores that additionally feed on producers occupy top trophic levels (Arim and Marquet 2004, Thompson et al. 2007). This potential for direct consumption of both producer and herbivore species has