The pervasiveness of omnivory is an issue of debate between theoretical modeling studies and empirical studies.  Where empirical data demonstrated omnivory was common in many food webs, the earliest models suggested that omnivory should be rare due to its destabilizing effects on food webs.  Others suggested that omnivory is stable at low productivity levels, but increasing unstable at higher productivity.  Further models suggested that weak interactions between the top predator and the basal resource and alternative basal resources could stabilize food webs with omnivory.  But the modeling efforts have ignored the finding that food chains tend to increase with productivity.  Here I examine how omnivory influences food chain length across a gradient of productivity using non-linear predator-prey models.  Food web structure is varied from straight chains of 4 species or with omnivory at the top predator or the penultimate predator or both.  Simulations were run over an order of magnitude of productivity and the persistence of the species were used as measures of stability.
Results/Conclusions

The results showed that omnivory could stabilize the food web and allow for persistence of the top predator at productivity levels below what is possible without omnivory.  This occurred even when the top predator was not an omnivory (i.e., feed only on the trophic level below it), but required that the penultimate predator was an omnivore.  The omnivorous interaction of the penultimate predator reduced its oscillations which in turn reduced strong oscillations of the top predator.  Strong oscillations tend to lead to over-consumption by the predator resulting in extinction of the prey or predator or both.  These results suggest that omnivory should be pervasive especially at the intermediate predator levels.  Almost whereas ecosystem exploitation hypothesis suggests that food chains are lengthened by consumers feeding only on the trophic level directly below, these results suggest that first omnivores will be allow to invade and persist at lower productivity levels, followed by non-omnivorous consumers.  These results further suggest that omnivory should occur at many levels in food webs.