The stability of omnivory: a geometrical reconciliation
The role of omnivory on food web stability has undergone a number of major theoretical upheavals in the last thirty years. Despite all this change little has been done to reconcile the largely conflicting theories that have emerged. In this paper I develop a geometrical procedure for constructing the full spectrum of equilibrium stability configurations in ecological models. This approach is applied to the fundamental module of same chain omnivory. In doing so I uncover a unified perspective of old and new theory for the role of omnivory on stability. Namely, of the vast potential configurations there are only six qualitative cases for the role of omnivory strength on stability. The majority of these cases exhibit stabilization via weak omnivory, with all six cases ultimately destabilized by strong omnivory. Finally, employing the methodology developed here, I revisit both classical and modern theory to show their results are consistent. Specifically, adopting the biological parameter constraints of classical theory, I show that omnivory tends to produce a large number of unstable configurations. However, for the same parameters I also show weak interactions would almost always stabilize the dynamics relative to the non-omnivorous food chain.