Acknowledgements

This research was supported by an NSERC Discovery Grant (Grant number: RGPIN-2015-05554) held by Dr. Jan Adamowski, as well as an FQRNT Bourse de 3e cycle, a Bourse du CRDI aux chercheurs candidats au doctorat (Award number 107759-99906075-017), a Bourse d’études supérieures du Canada Vanier and a Supplément pour études à l‘étranger Michael-Smith (Programme de bourses d‘études supérieures du Canada) scholarship held by Julien Malard.
Table : Comparison of critical extreme condition properties of common predatation equations.\(f\left(N,P\right)\) represents the predation rate per predator function and \(\backslash ng\left(N,P\right)=P*f\left(N,P\right)\)represents the total predation rate, where α is (theoretically) the maximum predation rate per predator, N and P are the prey and predator densities, respectively, and other variables are empirical constants.\(a,\ b,\ c\ \in\left[\left.\ 0,\ \infty\right)\right.\ ;m\in\left[0,\ 1\right]\). Shaded squares indicate undesirable behaviours. See Appendix A: Calculation of non-trivial limits and derivatives for details on the calculation of the results presented here.