Figure : Rankings of various equations, where lower ranks indicate better fit relative to the other equations, versus the Type II equation rank for the same experimental dataset. Each point represents ranking of one equation or group of equations (Type III, BD or KV) when fitted to one experimental dataset. Lines indicate linear model regression for each equation or group, and shaded areas represent 95% confidence intervals. Type II includes Hassell-Varley, prey-dependent and ratio-dependent equations with Holling Type II response; Type III includes the same equations with a Holling Type III response; BD indicates the Beddington-DeAngelis equation; KV indicates the Kovai equation.
As expected, the ranking of Type III equations improved as datasets moved away from a Type II response, and the BD equation, whose shape resembles a Holling Type II form, predictably improves in rank the closer the dataset is to a Type II functional response form.
The Kovai equation, however, ranked consistently across datasets, regardless of whether the data showed Type II functional response or not. This is most likely due to its parametrisation, which allows it to model both Type II and Type III functional responses. It is important to note, however, that as the Kovai equation supposes that prey availability will increase along with prey densities, it is not suitable for representing Type IV functional responses where increasing densities of dangerous prey reduce predators’ ability to hunt effectively.
In conclusion, the Kovai equation provides several main improvements over existing predation equations in the literature. 1) Its main contribution is its improved theoretical consistency, in particular in its predictions of total predation at high prey or predator densities and the rate of change of total predation as more prey is added to the system. 2) The Kovai equation also combines the best of prey and ratio dependent concepts in a mathematically consistent manner, by adjusting for predator competition (correctly partitioning available prey between predators when prey become limiting) while still distinguishing between low and high absolute prey density in the case of otherwise identical prey-predator ratios. 3) The equation also allows for a (mathematically consistent) smooth transition between Type II and Type III functional responses based on its parametrisation.