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.