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Sklaski and Gilliam [17] pointed out that predator-dependent functional responses such as described by Beddington-DeAngelis, Crowley-Martin, and Hassel-Varley can provide a better description of predator feeding over a range of predator-prey abundance settings.
It has been the source of controversy and can provide a better description of predator feeding over a range of predator-prey abundances, which are strongly supported by numerous field and laboratory experiments and observations.
The Beddington-DeAngelis functional functions (p u,v =frac{m u}{a+bu+cv}) were introduced independently by Beddington [6] and DeAngelis et al. [7], which provide a better description of predator feeding over a range of prey-predator abundances [41].
On the other hand, in 2001, Skalski and Gilliam [42] have presented statistical evidence from nineteen predator-prey systems that three predator-dependent functional responses (Beddington-DeAngelis, Crowley-Martin, and Hassell-Varley) can provide better description of predator feeding over a range of predator-prey abundances.
Here (f(S,u =frac{S}{1+m_{1}S+k_{1}u}) and (g(S,v =frac{S}{1+m_{2}S+k_{2}v}) are the Beddington DeAngelis (B D) functions (see [11, 24]), supported by numerous laboratory experiments and observations and providing better description of predator feeding over a range of predator prey abundances.
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By comparing statistical evidence from 19 predator-prey systems, Skalski and Gilliam claimed that the above three predator-dependent functional responses provided a better description of a predator feeding over a range of predator-prey abundances [2].
The predator's functional response is Holling type II in [40], the Beddington-DeAngelis functional response is similar to the Holling type II functional response, but it has an extra term bv in the denominator providing a better description of mutual interference by predators.
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