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FUNCTIONAL AND NUMERICAL RESPONSE OF PREDATION: Predation is the consumption of one living organism by another, a relationship in which one organism benefits at the other’s expense. In its broadest sense predation includes herbivory and parasitism.

Interactions between predator and prey have been described by the mathematical models of LOTKA and VOLTERRA, modified by others. Essentially all of these models predict oscillations of predator and prey populations. The oscillations may be stable, damped or unstable. Relationships between predator and prey populations result in two distinct responses. At density of prey increases, predators may take more of the prey, a FUNCTIONAL RESPONSE, or predators may become more numerous, a NUMERICAL RESPONSE.

The idea of a FUNCTIONAL RESPONSE was introduced by Solomon (1949) and explored in detail by Holling (1959, 1961, and 1966). Holling recognized three types of functional response.


TYPE I response is a specialized one, the sort assumed in the simple predation models. Predators of any given abundance capture food at a rate proportional to their encounter with prey items up to the point of satiation. There is density-independent mortality of the prey up to that point. In northern Finland, where Microtus vole populations are cyclic, the European kestrel (Falco tinnunculus), short-eared owl (Asio flammeus) and long-eared owl (Asio otus) exhibit a linear Type I functional response.


The Type II response is generally but not exclusively associated with invertebrate predators. It is described by the disk equation, named for an element in the experiment from which it is derived. In Holling’s experiment, the predator was represented by a blindfolded person and the prey by sandpaper disks 4 cm in diameter thumbtacked in different densities to a 1 m square table. The “predator” tapped the table with a finger until a prey was found and then removed the disk. The “predator” continued to search and encounter (tapping, discovery and removal) for 1 min. Holling found that the no of disks the predator could pick up increased at a progressively decreasing rate as the density of disks increased. Predator efficiency rose rapidly as the density of the disks increased up to the point where the predator so much time picking up and laying aside disks that the predator could handle only a maximum no. at a time.

Holling repeated this experiment using insect predators such as the praying mantis and insect prey such as flies. He found the same relationship between prey density and handling time experiment. HANDLING TIME increased as the density of the prey increased. Although search time was short, the predator could handle only a limited no. of prey in a given time. These experiments demonstrated several important components of predation: density of prey, attack rate of the predator, and handling time, including time spent pursuing, subduing, eating and digesting prey.

Type II functional response is described by the disk equation:

Na/p = aNT / 1+ aThN

Where Na is the number of prey or hosts killed or attacked, P is the no. of predators or parasitoids, N is the no. of prey, and Na/P is the no. of prey eaten per predator, a is a constant representing the attack rate of the predator or the rate of successful search, T is total time predator and prey are exposed, Th is handling time, and Ts is time spent by predator in search of prey, T is determined by the equation:

T = Ts + ThNa

The Type II response curve derive by Holling is identical to the MICHAELI’S – MENTEN EQUATION OF ENZYME KINECTICS:

b (N) = m N/ (w+N)

Where m is the maximum predato attack rate, w is prey density at which the attack rate is half saturated and N is prey density. This equation describing enzymes acting on a substrate is analogous to predators feeding on a prey. Although the Holling disk equation describes the Type II functional response, it is difficult to apply in Type III functional responses. The Michaeli’s- Menten equation is not.

Because handling time is the dominant component, rise in the no. of prey per unit time decelerates to a plateau while the no. of prey is still increasing. For this reason Type II functional response cannot act as a stabilizing force on a prey population unless the prey occurs in patches. Thus Type II is destabilizing.


Type III functional response is more complex then Type II.