Holling Type II Functional Response Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/9/2026
The prey consumption rate under the Holling type II functional response is calculated with (a × N) ÷ (1 + a × Th × N), where a is the attack rate, Th the handling time per prey, and N the prey density.
Explanation
The type II functional response, formalized by ecologist Crawford Stanley Holling in the 1950s through his famous "disc equation" (an experiment where a blindfolded secretary picked up sandpaper discs to simulate prey capture), describes how a predator's consumption rate changes with prey density: it rises quickly at low density, then slows down and eventually plateaus at a maximum rate, because the predator spends an increasing share of its time handling (capturing, killing, consuming) each prey rather than searching for new ones. This plateau, called the maximum consumption rate, equals exactly 1/Th: the shorter the handling time per prey, the higher this plateau. This model differs fundamentally from pure population growth dynamics (see our logistic growth calculator), which describe how a single population evolves over time without direct predator-prey interaction, while Holling's functional response specifically addresses the instantaneous feeding behavior of an individual predator facing a given prey density. The type II response differs from type I (a linear relationship with no plateau, a simplification rarely realistic) and type III (an S-shaped curve, where the consumption rate starts slowly at low density, typical of predators that must "learn" to recognize a rare prey or that have alternative prey available): type II remains the most commonly observed model among invertebrate predators and many vertebrates. It is often compared against the population growth rate calculator, since a predator's improved consumption efficiency at low prey density can itself accelerate the rate at which the prey population declines.
Example: a = 0.5, Th = 0.1 h, prey density = 20
Inputs
Attack rate: 0.5. Handling time: 0.1 h. Prey density: 20.
Calculation
Consumption rate = (0.5 × 20) ÷ (1 + 0.5 × 0.1 × 20) = 10 ÷ 2 = 5.
Result
The predator consumes about 5 prey per unit of time at this prey density.
Frequently asked questions
What is the maximum possible consumption rate under this model?
The consumption rate plateaus at 1/Th as prey density becomes very large, because the predator then spends nearly all its time handling prey rather than searching for it. With a handling time of 0.1 h, for example, the theoretical maximum rate is 1/0.1 = 10 prey per unit of time, no matter how much further prey density increases.
How does this model differ from the type I functional response?
The type I response assumes a strictly linear relationship between prey density and consumption rate, with no plateau at all — a simplification that ignores handling time and is only realistic for certain passive filter feeders. The type II response, more realistic for most active predators, incorporates this handling time and therefore produces a curve that slows down and then plateaus.
How are the attack rate and handling time estimated in practice?
These two parameters are usually estimated through controlled laboratory or enclosure experiments, exposing a predator to different prey densities and measuring the number of prey consumed per unit of time, then fitting the Holling equation to that measured data.