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Hollings disc equation

Holling's disc equation A method for calculating the functional response of predators to increased prey density. The equation is based on laboratory experimental data simulating predation. A human predator gathers discs (prey) from boards with different ‘prey’ densities. In theory, the efficiency with which the predator consumes the prey should decline as the prey density increases, owing to extra time spent handling the prey. Thus the relationship between prey density and numbers consumed by predators is not a straight line but a curve. This relationship was first summarized mathematically by C. S. Holling in 1959 as y = Ttax/(1 − abx) where y is the number of discs removed, x is the disc density, Tt is the total experimental time, a is a constant describing the probability of finding a disc at a given density, and b is the time taken to pick up a disc. Compare diversity index.

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