Holling¹s disk equation

Optimal diet models are largely derivatives of Holling¹s disk equation which gives a technique for calculating the rate of return from foraging behavior and takes into account the real-life variables of rate of reward collection, search time and handling time. What I like best about these models is that you can actually measure the components with real animals and test the theoretical predictions.

Holling actually had blindfolded students collect sandpaper disks that he arrayed on a table. He timed their movements and analyzed their strategies to generate this equation that describes the behavior of a forager. Because Holling used an empirical approach he did not actually derive the equation; rather, he fit an equation to his data. derive the disk equation by starting with a simpler formulation:

RATE = Energy gained in foraing/(time searching + time handling)

put into symbols, this equation reads:

R = Ef/(Ts + Th)

from which the more complex disk equation emerges (see Stephens and Krebs (1986) for the algebra):

R = (le - s)/(1 + lh)

where: s = cost of search per unit time l = rate of encounter with items h = handling time e = energy gained per encounter In theory, a forager finds the behavior that maximizes its return under this model. Basically, the forager needs to assess/remember the four elements of this equation. CAN FORAGERS ACTUALLY DO THIS?

Stephens and Krebs (Stephens, D. W. and J. R. Krebs. 1986. Foraging theory. Princeton University Press)