Watt Model

Watt (1959) took a similar approach to Ivlev (1955) but, in addition, argued that consumption will be related to the density of consumers, H, as well as the availability of resources, P. Simplifying Watt's argument by setting his intraspecific competition coefficient b = 2 (see Royama 1971 for the logic of this simplification), and letting the attack rate be inversely related to consumer density, we obtain Watt's modification of Ivlev's consumption equation

Integrating this equation provides us with the quantity of resources obtained per consumer as a function of consumer and resource densities

Like Ivlev's model, this equation also describes a Type II or cyrtoid behavioral response because the rate of consumption increases at a decreasing rate with respect to prey density. In addition, this model is a ratio-dependent functional response because consumption is now a function of the resource/consumer ratio (or supply/demand ratio, v_hP / d_hH). Remember that the Ivlev and Watt models are derived from differential equations which have not been integrated over time and, as such, must be considered an instantaneous consumption equation.

References

Ivlev, V. S. 1955. Experimental ecology of the feeding of fishes. Yale University Press, New

Royama, T. 1971. A comparative study of models for predation and parasitism. Researches on Population Ecology, Suppl.1: 1-91

Watt, K. E. F. 1959. A mathematical model for the densities of attacked and attacking species on the number attacked. Canadian Entomologist 91: 129-144.