functionalresponse

In ecology, a functional response describes how the rate at which a predator consumes prey changes as prey density varies. It focuses on the per capita rate of prey consumption by a single predator and is a key component of predator–prey models. The concept is distinct from the numerical response, which concerns changes in predator population size in response to prey density.

Historically, Holling identified three fundamental functional response forms. Type I is a linear increase in prey consumption with prey density up to a maximum, implying negligible handling time. Type II shows a decelerating rise, leveling off at higher prey densities due to handling time and processing limits. Type III is sigmoidal, with a slow start at low prey densities, accelerating as prey become more detectable or learned, then saturating at high densities. Common mathematical representations are: Type I f(N) = a N; Type II f(N) = (a N)/(1 + a h N); Type III f(N) = (a N^2)/(1 + a h N^2), where N is prey density, a is the attack rate, and h is handling time.

Extensions incorporate predator interference and multiple prey. For example, the Crowley–Dean or Beddington–DeAngelis forms add terms for predator density to account for interference: f(N,P) = (a N)/(1 + a h N + c P), where P is predator density and c measures interference. These refinements improve realism in multi-predator or multi-prey systems and in heterogeneous environments.

Applications include predicting population dynamics, stability of prey populations, and informing biological control and pest management. Functional responses are estimated from experiments and are subject to context, including prey switching, refuge effects, and environmental conditions.