Functional responses
A functional response describes how the rate at which one predator consumes prey depends on prey abundance.
Type I
\[f(N)=aN.\]Consumption increases linearly with prey density.
Type II
\[f(N)=\frac{aN}{1+ahN}.\]Here \(a\) is an attack-rate parameter and \(h\) is handling time. Consumption rises with prey density but approaches a maximum because predators require time to handle prey.
Type III
A common sigmoidal form is
\[f(N)=\frac{aN^2}{1+ahN^2}.\]Consumption is relatively low at low prey abundance and increases more rapidly at intermediate abundance before saturating.
Key idea. The functional response specifies the biological mechanism linking prey abundance to predator consumption and can strongly alter predator–prey dynamics.