Numerical response
The numerical response in ecology is the change in predator density as a function of change in prey density. The term numerical response was coined by M. E. Solomon in 1949. It is associated with the functional response, which is the change in predator's rate of prey consumption with change in prey density. As Holling notes, total predation can be expressed as a combination of functional and numerical response. The numerical response has two mechanisms: the demographic response and the aggregational response. The numerical response is not necessarily proportional to the change in prey density, usually resulting in a time lag between prey and predator populations. For example, there is often a scarcity of predators when the prey population is increasing.
The demographic response consists of changes in the rates of predator reproduction or survival due to a changes in prey density. The increase in prey availability translates into higher energy intake and reduced energy output. This is different from an increase in energy intake due to increased foraging efficiency, which is considered a functional response. This concept can be articulated in the Lotka-Volterra Predator-Prey Model.
a = conversion efficiency: the fraction of prey energy assimilated by the predator and turned into new predators
P = predator density
V = prey density
m = predator mortality
Demographic response consists of a change in dP/dt due to a change in V and/or m. For example, if V increases, then predator growth rate (dP/dt) will increase. Likewise if the energy intake increases (due to greater food availability) and a decrease in energy output (from foraging), then predator mortality (m) will decrease and predator growth rate (dP/dt) will increase. In contrast, the functional response consists of a change in conversion efficiency (a) or capture rate (c).
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