Predator–prey models
Predator–prey models describe two populations in which predators benefit from consuming prey while prey experience increased mortality through predation.
Variables
Let \(N(t)\) denote prey abundance and \(P(t)\) predator abundance. Their changes are coupled because encounters between the populations affect both species.
General structure
\[\frac{dN}{dt}=\text{prey growth}-\text{loss to predation},\]\[\frac{dP}{dt}=\text{predator gain from prey}-\text{predator loss}.\]The precise form of the predation term determines how predator consumption changes with prey abundance.
Coupled dynamics
Changes in prey abundance alter food availability for predators, while changes in predator abundance alter mortality pressure on prey. This feedback can generate oscillations and other population patterns.
Key idea. Predator and prey populations cannot generally be modelled independently because the growth rate of each depends on the state of the other.