Nicholson–Bailey model
The Nicholson–Bailey model was developed in the 1930s to describe the population dynamics of a coupled host-parasitoid system. It is named after Alexander John Nicholson and Victor Albert Bailey. Host-parasite and prey-predator systems can also be represented with the Nicholson-Bailey model. The model is closely related to the Lotka–Volterra model, which describes the dynamics of antagonistic populations (preys and predators) using differential equations.
The model uses (discrete time) difference equations to describe the population growth of host-parasite populations. The model assumes that parasitoids search for hosts at random, and that both parasitoids and hosts are assumed to be distributed in a non-contiguous ("clumped") fashion in the environment. In its original form, the model does not allow for stable coexistence. Subsequent refinements of the model, notably adding density dependence on several terms, allowed this coexistence to happen.
A credible, simple alternative to the Lotka–Volterra predator–prey model and its common prey dependent generalizations (like Nicholson–Bailey) is the ratio-dependent or Arditi–Ginzburg model. The two are the extremes of the spectrum of predator interference models. According to the authors of the alternative view, the data show that true interactions in nature are so far from the Lotka–Volterra extreme on the interference spectrum that the model can simply be discounted as wrong. They are much closer to the ratio dependent extreme, so if a simple model is needed one can use the Arditi–Ginzburg model as the first approximation.
The model is defined in discrete time. It is usually expressed as:
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