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reaction-diffusion equation
Sharpness of saturation in harvesting and predation
Harvesting and predation occur through contact processes in which the rate
at which the managed (prey) population can be found depends on the
population size, usually saturating at high densities. Many models
incorporate saturation in this process without considering the effects
of the particular function used to describe it. We show that the sharpness
with which this saturation occurs has an important effect upon the resulting
population dynamics, with bistability (sometimes involving a stable
equilibrium and a stable limit cycle) occurring for saturation that is
any sharper than the commonly used Michaelis-Menten (Holling type II)
functional response. This sharpness threshold occurs across a wide range
of model types, from simple harvesting to density-dependent and
ratio-dependent predation.