Sharpness of saturation in harvesting and predation - Christopher M. Kribs-Zaleta (Mathematical Biosciences and Engineering)
Harvesting and predation occur through contact processes in which the rateat which the managed (prey) population can be found depends on thepopulation size, usually saturating at high densities. Many modelsincorporate saturation in this process without considering the effectsof the particular function used to describe it. We show that the sharpnesswith which this saturation occurs has an important effect upon the resultingpopulation dynamics, with bistability (sometimes involving a stableequilibrium and a stable limit cycle) occurring for saturation that isany sharper than the commonly used Michaelis-Menten (Holling type II)functional response. This sharpness threshold occurs across a wide rangeof model types, from simple harvesting to density-dependent andratio-dependent predation.