The paradox of biological control revisited: per capita non-linearities

In what is called biological control, predators or parasites are introduced with the purpose to suppress the density of a pest population. For biological control to be effective the pest population density needs to be permanently held at low levels. A paradox for the biological control of pests has recently been raised, in that available data suggest that severely suppressed pests exhibit fairly stable dynamics. This is in opposition with conventional predator-prey and parasitoid-host theory, which predicts that a prey population that is severely suppressed will fluctuate violently in density. I argue here that there need not be any paradox. If the selfregulation of the pest, expressed as the per capita rate of population change as a function of density, is a non-linear downward convex function, even prey populations that get suppressed almost to extinction may have stable dynamics or very low amplitude cycles. Such forms of the non-linear per capita selfregulation have been suggested for insect types of prey, while mammal types of prey have been suggested to have a downward concave per capita rate of population change as a function of density. This suggest that it might in general be more complex to biologically control mammal pests than insect pests.