A remark on “Biological control through provision of additional food to predators: A theoretical study” [Theor. Popul. Biol. 72 (2007) 111–120]

Abstract Biological control, the use of predators and pathogens to control target pests, is a promising alternative to chemical control. It is hypothesized that the introduced predators efficacy can be boosted by providing them with an additional food source. The current literature (Srinivasu, 2007; 2010; 2011) claims that if the additional food is of sufficiently large quantity and quality then pest eradication is possible in finite time. The purpose of the current manuscript is to show that to the contrary, pest eradication is not possible in finite time, for any quantity and quality of additional food. We show that pest eradication will occur only in infinite time, and derive decay rates to the extinction state. We posit a new modeling framework to yield finite time pest extinction. Our results have large scale implications for the effective design of biological control methods involving additional food.