A geometric model of mortality and crop protection for insects feeding on discrete toxicant deposits.

Current theory governing the biological effectiveness of toxicants stresses the dose-response relationship and focuses on uniform toxicant distributions in the insect's environment. However, toxicants are seldom uniformly dispersed under field conditions. Toxicant distribution affects bioavailability, but the mechanics of such interactions is not well documented. We present a geometric model of the interactions between insects and heterogeneously distributed toxicants. From the model, we conclude the following: 1) There is an optimal droplet size, and droplets both smaller and larger than this optimum will decrease efficacy. 2) There is an ideal droplet distribution. Droplets should be spaced based on two criteria: calculate the allowable damage, double this quantity, and one lethal deposit should be placed in this area; and define the quantity of leaf the larva could eat before the toxicant decays below the lethal level and place one lethal deposit within this area. 3) Distributions of toxicant where deposits are sublethal will often be ineffective, but the application is wasteful if deposits contain more than a lethal dose. 4) Insect behavior both as individuals and collectively influences the level of crop production provided by an application. This conclusion has implications for both crop protection and natural plant-insect interactions. The effective utilization of new more environmentally sensitive toxicants may depend on how well we understand how heterogeneous toxicant distributions interact with insect behavior to determine the biological outcome.