Linear relationship between peak and season-long abundances in insects

An accurate quantitative relationship between key characteristics of an insect population, such as season-long and peak abundances, can be very useful in pest management programs. To the best of our knowledge, no such relationship has yet been established. Here we establish a predictive linear relationship between insect catch M(pw) during the week of peak abundance, the length of seasonal flight period, F (number of weeks) and season-long cumulative catch (abundance) A = 0.41M(pw)F. The derivation of the equation is based on several general assumptions and does not involve fitting to experimental data, which implies generality of the result. A quantitative criterion for the validity of the model is presented. The equation was tested using extensive data collected on captures of male gypsy moths Lymantria dispar (L.) (Lepidoptera: Erebidae) in pheromone-baited traps during 15 years. The model was also tested using trap catch data for two species of mosquitoes, Culex pipiens (L.) (Diptera: Culicidae) and Aedes albopictus (Skuse) (Diptera: Culicidae), in Gravid and BG-sentinel mosquito traps, respectively. The simple, parameter-free equation approximates experimental data points with relative error of 13% and R(2) = 0.997, across all of the species tested. For gypsy moth, we also related season-long and weekly trap catches to the daily trap catches during peak flight. We describe several usage scenarios, in which the derived relationships are employed to help link results of small-scale field studies to the operational pest management programs.