Active space of pheromone plume and its relationship to effective attraction radius in applied models

The release rate of a semiochemical lure that attracts flying insects has a specific effective attraction radius (EAR) that corresponds to the lure's orientation response strength. EAR is defined as the radius of a passive sphere that intercepts the same number of insects as a semiochemical-baited trap. It is estimated by calculating the ratio of trap catches in the field in baited and unbaited traps and the interception area of the unbaited trap. EAR serves as a standardized method for comparing the attractive strengths of lures that is independent of population density. In two-dimensional encounter rate models that are used to describe insect mass trapping and mating disruption, a circular EAR (EAR(c)) describes a key parameter that affects catch or influence by pheromone in the models. However, the spherical EAR, as measured in the field, should be transformed to an EAR(c) for appropriate predictions in such models. The EAR(c) is calculated as (pi/2EAR(2))/F-L, where F-L is the effective thickness of the flight layer where the insect searches. F-L was estimated from catches of insects (42 species in the orders Coleoptera, Lepidoptera, Diptera, Hemiptera, and Thysanoptera) on traps at various heights as reported in the literature. The EAR(c) was proposed further as a simple but equivalent alternative to simulations of highly complex active-space plumes with variable response surfaces that have proven exceedingly difficult to quantify in nature. This hypothesis was explored in simulations where flying insects, represented as coordinate points, moved about in a correlated random walk in an area that contained a pheromone plume, represented as a sector of active space composed of a capture probability surface of variable complexity. In this plume model, catch was monitored at a constant density of flying insects and then compared to simulations in which a circular EAR(c) was enlarged until an equivalent rate was caught. This demonstrated that there is a circular EAR(c), where all insects that enter are caught, which corresponds in catch effect to any plume. Thus, the EAR(c), based on the field-observed EAR, can be used in encounter rate models to develop effective control programs based on mass trapping and/or mating disruption.