Byers, John 
Submitted to: Journal of Theoretical Biology
Publication Type: Peer Reviewed Journal Publication Acceptance Date: 9/4/2008 Publication Date: 1/15/2009 Citation: Byers, J.A. (2009). Modeling distributions of flying insects: Effective attraction radius of pheromone in two and three dimensions. Journal of Theoretical Biology. Journal of Theoretical Biology, 256:8189. Interpretive Summary: The radius of a passive “sticky” sphere that would intercept the same number of flying insects as an attractive pheromonebaited trap is termed the effective attraction radius (EAR). The spherical EAR for a particular attractant and insect species in nature can be transformed into a circular EARc that is used in twodimensional models of mass trapping and mating disruption using behavioral chemicals (pheromones) to control pest insects. The EARc equation requires an estimate of the effective thickness of the layer where the insect flies in search of mates and food or habitat. The standard deviation (SD) of flight height was determined for several insect species from catches on traps of increasing heights as reported in the scientific literature. The thickness of the effective flight layer (FL) was assumed equal to SD times 2.5 because the probability area equal to the height of the normal distribution times the FL is equal to the area under the normal curve. To test the validity of this assumption, 2000 simulated insects were allowed to move about in a threedimensional 10m thick layer where an algorithm caused them to redistribute according to a normal distribution with specified SD and mean flight height at the midpoint of this layer. Under the same conditions, a spherical EAR was placed at the center of the 10m layer and intercepted flying insects distributed normally for a set period of time. The number caught was equivalent to that caught in another simulation with a uniform flight density in a morenarrow layer equal to FL, thus verifying the equation to calculate FL. The EAR and FL were used to obtain a smaller EARc for use in a twodimensional model that caught an equivalent number of insects as that with EAR in three dimensions. This verifies that the FL estimation equation and EAR to EARc conversion methods are appropriate so the EARc can be used in models predicting the efficiency of traps and confusing methods with pheromone in pest management and control using pheromones. Technical Abstract: The effective attraction radius (EAR) of an attractive pheromonebaited trap was defined as the radius of a passive “sticky” sphere that would intercept the same number of flying insects as the attractant. The EAR for a particular attractant and insect species in nature is easily determined by a catch ratio on attractive and passive (unbaited) traps, and the interception area of the passive trap. The spherical EAR can be transformed into a circular EARc that is convenient to use in twodimensional encounter rate models of mass trapping and mating disruption with semiochemicals to control insects. The EARc equation requires an estimate of the effective thickness of the layer where the insect flies in search of mates and food/habitat. The standard deviation (SD) of flight height of several insect species was determined from their catches on traps of increasing heights reported in the literature. The thickness of the effective flight layer (FL) was assumed to be SD (2 X pi) , because the probability area equal to the height of the normal distribution, 1/SD (2 X pi), times the FL is equal to the area under the normal curve. To test this assumption, 2000 simulated insects were allowed to fly in a threedimensional correlated random walk in a 10m thick layer where an algorithm caused them to redistribute according to a normal distribution with specified SD and mean at the midpoint of this layer. Under the same conditions, a spherical EAR was placed at the center of the 10m layer and intercepted flying insects distributed normally for a set period. The number caught was equivalent to that caught in another simulation with a uniform flight density in a narrower layer equal to FL, thus verifying the equation to calculate FL. The EAR and FL were used to obtain a smaller EARc for use in a twodimensional model that caught an equivalent number of insects as that with EAR in three dimensions. This verifies that the FL estimation equation and EAR to EARc conversion methods are appropriate.
