Modeling distributions of flying insects: effective attraction radius of pheromone in two and three dimensions

The effective attraction radius (EAR) of an attractive pheromone-baited 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 EAR(c) that is convenient to use in two-dimensional encounter rate models of mass trapping and mating disruption with semiochemicals to control insects. The EAR(c) 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 (F(L)) was assumed to be SD x square root of 2pi, because the probability area equal to the height of the normal distribution,1/(SD x square root of 2pi), times the F(L) is equal to the area under the normal curve. To test this assumption, 2000 simulated insects were allowed to fly in a three-dimensional correlated random walk in a 10-m 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 10-m 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 F(L), thus verifying the equation to calculate F(L). The EAR and F(L) were used to obtain a smaller EAR(c) for use in a two-dimensional model that caught an equivalent number of insects as that with EAR in three dimensions. This verifies that the F(L) estimation equation and EAR to EAR(c) conversion methods are appropriate.