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

Abstract

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 · 2 · π , because the probability area equal to the height of the normal distribution, 1 / ( SD · 2 · π ) , 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.