Byers, J.A. 2009. Modeling distributions of flying insects: Effective attraction radius of pheromone in two and three dimensions. Journal of Theoretical Biology 256:81-89.
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 EARc that is convenient to use in two-dimensional 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 × sqrt(2 × pi), because the probability area equal to the height of the normal distribution,1/(SD × sqrt(2 × 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 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 FL, thus verifying the equation to calculate FL. The EAR and FL were
used to obtain a smaller EARc 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 FL estimation equation and EAR to EARc conversion methods are appropriate.