A Model for Peak and Width of Signaling Windows: Ips duplicatus and Chilo partellus Pheromone Component Proportions--Does Response have a Wider Window than Production?

Abstract

Pheromone communication systems have a reliable signal with a restricted window of amounts and ratios released and perceived. We propose a model based on a Gaussian response profile that allows a quantification of the response peak (location of optimum) and a measure of the peak width (response window). Interpreting the Gaussian curve, fitted by nonlinear regression (NLR), as a standard normal distribution, the peak location equals the mean (μ) and the window width equals 2× the standard deviation (2σ). The NLR procedure can provide an objective measure for both peak location and width for a wide range of data sets. Four empirical data sets as well as 10 literature data sets were analyzed. The double-spined spruce engraver, Ips duplicatus, was field tested in four populations to find the optimum proportion for attraction to the two male aggregation pheromone components, ipsdienol (Id) and (E)-myrcenol (EM), ranging from 0 to 100% of Id. Tests in Norway and the Czech Republic confirmed the preference of western populations for a blend between 50 and 90% Id. A population in Inner Mongolia showed a preference for traps with the 10 and 50% Id baits. The NLR fitted values for response peak and width (μ; 2σ) were: Norway 0.64, 0.73; Czech Republic 0.53, 0.73; NE China 0.77, 0.29; and Inner Mongolia 0.33, 0.50. The signal produced by Norwegian field-collected males had a narrower window width (2σ = 0.12). Males of the maize stem borer, Chilo partellus, were tested in a flight tunnel for their response to variation in the two major female sex pheromone gland components, (Z)-11-hexadecenal and the corresponding alcohol (OH). Variation of the alcohol in seven levels from 2 to 29% OH showed the highest male response for 17% OH. For all behavioral steps, the peak of male response was near μ = 0.14, while the window width fell from 2σ = 0.5 to 0.2 for eight sequential behavioral steps from take-off to copulation. Female production had a similar peak location (μ = 0.13) but a narrower width, 2σ = 0.14. Literature data from other moth species showed similar patterns, with a wider male response relative to the female production windows. Literature data on response to enantiomer ratios in a hymenopteran and to pheromone amounts in a dipteran were also described by our model. In a bark beetle population (Ips pini), with two hybridizing enantiomeric strains, the production peaks were narrower (0.1) than the response peaks (0.5). Thus, it in general, seems that in the pheromone systems analyzed, the width of the response window (2σ = 0.1 to 0.8) is larger than that of the production window (2σ = 0.03 to 0.14), irrespective of the sex of the sender.