A mathematical model for the flight of pea moth to pheromone traps through a crop

Abstract

A model is presented that describes the average resultant track of a population of male pea moth, Cydia nigricana (F.), flying through a crop to a continuously emitting pheromone trap containing 100 pg (E,E)-8,10-dodecadien-1-yl acetate. This model, based on work by C. T. David, J. S. Kennedy, A. R. Ludlow, J. N. Perry and C. Wall J. chem. Ecol . 8, 1207 (1982), and modified for the effect of a crop, has particular reference to a line of interacting pheromone traps equally spaced along the mean wind direction at an emergence site. It is derived after extensive field observations. The model relates to the average flight behaviour of a population of moths, and is compatible with both the anemotactic theory and a system of integrated anemotaxis and longitudinal chemo-klinotaxis. We give two theoretical reasons and cite observational evidence which suggest that, within a wheat crop, a discrete plume breaks up at around 10—15 m from the source and that beyond this distance pheromone exists at a non-zero concentration at all downwind positions. Close to the source moths are assumed to respond to a discrete plume as described by David et al . (1982) and further from it to receive pheromone continuously and fly, on average, upwind. Because of the effects of the crop we suggest that equations ofatmospheric diffusion derived to predict time-averaged concentrations of pheromone may hold instantaneously. The average behaviour of a population of responding moths under these conditions is discussed. Far from the source there is a concentration of pheromone below which such moths sampling it are assumed not to respond; this is termed the threshold concentration and the positions where it occurs are termed the threshold contour. The contour is sketched for single and multiple sources. Such moths flying upwind to this contour are assumed to stop and then cast (move in a crosswind direction). This results in the moths either moving inside the contour to a region of concentration above the threshold, and resuming upwind flight, or moving outside the contour and, eventually, not responding further. Net movement in the former is therefore towards the source and such moths may eventually be caught. The model allows for random flight by non-responding moths outside the threshold contour, and for moths to ‘lose’ the discrete plume of one source and continue upwind flight to encounter that of the next source upwind. The model has ten parameters, five relate directly to moth flight behaviour, one to the degree of random flight, one to meteorological conditions, two describe the number and spacing of traps and the last governs numerical accuracy. Predictions from the model of proportional catch in each of a line of traps were made using a computer program. An extensive body of 406 sets of data concerning trap interactions was collected over six years and the model provided excellent fits to this data. Throughout this paper the model is described in biological terms, formulae are provided when necessary.