Interpreting Data from Trapping of Stochastic Movers

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This collaboration between mathematical physicist Prof. Jeff Schenker and entomologist Prof. James Miller aims at a fundamental understanding of the science of trapping of insects, particularly agricultural pests. Capture of individual insects in traps baited with a lure, often a pheromone, has long been a critical measurement technique in field biology. The number of individuals caught in a trap can reveal which insects are present and when they active. However, the difficult problem of converting the number captured into an accurate estimate of pest density (the number of pests to be found in a given region) is at present poorly understood. This project aims to solve that problem through a combination of field experiments, computer simulations, and theoretical investigations into random movements that approximate insect flight. Better understanding of trapping will be of use to agricultural pest managers, in the detection and management of invasive species, and in monitoring and controlling the spread of insect disease vectors. In particular, the aimed-for improvements in population estimation will be a boon for farmers, allowing pest managers to recommend interventions like insecticide sprays only when there is clear scientific evidence that the cost of application is offset by the potential loss to the grower. The work will follow an integrated program of mathematical investigations on competitive trapping of stochastic movers and field experiments of marked release/capture of insects. The aim is to answer two questions: (1) Given an array of several traps what information about the dispersal, mobility and population density may be inferred from the various catches? (2) Given several traps how may we best arrange them to accurately infer estimates on population density from catch data? In the past, a missing link in regards to both problems has been an accurate representation of the probability of catch as it varies with the distances animals originated from the trap. The investigators have made considerable progress on modeling catch using computer simulated random walkers. By bringing mathematical analysis and numerical study of diffusion and random walks to bear on the problem, the research team anticipates being able to extract important scientific measurements from data that can be gathered easily and inexpensively in the field.