Interpreting Data from Trapping of Stochastic Movers

数学物理学家Jeff Schenker教授和昆虫学家James Miller教授的这项合作旨在从根本上了解捕获昆虫，特别是农业害虫的科学。用诱饵（通常是信息素）诱捕昆虫个体一直是野外生物学中一项重要的测量技术。陷阱中捕获的个体数量可以显示出存在哪些昆虫以及它们何时活跃。然而，将捕获的害虫数量转化为害虫密度的准确估计（在某一地区发现的害虫数量）的难题目前尚不清楚。这个项目旨在通过结合实地实验、计算机模拟和对近似昆虫飞行的随机运动的理论研究来解决这个问题。更好地了解诱捕将有助于农业害虫管理人员、发现和管理入侵物种以及监测和控制昆虫病媒的传播。特别是，对种群估计的目标改进对农民来说将是一个福音，只有在有明确的科学证据表明施用成本被种植者的潜在损失所抵消的情况下，害虫管理人员才可以推荐杀虫剂喷洒等干预措施。这项工作将遵循一项综合计划，即对随机移动者的竞争性诱捕进行数学调查，并对昆虫的标记释放/捕获进行实地试验。目的是回答两个问题：(1)给定一系列陷阱，从各种捕获物中可以推断出关于扩散、流动性和种群密度的哪些信息？(2)给定几个陷阱，我们如何最好地安排它们，以便从捕获数据中准确地推断出种群密度的估计值？在过去，关于这两个问题的一个缺失环节是准确地表示捕获概率，因为它随着动物从陷阱出发的距离而变化。研究人员在利用计算机模拟随机步行者的捕捉模型方面取得了相当大的进展。通过对扩散和随机游走的数学分析和数值研究来解决这个问题，研究小组期望能够从数据中提取重要的科学测量值，这些数据可以在现场轻松而廉价地收集。

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.