Formulation and Analysis of Deterministic Models of Predation Among Acarine Populations

研究者开发并分析了捕食性和草食性螨虫在当地自我灭绝种群的持续行为模型。该项目受到Huffaker经典实验的启发，该实验首次证明了空间过程在某些生态相互作用中的中介作用。Huffaker注意到，在寄主植物中，食草螨和捕食它们的螨的局部聚集在种群周期阶段的同步性偶尔会蔓延到整个地区，但这种同步性可能会被人口和环境的随机性打破。他推测产生同步性的互补规则机制和产生非同步性的互补随机机制共同产生了在自然界中这些捕食者-猎物相互作用中所看到的复杂波和模式。现有的随机斑块模型已经成功地模拟了复杂的、明显混乱的时空模式，这些模式通常伴随着持续的动态。因此，由于在重复数据集中看到的大方差，这种模型很难提供可靠的行为预测。这极大地限制了它们在作物生物防治方面的实际应用。在之前的工作中，研究者制定了一系列确定性模型，包括定义一类反应扩散系统的理想化范例。他研究了两个与反应扩散系统及其模型的分析和实际应用有关的一般问题。首先，他研究了几个不同的稳定波族和这些方程的空间模式的存在，它们的不稳定性和分岔，以及奇异波样模式的存在。通过分析和近似相结合的方法，他描述了理论机制，通过这种机制，这种稳定的波可以形成时空混沌的组织中心，而在其他制度下，复杂但非混沌的稳定的时空模式会自发出现。第二个主题涉及模型的推导，这是基于实验的。这解决了反应扩散模型通过假设增长率中的低密度阈值来模拟随机性的方式。研究者研究了混合数值过程，解决了参数估计的关键问题，这对于随机斑块模型和反应扩散模型都是有问题的，但在相反的时空尺度上。例如，低密度阈值涉及少数个体的微观局部动态，而在大区域的大规模迁移难以在实验室中测量。然而，简单的稳定波可能表明这是可能的。研究者用补丁模型的数值模拟来检验这一点，这可能构成新的和更简单的实验设计的基础，可以检测这种行为。总之，这两种方法呈现了一幅统一的图景，即由某些不稳定波动和时空模式的存在驱动的“动态随机性”如何在理论上与控制最小微局部尺度上行为的种群变化参数联系起来，从而通过人口和环境随机性产生异步。以植物为食的螨虫，以及反过来以它们为食的螨虫，在数量上经常表现出密切相关的增长和下降的周期。有时种群数量迅速下降到濒临灭绝的水平。但在一个经典的实验中，赫芬顿克和他的同事们表明，这些强烈耦合的周期可以通过人口或地理因素的微小变化来调节，从而导致两个物种的长期生存，在时间和空间上显示出捕食者和猎物螨的数量模式。当然，当被捕食的螨虫正在吃掉一种有价值的作物时，人们希望两个螨虫种群都灭绝。因此，螨虫种群如何共同变化的问题在作物害虫的生物防治中具有相当重要的实际意义。植食性物种的经济影响是相当大的，尽管在某些地方农业中广泛使用掠食性螨作为生物控制手段，但许多农业企业依赖化学害虫控制。化学控制提供了一个短期的解决方案，但有许多破坏性的长期影响。然而，生物害虫防治的风险和不确定性由于其复杂和不可预测的行为模式而难以量化。研究者的数值模拟表明存在许多不同种类的混乱，其中一些达到了更好的抑制食草动物种群和作物损害的水平。该项目探索新的理论和计算工具，可能在作物害虫的生物控制中找到实际应用，以及在其他情况下，某些外来物种的接种控制。

Gardner The investigator develops and analyzes models of persistentbehavior of locally self-annihilating populations of predatoryand herbivorous mites. The project is stimulated by Huffaker'sclassic experiment, which provided the first demonstration of themediating role of spatial processes in certain ecologicalinteractions. Huffaker noted that synchronies in the phases ofpopulation cycles of localized aggregates within host plants ofherbivorous mites and of the mites that preyed upon themoccasionally spread over an entire area, but that the synchronycan be broken by demographic and environmental stochasticity. Heconjectured that the complementary regularizing mechanisms thatgenerate synchrony, and the complementary stochastic mechanismsthat generate asynchrony, together generate the complex waves andpatterns seen in these predator-prey interactions in nature.Existing stochastic patch models have been formulated thatsuccessfully simulate complex, and evidently chaotic,spatio-temporal patterns that have typically accompaniedpersistent dynamics. Accordingly, such models have difficulty inproviding reliable predictions of behavior due to the largevariance seen in replicate data sets. This substantially limitstheir practical application to the biological control of croppests. In previous work, the investigator formulated a family ofdeterministic models, including an idealized paradigm defining aclass of reaction-diffusion systems. He studies two generalissues relating to the analysis and practical applications of thereaction-diffusion system and related models. First, heinvestigates the presence of several distinct families of stablewaves and spatial patterns of these equations, theirinstabilities and bifurcations, and the presence of exoticwave-like patterns. By combined analytical and approximatemethods, he describes theoretical mechanisms by which suchunstable waves can form the organizing center of spatio-temporalchaos, while in other regimes, complex but non-chaotic, stablespatio-temporal patterns appear spontaneously. A second topicconcerns the derivation of the model, which is based onexperiment. This addresses the manner in which thereaction-diffusion model simulates stochasticity throughpostulated low-density thresholds in the growth rates. Theinvestigator studies hybrid numerical procedures addressing thecrucial issue of parameter estimation, which can be problematicboth for stochastic patch models and for the reaction-diffusionmodel, but at opposite spatio-temporal scales. For example, thelow-density thresholds involve the micro-local dynamics of asmall number of individuals, whereas large-scale emigration overlarge regions is difficult to measure in a laboratory. However,simple stable waves may suggest one instance in which this may bepossible. The investigator examines this in numericalsimulations with patch models, which may form the basis for newand simpler experimental designs that can detect such behavior.Together, these two approaches present a unified picture of how"dynamic stochasticity" driven by the presence of certainunstable waves and spatio-temporal patterns is theoreticallylinked to parameters of population change governing behavior atthe smallest micro-local scales, and thus the generation ofasynchrony through demographic and environmental stochasticity. Plant-eating mites, and the mites that eat them in turn,often show cycles of growth and decline in numbers that areclosely related. Sometimes the populations decline rapidly tonear-extinction levels. But in a classic experiment Huffaker andcolleagues showed that these strongly coupled cycles can bemoderated by small changes in demographic or geographic factors,leading to a long-term survival of both species that shows itselfin patterns, in time and space, of the numbers of predator andprey mites. Of course, when the prey mite is eating a valuablecrop, one wants both mite populations to go extinct. So issues ofhow mite populations vary together are of considerable practicalimportance in the biological control of crop pests. The economicimpact of phytophageous species is considerable, and although theuse of predatory mites as a biological control is widespread incertain local agricultures, many agricultural enterprises rely onchemical pest controls. Chemical controls provide a short-termsolution, but have many damaging long-term effects. However, therisks and uncertainties of biological pest control are difficultto quantify due to their complex and unpredictable patterns ofbehavior. The investigator's numerical simulations indicate thepresence of many different kinds of chaos, some of which achievebetter levels of suppression of both herbivore populations andcrop damage. The project explores new theoretical andcomputational tools that may find practical application in thebiological control of crop pests and, in other contexts, ininoculative control of certain exotic species.