Formulation and Analysis of Deterministic Models of Predation Among Acarine Populations

加德纳 研究者开发和分析了捕食性和草食性螨类局部自我消灭种群的持续行为模型。 Huffaker的经典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，该实验激发了该项目。 Huffaker指出，食草螨和捕食它们的螨在寄主植物内的局部聚集体的种群周期阶段的同步性偶尔会遍布整个区域，但这种同步性可能会被人口统计和环境随机性打破。 他猜想，产生同步的互补正则化机制和产生同步的互补随机机制共同产生了自然界中这些捕食者-被捕食者相互作用中所见的复杂波和模式。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，这些时空模式具有典型的持续动力学特性。 因此，这种模型很难提供可靠的行为预测，因为在重复数据集中看到的差异很大。 这大大限制了它们在作物害虫生物防治中的实际应用。 在以前的工作中，研究人员制定了一个家庭ofdeterministic模型，包括一个理想化的范式定义一类反应扩散系统。 他研究了与反应扩散系统及其相关模型的分析和实际应用有关的两个一般性问题。 首先，他研究了几个不同的家庭的稳定波和空间模式的这些方程，他们的不稳定性和分叉，并存在exoticwave-like模式的存在。 通过结合分析和近似的方法，他描述了理论机制，这种不稳定的波可以形成时空混沌的组织中心，而在其他制度，复杂的，但非混沌，稳定的时空模式自发出现。 第二个主题涉及的模型，这是基于实验的推导。 这解决了反应扩散模型通过假定的低密度阈值的增长率来模拟随机性的方式。 调查研究混合数值程序解决的关键问题的参数估计，这可能是问题的随机补丁模型和反应扩散模型，但在相反的时空尺度。 例如，低密度阈值涉及少量个体的微观局部动态，而过大区域的大规模移民很难在实验室中测量。 然而，简单的稳定波可能表明这是可能的。 研究人员在使用补丁模型的数值模拟中对此进行了研究，这可能成为可以检测这种行为的新的和更简单的实验设计的基础。这两种方法一起提供了一个统一的画面，即由某些不稳定波和时空模式的存在驱动的“动态随机性”如何在理论上与最小微观局部尺度上的种群变化控制行为的参数联系在一起，因此，通过人口统计和环境的随机性， 以植物为食的螨类，以及依次以它们为食的螨类，其数量的增长和减少往往呈现出周期性的变化，而这种变化是紧密相关的。 有时候，种群数量会迅速下降到濒临灭绝的水平。 但是在一个经典的实验中，Huffaker和他的同事们发现，这些强耦合的周期可以被人口或地理因素的微小变化所缓和，从而导致两个物种的长期生存，这显示了捕食者和猎物螨数量在时间和空间上的模式。 当然，当被捕食的螨正在吃一种有价值的作物时，人们希望两个螨种群都灭绝。 因此，螨类种群如何共同变化的问题在作物害虫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，虽然使用捕食螨作为生物控制在某些地方农业中很普遍，但许多农业企业依赖于化学害虫控制。 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，由于害虫生物防治的行为模式复杂且不可预测，其风险和不确定性难以量化。 研究人员的数值模拟表明，存在许多不同类型的混沌，其中一些能够更好地抑制食草动物种群和农作物损害。 该项目探索了新的理论和计算工具，这些工具可能在作物害虫的生物控制中找到实际应用，并在其他情况下，在某些外来物种的接种控制中找到实际应用。

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.