Formulation and Analysis of Deterministic Models of Predation Among Acarine Populations

加德纳是一名研究人员，他开发并分析了捕食性和食草性螨类局部自灭种群的持续行为模型。该项目是由赫夫克的经典实验刺激的，该实验首次展示了空间过程在某些生态相互作用中的中介作用。赫夫克指出，食草性螨类寄主植物内局部聚集体和捕食它们的螨类的种群周期阶段的同步偶尔会扩散到整个地区，但这种同步可能会被人口和环境的随机性打破。他推测，产生同步的互补正则化机制和产生异步的互补随机机制一起产生了自然界中这些捕食者-猎物相互作用中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、明显是混沌的、典型地伴随持续动态的时空模式。因此，由于在复制数据集中看到的巨大差异，这样的模型很难提供对行为的可靠预测。这大大限制了它们在农作物病虫害生物防治中的实际应用。在以前的工作中，研究人员建立了一族确定性模型，包括定义一类反应扩散系统的理想化范式。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，他研究了几种不同的稳定波和这些方程的空间模式的存在，它们的不稳定性和分叉，以及奇异波状模式的存在。他用解析和近似相结合的方法描述了这样的稳定波可以形成时空混沌的组织中心的理论机制，而在其他机制中，复杂但非混沌的稳定时空图案自发出现。第二个话题是建立在实验基础上的模型的推导。这解决了反应扩散模型通过假定的低密度增长率阈值来模拟随机性的方式。研究人员研究了解决参数估计这一关键问题的混合数值方法，这对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，低密度阈值涉及少量个体的微观局部动态，而大范围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一种情况。研究者用斑块模型的数值模拟来检验这一点，这可能形成新的和更简单的可以检测这种行为的实验设计的基础。这两种方法一起展示了一幅统一的图景，即由某些不稳定波和时空模式的存在所驱动的“动态随机性”如何在理论上与控制最小微观局部尺度上的行为的人口变化参数相联系，从而通过人口和环境随机性产生异步性。以植物为食的螨类，以及反过来以它们为食的螨类，通常表现出数量的增长和下降的周期，这与它们的数量密切相关。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，赫夫克和他的同事们表明，这些强耦合的循环可以被人口统计或地理因素的微小变化所遗憾，导致这两个物种的长期生存，显示出捕食者和被捕食者的数量在时间和空间上的模式。当然，当被捕食者吃的是一块价值不菲的树叶时，人们希望这两个种群都灭绝。因此，在作物病虫害的生物防治中，螨类种群如何一起变化的问题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捕食性螨类作为生物防治，但许多农业企业依赖于化学防治虫害。化学控制提供了一种短期解决方案，但也有许多破坏性的长期影响。然而，由于其复杂和不可预测的行为模式，生物害虫防治的风险和不确定性很难量化。这位研究人员的数值模拟表明，存在许多不同类型的混沌，其中一些对食草动物种群和作物损害的抑制程度都更好。该项目探索了新的理论和计算工具，这些工具可能会在作物病虫害的生物防治中找到实际应用，在其他情况下，也可能在某些外来物种的接种控制中找到应用。

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.