Formulation and Analysis of Deterministic Models of Predation Among Acarine Populations

螨种群捕食确定性模型的制定和分析

• 批准号: 0316192
• 负责人: Robert Gardner
• 金额: $ 12.6万
• 依托单位: University of Massachusetts Amherst
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-08-15 至 2006-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0316192&HistoricalAwards=false
• 关键词: Formulation; Analysis; Deterministic; Models; Predation

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.

加德纳 研究人员开发并分析了捕食性和食草性螨虫局部自我毁灭种群的持续行为模型。 该项目受到赫法克经典实验的启发，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。 赫法克指出，食草螨寄主植物内的局部聚集体和偶尔捕食它们的螨虫在种群周期阶段的同步性会分布在整个区域，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共同产生了自然界中捕食者-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被公式化，可以成功地模拟复杂的、明显混沌的空间。通常伴随持续动态的时间模式。 因此，由于复制数据集中存在较大差异，此类模型难以提供可靠的行为预测。 这极大地限制了它们在农作物害虫生物防治中的实际应用。 在之前的工作中，研究人员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式。 他研究了与反应扩散系统及相关模型的分析和实际应用相关的两个一般性问题。 首先，他研究了几个不同的稳定波族的存在和这些方程的空间模式、它们的不稳定性和分岔，以及奇异波状模式的存在。 通过结合解析和近似方法，他描述了这种不稳定波形成时空混沌组织中心的理论机制，而在其他体系中，复杂但非混沌的稳定时空模式自发出现。 第二个主题涉及基于实验的模型推导。 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。 研究人员研究了混合数值程序，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可能存在问题，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，而大范围的大规模移民则很难在实验室中测量。 然而，简单的稳定波可能暗示了这种情况可能发生的一种情况。 研究人员用斑块模型在数值模拟中对此进行了研究，这可能构成能够检测这种行为的新的、更简单的实验设计的基础。这两种方法共同呈现了一幅统一的图景，说明某些不稳定波和空间的存在如何驱动“动态随机性” -时间模式理论上与最小微观局部尺度上控制行为的人口变化参数相关，从而通过人口和环境随机性产生异步。 以植物为食的螨虫，以及反过来吃它们的螨虫，通常表现出密切相关的数量增长和下降周期。 有时，种群数量会迅速下降到接近灭绝的水平。 但在一个经典的实验中，赫法克和他的同事表明，这些强耦合的循环可以通过人口或地理因素的微小变化来调节，从而导致这两个物种的长期生存，这在捕食者和猎物的数量、时间和空间模式上表现出来螨虫。 当然，当被捕食的螨虫正在吃一种有价值的农作物时，人们希望两种螨虫种群都灭绝。 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大的实际意义。 植食性物种的经济影响相当大，尽管在某些当地农业中广泛使用捕食性螨虫作为生物防治方法，但许多农业企业仍依赖化学害虫防治。 化学控制提供了短期解决方案，但具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且不可预测的行为模式而难以量化。 研究人员的数值模拟表明存在许多不同类型的混沌，其中一些混沌可以更好地抑制食草动物种群和农作物受损。 该项目探索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以及在其他情况下在某些外来物种的接种控制中得到实际应用。