Collaborative Research: Non-Linear Population Dynamics: Mathematical Models, Biological Experiments and Data Analysis

合作研究：非线性种群动态：数学模型、生物学实验和数据分析

• 批准号: 9981458
• 负责人: Brian Dennis
• 金额: $ 8.4万
• 依托单位: Regents of the University of Idaho
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-09-01 至 2002-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9981458&HistoricalAwards=false
• 关键词: Collaborative; Research; Non; Linear; Population

Dennis9981458 Understanding the fluctuations in animal numbers is acentral issue in population biology that has far-reaching impacton and implications for problems ranging from food production tothe conservation of species. Nonlinear dynamics opens the way toa new phase of population research in which theory andexperimentation focus on phenomena such as cycles andquasi-periodicity, chaos and strange attractors, multipleattractors and complicated basins of attraction, saddle sets andtheir stable manifolds, and so on. This interdisciplinaryproject, in which Robert Costantino, Jim Cushing, Brian Dennis,Robert Desharnais, and Shandelle Henson collaborate, covers aspectrum of activities essential to testing nonlinear populationtheory: the translation of the biology into the language ofmathematics and back again, the analysis of deterministic andstochastic models, the development and application of statisticaltechniques for the analysis of data, and the design andimplementation of biological experiments. A series of experimentswith flour beetles of the genus Tribolium provide rigorousexperimental tests of nonlinear phenomena. Topics includenonlinearity in the context of stochasticity, chaos andpopulation control, the impact of periodic environments on animalabundance, demographic dynamics and natural selection,nonequilibrium species interactions, and statistical questionsconcerning parameterization and validation of models. With a sound understanding of the underlying dynamics ofanimal populations, ecologists can anticipate the consequences ofenvironmental degradation and learn better ways to manage naturalpopulations and control populations of pests. For example, one ofthe experiments suggests that, by taking advantage of the"sensitivity to initial conditions" that is the hallmark of achaotic system, managers can dramatically decrease pestpopulation numbers without the use of chemical pesticides bymaking small perturbations at critical times. The marriage ofecological theory and experiments by the interdisciplinaryresearch team leads to new techniques for the application ofmathematics to ecological problems. The project is supported bythe Applied Mathematics, Computational Mathematics, andStatistics programs in MPS and the Population Biology and Ecologyprograms in BIO.

丹尼斯9981458 了解动物数量的波动是种群生物学的一个中心问题，它对从食物生产到物种保护等问题都有深远的影响和意义。 非线性动力学开辟了人口研究的新阶段，其中理论和实验集中在周期和准周期性，混沌和奇怪吸引子，多重吸引子和复杂的吸引域，鞍集和它们的稳定流形等现象。这个跨学科的项目，其中罗伯特Costantino，吉姆库欣，布赖恩丹尼斯，罗伯特Desharnais和尚德尔汉森合作，涵盖了测试非线性种群理论所必需的活动的各个方面：将生物学翻译成数学语言，然后再翻译回来，分析确定性和随机性模型，开发和应用数据分析的数学技术，以及设计和实施生物实验。 对拟谷盗属的面粉甲虫进行的一系列实验为非线性现象提供了严格的实验测试。 主题包括非线性背景下的随机性，混沌和人口控制，周期性环境的影响animalabundance，人口动态和自然选择，非平衡物种相互作用，和统计问题有关的参数化和验证模型。 有了对动物种群潜在动态的充分理解，生态学家可以预测环境退化的后果，并学习更好的方法来管理自然种群和控制害虫种群。 例如，其中一个实验表明，通过利用“对初始条件的敏感性”这一混沌系统的标志，管理人员可以在关键时刻进行小扰动，从而在不使用化学杀虫剂的情况下大幅减少害虫种群数量。 跨学科研究小组将生态理论与实验结合起来，为数学在生态问题中的应用带来了新的技术。 该项目由MPS的应用数学、计算数学和统计学项目以及BIO的人口生物学和人口统计学项目支持。