COLLABORATIVE RESEARCH: Nonlinear Demographic Dynamics: Mathematical Models, Biological Experiments, Data Analyses

合作研究：非线性人口动态：数学模型、生物学实验、数据分析

• 批准号: 9306271
• 负责人: Jim Cushing
• 金额: $ 32万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-08-01 至 1997-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9306271&HistoricalAwards=false
• 关键词: COLLABORATIVE; RESEARCH; Nonlinear; Demographic; Dynamics

9306271 Cushing The investigators conduct an interdisciplinary research program to test nonlinear population theory: they construct and analyze mathematical models, design and implement biological experiments, develop and apply statistical techniques for the analysis of data. For the biological experiments an organism is used that is easy to culture, has a short generation time (i.e. yields long time series data) and allows an accurate census of animal numbers: flour beetles of the genus Tribolium. In the first part of the study the objectives are model identification and parameter estimation. In the second part, the concern is to document transitions in the qualitative behavior of the demographic dynamics. Rates of reproduction and adult mortality are manipulated in order to cross boundaries in parameter space from stable equilibria, to periodic cycles, to chaos. In phase three the objectives are to test hypotheses concerning the existence of these unusual demographic dynamics and develop methods for identifying these phenomena in experimental data. A major contribution of this project is an unequivocal example of experimentally manipulated transitions between qualitatively different dynamical behaviors of a biological population as predicted by a mathematical model. In the last ten years or so, the recognition that simple equations can generate complex dynamics has led to an outpouring of fascinating theoretical possibilities for the explanation of population time series data. Understanding the observed fluctuations in animal population numbers is a central question in population biology; it has far-reaching applications in areas ranging from food production and pest control, to the management of renewable resources, to the conservation of species diversity. The hypothesis that fluctuations are the result of nonlinear dynamic forces has proved to be elusive to test due to the difficulties of gathering adequate ecological data, of experimentall y manipulating ecological systems, and of evaluating complex mathematical models with ecological data. In this research project the investigators' approach to testing nonlinear population theory is to connect mathematical models rigorously with experimental biological data by means of newly developed statistical methods for nonlinear time series. The project is unique in its interdisciplinary approach because it involves both theory and experimentation and utilizes the talents of the biologist, statistician, and mathematician. It is unusual in the field of population biology to have an interdisciplinary effort in which investigators from all of these disciplines are involved in all aspects of the project, from experimental design and implementation, through theoretical modeling and analysis, to statistical testing and verification. The ultimate goal is to demonstrate the usefulness and importance of nonlinear mathematics in gaining a rigorous understanding of the dynamics of animal populations and in particular of fluctuations in population numbers, be these fluctations regular or "chaotic."

9306271 cushing研究人员进行了跨学科研究计划，以测试非线性人群理论：他们构建和分析数学模型，设计和实施生物学实验，开发和应用统计技术来分析数据。 对于生物学实验，使用了易于培养的生物体，具有很短的生成时间（即产生长时间的数据），并允许精确的动物数量人口普查：Tribolium属的面粉甲虫。 在研究的第一部分中，目标是模型识别和参数估计。 在第二部分中，关注的是记录人口动态定性行为的过渡。 为了使从稳定平衡到周期性周期到混乱的参数空间中的边界跨越边界。 在第三阶段中，目标是检验有关这些异常人口动力学存在的假设，并开发出在实验数据中识别这些现象的方法。 该项目的一个主要贡献是通过数学模型预测的生物种群的定性动力学行为之间实验操纵的过渡的明确示例。 在过去的十年左右的时间里，对简单方程式可以产生复杂动力学的认识导致了人们对人口时间序列数据的解释的引人入胜的理论可能性的涌入。 了解动物种群中观察到的波动是人群生物学的核心问题。它在从粮食生产和防治，到可再生资源的管理到物种多样性的领域中具有深远的应用。 事实证明，由于收集适当的生态数据的困难，操纵生态系统的实验以及用生态数据评估复杂的数学模型，因此被证明是非线性动力学的结果的假设。 在该研究项目中，研究者测试非线性人群理论的方法是通过新开发的非线性时间序列的统计方法将数学模型与实验生物学数据进行了严格的联系。 该项目的跨学科方法是独一无二的，因为它涉及理论和实验，并利用生物学家，统计学家和数学家的才能。 在人口生物学领域，要进行跨学科的努力是不寻常的，其中所有这些学科的研究人员都参与了项目的各个方面，从实验设计和实施到理论建模和分析到统计测试和验证。 最终目标是证明非线性数学在对动物种群的动态（尤其是人口数量波动的动力学）方面的有用性和重要性，是否是规则的波动或“混乱”。