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 库欣 研究人员进行了一项跨学科研究计划来测试非线性总体理论：他们构建和分析数学模型，设计和实施生物实验，开发和应用统计技术来分析数据。 对于生物实验，使用易于培养、世代时间短（即产生长时间序列数据）并允许准确普查动物数量的生物体：谷盗属的面粉甲虫。 在研究的第一部分中，目标是模型识别和参数估计。 第二部分关注的是记录人口动态的定性行为的转变。 控制繁殖率和成人死亡率，以便跨越参数空间的边界，从稳定平衡到周期性循环，再到混沌。 第三阶段的目标是检验有关这些不寻常的人口动态是否存在的假设，并开发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实验操纵数学模型预测的生物群体的不同性质的动态行为之间的转变的明确例子。 在过去十年左右的时间里，人们认识到简单的方程可以产生复杂的动力学，这导致了解释人口时间序列数据的大量令人着迷的理论可能性。 了解观察到的动物种群数量的波动是种群生物学的一个核心问题。它在粮食生产和害虫防治、可再生资源管理和物种多样性保护等领域具有深远的应用。 由于收集足够的生态数据、通过实验操纵生态系统以及用生态数据评估复杂的数学模型的困难，波动是非线性动态力的结果的假设已被证明难以检验。 在这个研究项目中，研究人员检验非线性总体理论的方法是通过新开发的非线性时间序列统计方法将数学模型与实验生物数据严格联系起来。 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，并利用了生物学家、统计学家和数学家的才能。 在群体生物学领域，跨学科的努力是不寻常的，来自所有这些学科的研究人员都参与该项目的各个方面，从实验设计和实施，到理论建模和分析，再到统计测试和验证。 最终目标是证明非线性数学在严格理解动物种群动态，特别是种群数量波动（无论这些波动是规律的还是“混乱的”）方面的有用性和重要性。