RUI: Collaborative Research-Nonlinear Demographic Dynamics: Mathematical Models, Biological Experiments, Data Analyses

小行星9319073 研究人员和他的同事进行跨学科的研究计划，以测试非线性人口理论：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进行数据分析。 在生物学实验中，使用了一种易于培养、世代时间短（即产生长时间序列数据）并允许精确统计动物数量的生物体：拟谷盗属的面粉甲虫。 在第一部分的研究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的定性行为的转变。 繁殖率和成人死亡率的操纵，以跨越边界的参数空间从稳定的平衡，周期性的周期，混沌。 第三阶段的目标是检验关于是否存在这些不寻常的人口动态的假设，并制定在实验数据中识别这些现象的方法。 这个项目的一个主要贡献是一个明确的例子，实验操纵的生物种群的定性不同的动力学行为之间的过渡，预测的数学模型。 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，这导致了大量解释人口时间序列数据的迷人理论可能性。 了解观察到的动物种群数量的波动是种群生物学的一个中心问题;它在从粮食生产和害虫控制到可再生资源管理，再到物种多样性保护等领域都有深远的应用。 波动是非线性动力的结果这一假设已被证明是难以捉摸的测试，由于收集足够的生态数据，实验操作生态系统，并评估复杂的数学模型与生态数据的困难。 在这个研究项目中，研究人员检验非线性种群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。 该项目是独特的跨学科方法，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人才。 在种群生物学领域，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了项目的各个方面，从实验设计和实施，通过理论建模和分析，到统计测试和验证。 最终的目标是证明非线性数学的有用性和重要性，以获得严格的理解动态的动物种群，特别是在人口数量的波动，这些波动规则或“混沌”。"

9319073 Desharnais The investigator and his colleagues 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 da ta, of experimentally 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."