Mathematical Sciences: Nonlinear Demographic Dynamics: Mathematical Models, Biological Experiments, and Data Analysis

研究人员承担了一个跨学科的项目来测试非线性人口理论，包括数学模型的构建和分析，生物实验的设计和实施，以及数据分析统计技术的发展和应用。他们使用磨粉虫属的粉甲虫作为实验生物。在项目的第一部分，他们确定适当的模型，并估计控制模型详细行为的参数。在第二部分中，他们记录了人口动态定性行为的转变。他们使用了生殖率和成人死亡率的组合，这些组合跨越了参数空间的边界，从稳定的平衡到不变的循环，再到混乱。在第三部分中，他们检验了关于这些不寻常的人口现象存在的假设，并开发了识别实验数据中现象的方法。理解观察到的动物数量波动是种群生物学的一个核心问题；事实上，它具有从粮食生产到物种多样性保护的深远影响。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。该项目旨在探索种群表现出类似于其他物理现象的混沌行为的可能性。如上所述，这种行为将产生严重的后果。

The investigators undertake an interdisciplinary project to test nonlinear population theory, incorporating the construction and analysis of mathematical models, the design and implementation of biological experiments, and the development and application of statistical techniques for the analysis of data. They use flour beetles of the genus Tribolium as the experimental organism. In the first part of the project they identify appropriate models and estimate the parameters that control the detailed behavior of the models. In the second part they document transitions in the qualitative behavior of the demographic dynamics. They use combinations of reproductive rates and adult mortality rates that span boundaries in parameter space from stable equilibria, to invariant cycles, to chaos. In the third part they test hypotheses concerning the existence of these unusual demographic phenomena and develop methods for identifying the phenomena in experimental data. Understanding the observed fluctuations in animal numbers is a central question in population biology; indeed, it has far-reaching impacts ranging from food production to the conservation of species diversity. In the past 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. This project aims to explore the possibility that populations can exhibit chaotic behavior similar to that seen in other physical phenomena. As indicated above, such behavior would have significant consequences.