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

研究人员进行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，以及用于数据分析的统计技术的开发和应用。他们使用Tribolium属的面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的详细行为的参数。在第二部分中，他们记录了人口动态质量行为的转变。他们使用繁殖率和成人死亡率的组合，这些组合跨越参数空间中的边界，从稳定平衡到不变周期，再到混沌。在第三部分中，他们测试了关于这些不寻常的人口现象存在的假设，并开发了在实验数据中识别这些现象的方法。了解观察到的动物数量波动是种群生物学中的一个中心问题；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，这导致了解释人口时间序列数据的许多有趣的理论可能性的涌现。这个项目旨在探索种群可能表现出类似于其他物理现象的混乱行为的可能性。如上所述，这种行为将产生重大后果。

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.