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

9625576库欣种群生物学的一个中心问题是理解和解释观察到的动物数量波动。非线性动力学的研究为种群研究开辟了一个新的阶段，在这个阶段中，实验直接关注平衡、周期和非周期周期以及混沌等现象。研究人员承担了一系列对非线性人口理论测试至关重要的活动：从将生物学翻译成正式的数学语言，到数学模型的分析，到数据分析统计技术的开发和应用，再到生物实验的设计和实施。实验中使用了Tribolium属粉甲虫的实验室种群。通过他们的研究，研究者对非线性种群现象和行为提供了严格的实验检验。这些包括：(1)从稳定平衡到不变循环（非周期），到周期锁定，到奇异吸引子和混沌的动态转变；(2)瞬态和间歇动力学，旨在定义用于随机种群模型的实际间歇概念，并对随机非线性模型预测的一些异常瞬态行为进行测试；(3)以迁徙联系的甲虫种群为单位的元种群动态；(4)环境周期性与非线性人口效应相互作用所产生的动力学行为。研究人员研究生物种群（特别是昆虫种群）如何随时间波动，以及不同的环境如何导致这些波动中截然不同的，有时是意想不到的变化。本研究是通过一个跨学科项目进行的，该项目结合了复杂的数学模型和统计分析的使用，以及使用具有重要经济意义的害虫甲虫物种的实验室实验的设计和实施。研究人员试图描述和解释人口波动的各种模式，从那些规则和可预测的到那些不规则和“混乱”的。他们试图了解产生这些不同种群行为的环境条件。如果要预测（人为或自然）环境扰动和操纵对生物种群的影响，这种理解是必不可少的。这些影响具有深远的影响，从粮食生产和虫害防治到野生动物管理和物种多样性保护。

9625576 Cushing A central question in population biology is that of understanding and explaining observed fluctuations in animal numbers. The study of nonlinear dynamics has opened the way to a new phase of population research in which experiments are focused directly on phenomena such as equilibria, periodic and aperiodic cycles, and chaos. The investigators undertake a spectrum of activities essential to the testing of nonlinear population theory: from the translation of biology into the formal language of mathematics, to the analysis of mathematical models, to the development and application of statistical techniques for the analysis of data, to the design and implementation of biological experiments. Laboratory populations of flour beetles of the genus Tribolium are used in the experiments. By means of their studies the investigators provide rigorous experimental tests of nonlinear population phenomena and behavior. These include: (1) dynamical transitions from stable equilibria, to invariant loops (aperiodicities), to period locking, to strange attractors and chaos; (2) transient and intermittent dynamics with aims towards defining practical concepts of intermittency for use with stochastic population models and the testing of some of the unusual transient behaviors forecast by stochastic nonlinear models; (3) the dynamics of meta-populations using beetle populations linked by migration; and (4) the dynamical behaviors that can be produced by the interaction of environmental periodicities with nonlinear demographic effects. The investigators study how biological populations (in particular, populations of insects) fluctuate in time and how different circumstances can lead to drastically different, and sometimes unexpected, changes in these fluctuations. This study is carried out by means of an interdisciplinary program that integrates the use of sophisticated mathematical models and statistical analysis with the design and implementation of l aboratory experiments using species of beetles that are economically important insect pests. The investigators seek to describe and explain a variety of patterns in population fluctuations, ranging from those that are regular and predictable to those that are irregular and "chaotic." They seek to understand the environmental conditions that give rise to these various kinds of population behavior. This understanding is essential if the impact on biological populations of environmental perturbations and manipulations (by Man or by Nature) is to be predicted. These impacts have far-reaching consequences, ranging from food production and pest control to wildlife management and the conservation of species diversity.