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

数学科学：非线性人口动态：数学模型、生物实验和数据分析

• 批准号: 9625576
• 负责人: Jim Cushing
• 金额: $ 35.5万
• 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: 1996
• 资助国家: 美国
• 起止时间: 1996-08-15 至 1999-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9625576&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Demographic; Dynamics

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.

9625576 库欣 群体生物学的一个核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的新阶段开辟了道路，其中实验直接关注平衡、周期性和非周期性循环以及混沌等现象。 研究人员承担了一系列对非线性总体理论的检验至关重要的活动：从生物学到数学的形式语言的翻译，到数学模型的分析，到用于数据分析的统计技术的开发和应用，到生物实验的设计和实施。 实验中使用了谷盗属实验室的面粉甲虫种群。 通过他们的研究，研究人员对非线性群体现象和行为进行了严格的实验测试。 这些包括：（1）从稳定平衡到不变环（非周期性）、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，旨在定义与随机总体模型一起使用的间歇性实用概念，并测试随机非线性模型预测的一些异常瞬态行为； (3) 使用通过迁移联系起来的甲虫种群的综合种群动态； (4)环境周期性与非线性人口效应相互作用所产生的动态行为。 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发生截然不同的、有时甚至是意想不到的变化。 这项研究是通过跨学科计划进行的，该计划将复杂的数学模型和统计分析的使用与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相结合。 研究人员试图描述和解释人口波动的各种模式，从有规律和可预测的模式到不规则和“混乱”的模式。他们试图了解导致这些不同群体行为的环境条件。 如果要预测环境扰动和操纵（人为或自然）对生物种群的影响，这种理解至关重要。 这些影响具有深远的影响，从粮食生产和害虫控制到野生动物管理和物种多样性保护。