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在人口生物学中提出的一个核心问题是理解和解释动物数量波动的观察到。 对非线性动力学的研究为新的人群研究开辟了道路，在该研究中，实验直接集中在诸如均衡，周期性和周期性周期和混乱等现象上。 研究人员对非线性人口理论的测试必不可少的活动进行：从将生物学转化为数学的形式语言，到数学模型的分析，再到用于分析数据分析的统计技术，再到生物学实验的设计和实施。 实验中使用了围属面粉甲虫的实验室甲虫。 通过他们的研究，研究人员对非线性人口现象和行为进行了严格的实验测试。 其中包括：（1）从稳定的平衡，不变的循环（Aperiodicities）到周期锁定，到奇怪的吸引者和混乱的动态过渡； （2）瞬时和间歇性动力学旨在定义与随机种群模型使用的间歇性的实际概念，并测试通过随机非线性模型预测的某些异常的短暂行为； （3）使用通过迁移链接的甲虫种群的元群体动力学； （4）环境周期性与非线性人口效应的相互作用可以产生的动力行为。 研究人员研究了生物种群（尤其是昆虫种群）如何随着时间的流逝而波动，以及不同情况如何导致这些波动的截然不同，有时甚至是意外的变化。 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与使用经济上重要的虫害的甲虫物种的设计和实施相结合。 研究人员试图描述和解释种群波动中的各种模式，从规则且可预测的模式到不规则和“混乱”的模式。他们试图了解引起各种种群行为的环境条件。 如果要预测对环境扰动和操纵的生物群体的影响（人类或本质上），那么这种理解是必不可少的。 这些影响具有深远的后果，从粮食生产和害虫控制到野生动植物管理以及物种多样性的保护。