QEIB: Stochastic Nonlinear Population Dynamics: Mathematical Models, Biological Experiments, and Data Analyses

QEIB：随机非线性种群动态：数学模型、生物学实验和数据分析

• 批准号: 0210474
• 负责人: Jim Cushing
• 金额: $ 22.5万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-09-01 至 2004-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0210474&HistoricalAwards=false
• 关键词: QEIB; Stochastic; Nonlinear; Population; Dynamics

Cushing0210474 The project entails a theoretical and experimental studythat examines nonlinear population dynamics phenomena in thecontext of stochasticity and that addresses fundamental conceptsof how stochastic and nonlinear forces combine to produceobserved population phenomena. The methodology involves aninterdisciplinary effort that features a thorough integration ofbiologically based modeling (deterministic and stochastic),mathematical and numerical analyses of model dynamics, and thederivation and application of statistical techniques forconnecting models with data (including parameter estimation andmodel evaluation). The investigators study the fundamentalquestion about how (demographic) stochasticity at the individuallevel propagates to the population level. A promising class ofmodels that incorporates both demographic and environmentalstochasticity is pursued. A variety of statistical andmathematical questions that arise from these studies areinvestigated. The validity of this modeling methodology andaccuracy of a priori model predictions is directly testable byexperiments. The project study includes an experimental test ofthis modeling approach to demographic and environmentalstochasticity, using a laboratory model that the investigatorshave successfully used in a wide variety of population dynamicsand modeling studies during the last decade. The modelingmethodology is also applicable to field populations and theinvestigators pursue the development of field studies withseveral researchers who have expressed interest in such acollaboration. These collaborators include colleagues at (1) theCenter for Environmental Analysis at California State University,Los Angeles in a project modeling the spatially structureddynamics of seashore species, (2) the University of California,Davis in a project to model a lupine-caterpillar-nematode system,(3) Andrews University on mathematical/statistical models of thedistribution of marine birds and mammals on Protection IslandNational Wildlife Refuge in the Strait of Juan de Fuca, and (4)the Virginia Institute of Marine Science on nonlinear models ofthe blue crab in the Exuma Cays. An understanding of the dynamics of biological populationsis fundamental to the understanding of ecological andenvironmental problems. Mathematical models can be a valuabletool that provides this understanding. They can also provide themeans to predict the future of ecosystems and the species thatthey include. An accurate descriptive and predictive capabilitygained through mathematical models provides not only a basicunderstanding of ecological problems, but also the ability todesign programs for the assessment, management, and control ofecosystems and for the solution of environmental problems. Afundamental difficulty in the application of mathematical modelsto ecological problems has been the lack of a close connection ofmodels with biological data. A key problem is the ability ofmodels to incorporate random effects and disturbances. Theinvestigators extend, analyze, and apply a modeling methodologythey have developed during a decade of experimental studies, in acontrolled laboratory setting, that addresses these difficulties.The methods are not restricted to laboratory populations,however, and the project also includes collaborations with newcolleagues for the purpose of applying the methods to fieldstudies of natural populations.

Cushing0210474 该项目需要进行理论和实验研究，研究随机性背景下的非线性总体动力学现象，并解决随机力和非线性力如何结合产生观察到的总体现象的基本概念。 该方法涉及跨学科的努力，其特点是彻底整合基于生物学的建模（确定性和随机）、模型动力学的数学和数值分析，以及用于连接模型与数据的统计技术的推导和应用（包括参数估计和模型评估）。 研究人员研究了关于个体层面的（人口统计）随机性如何传播到群体层面的基本问题。 我们正在寻求一类包含人口统计和环境随机性的有前途的模型。 对这些研究中出现的各种统计和数学问题进行了调查。 该建模方法的有效性和先验模型预测的准确性可以通过实验直接检验。 该项目研究包括对这种人口和环境随机性建模方法的实验测试，使用了研究人员在过去十年中成功用于各种人口动态和建模研究的实验室模型。 该建模方法也适用于实地人群，研究人员与几位对此类合作表示感兴趣的研究人员一起开展实地研究。 这些合作者包括 (1) 洛杉矶加州州立大学环境分析中心的同事，参与了一个模拟沿海物种空间结构动力学的项目；(2) 加州大学戴维斯分校的同事参与了一个模拟羽扇豆毛毛虫线虫的项目系统，(3) 安德鲁斯大学关于胡安德富卡海峡保护岛国家野生动物保护区内海洋鸟类和哺乳动物分布的数学/统计模型，以及 (4) 弗吉尼亚州海洋科学研究所研究埃克苏马群岛蓝蟹的非线性模型。 了解生物种群的动态是理解生态和环境问题的基础。 数学模型可以成为提供这种理解的有价值的工具。 它们还可以提供预测生态系统及其所包含的物种的未来的方法。 通过数学模型获得的准确描述和预测能力不仅提供了对生态问题的基本理解，而且提供了设计生态系统评估、管理和控制方案以及解决环境问题的能力。 将数学模型应用于生态问题的一个根本困难是模型与生物数据缺乏紧密的联系。 一个关键问题是模型纳入随机效应和干扰的能力。 研究人员在受控实验室环境中扩展、分析和应用了他们在十年的实验研究中开发的建模方法，以解决这些困难。然而，这些方法并不局限于实验室人群，该项目还包括与新同事的合作将这些方法应用于自然种群的实地研究的目的。