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该项目需要一项理论和实验研究，研究了随机性的thecontext中的非线性种群动力学现象，并探讨了随机和非线性力量如何结合起来以产生观察的种群现象的基本概念。 该方法涉及一个学科的工作，其中包括基于生物学的建模（确定性和随机性），模型动力学的数学和数值分析，以及用于通过数据（包括参数估计和模型评估）连接模型的统计技术的数学和数值分析，以及统计技术的统计技术。 研究人员研究了有关个人水平（人口）随机性如何传播到人群水平的基本问题。 追求了一个有前途的阶级模型，同时结合了人口统计和环境综合性。 这些研究引起的各种统计和数学问题已被评估。 这种建模方法的有效性和先验模型预测的准确性是可直接测试的。 该项目研究包括对人口统计和环境综合性的这种建模方法的实验测试，使用了一个实验室模型，该模型在过去十年中，研究人员成功地用于各种种群动力学和建模研究中。 模拟方法也适用于现场人群，而对田间研究的研究人员则在对这种兴趣的研究人员进行现场研究的发展。 这些合作者包括（1）在加利福尼亚州立大学的（1）洛杉矶的环境分析的同事，该项目模拟了海滨物种的空间结构型动力学，（2）加利福尼亚州戴维斯的项目，旨在建模羽扇豆植物/统计学模型的羽绒被式/统计学模型，旨在建模。 Juan de Fuca海峡的野生动物保护区，以及（4）弗吉尼亚海洋科学研究所在Exuma Cays中的蓝蟹非线性模型。 了解生物种群的动力学，这是对生态和环境问题的理解。 数学模型可以是提供这种理解的宝库。 他们还可以为他们提供预测生态系统的未来以及包括的物种的未来。 通过数学模型获得的准确的描述性和预测能力不仅可以对生态问题进行基本理解，还提供了托德设计程序的能力，用于评估，管理和控制生态系统以及解决环境问题的解决方案。 在应用数学模型的生态问题的应用中，难度是缺乏与生物学数据的密切联系。 一个关键问题是模型纳入随机效果和干扰的能力。 评估器扩展，分析和应用建模方法学在十年的实验研究中开发了解决这些困难的实验室环境中。但是，该方法不仅限于实验室人群，但是该项目还包括与新的核对资料合作，以将方法应用于现场群体自然群体的方法。