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

库欣0210474 该项目需要一个理论和实验研究，探讨非线性人口动态现象的背景下的随机性和地址的基本概念如何随机和非线性力联合收割机生产观察到的人口现象。 该方法涉及一个跨学科的努力，其特点是生物学为基础的建模（确定性和随机性），数学和模型动力学的数值分析，并推导和应用统计技术连接模型与数据（包括参数估计和模型评估）的彻底整合。 研究者们研究的基本问题是，个体水平的随机性如何传播到群体水平。 一个有前途的类ofmodels，结合人口和环境的随机性追求。 从这些研究中产生的各种统计和数学问题进行了调查。 这种建模方法的有效性和先验模型预测的准确性是直接通过实验测试。 该项目研究包括对人口和环境随机性的这种建模方法的实验测试，使用的实验室模型在过去十年中已成功地用于各种人口动态和建模研究。 建模方法也适用于现场人口和调查人员追求的发展领域的研究与几个研究人员谁表示有兴趣在这样一个集体。 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，他们的项目是模拟海滨物种的空间结构动力学，（2）加州大学戴维斯分校的同事，他们的项目是模拟羽扇豆-毛虫-线虫系统，（3）安德鲁斯大学数学/胡安德富卡海峡保护岛国家野生动物保护区海洋鸟类和哺乳动物分布的统计模型，（4）弗吉尼亚海洋科学研究所关于埃克苏马礁蓝蟹非线性模型的研究。 理解生物种群的动态是理解生态和环境问题的基础。 数学模型可以是一个有价值的工具，提供这种理解。 它们还可以提供方法来预测生态系统和其中包含的物种的未来。 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，而且还提供了设计评估、管理和控制生态系统以及解决环境问题的方案的能力。 数学模型应用于生态学问题的一个基本困难是模型与生物学数据之间缺乏密切的联系。 一个关键问题是模型纳入随机效应和干扰的能力。 研究人员扩展、分析和应用了他们在受控实验室环境中进行的十年实验研究中开发的一种建模方法，该方法解决了这些困难。然而，该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，目的是将该方法应用于自然人群的实地研究。

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.