BIOCOMPLEXITY, Incubation Activity: Application of Mathematical Methods and Scientific Computation to Complex Ecological Problems

生物复杂性，孵化活动：数学方法和科学计算在复杂生态问题中的应用

• 批准号: 0083894
• 负责人: Paulo Lima-Filho
• 金额: $ 9.69万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-09-15 至 2003-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0083894&HistoricalAwards=false
• 关键词: BIOCOMPLEXITY; Incubation; Activity; Application; Mathematical

0083894 Lima-FilhoABSTRACTMuch current ecological theory has evolved from empirically fitted data, however these models often lack the mathematical depth, rigor and complexity required for multi-scale analysis of natural phenomena that are intrinsically non-linear. On the other hand, many mathematical models explaining ecological phenomena lack a substantial corroborating empirical validation. These weaknesses are in part due to the broad spectrum of knowledge required to develop an integrated conceptual framework in the study of ecological systems. This project is a multi-disciplinary collaborative effort, combining an array of different - but interrelated - areas of expertise. These areas involve the mathematical fields of geometry, topology, continuum mechanics and computational inverse problems; the fields of scientific computation and information technology; and the fields of wildlife ecology and spatial methods in biodiversity. Interdisciplinary collaborative initiatives can integrate recent breakthroughs in the various mathematical areas described above, with technological advances in Geographical Information Systems (GIS) and spatial methods in the study of biodiversity and wildlife ecology. Implementation and validation of models will lead to the translation of the hierarchy of models created into a network of interconnected programming modules, in a similar fashion to process modeling. Such implementation should eventually have both simulation and prediction capabilities, which can be tailored to specific situations, involving various degrees of complexity. Educational Initiatives will be implemented to create a human resources infrastructure with expertise on the subject. Existing educational resources (REU and VIGRE grants) are being used to develop interdisciplinary courseware and interdisciplinary research activities. These materials and the seminars and workshops supported by the Incubation Grant provide the basis for the implementation of a rigorous graduate program to train students in the application of advanced mathematics and scientific computation in ecology and environmental science.Ecology and the environmental sciences have lagged behind the natural sciences in generating predictive models with management and industrial applications. Although there is a great deal of theory on how natural systems function and how these systems are impacted by human activities, we do not have a good understanding of how to best restore damaged ecosystems, or how to predict the long-term consequences of human activities. Natural systems are extremely complex and are influenced by both regular, predictive processes like the changing seasons, and by rare, severe events like storms and fire. The interactions among species are also complex. If scientists are ever to develop a reasonable predictive capability regarding natural systems, then they must be able to describe and model natural systems with increasing accuracy and precision. This means that they must be able to develop mathematical models and descriptions of these systems and computational methods to analyze them. This project will develop several pilot research endeavors to begin cross-disciplinary collaboration among ecologists, mathematicians, and computer scientists. In addition, the project will hold workshops and seminars to initiate the creation of a graduate degree program in mathematical and computational ecology, to train a new generation of researchers to better manage and restore our natural systems.

0083894 Lima-Filho摘要当前许多生态学理论都是从经验拟合的数据发展而来的，然而这些模型往往缺乏对本质上非线性的自然现象进行多尺度分析所需的数学深度、严谨性和复杂性。另一方面，许多解释生态现象的数学模型缺乏实质性的实证验证。 这些弱点部分是由于在生态系统研究中发展一个综合概念框架所需的广泛知识。 该项目是一个多学科的合作努力，结合了一系列不同但相互关联的专业领域。 这些领域涉及几何学、拓扑学、连续介质力学和计算逆问题的数学领域;科学计算和信息技术领域;以及野生生物生态学和生物多样性空间方法领域。 跨学科合作倡议可以将上述各种数学领域的最新突破与地理信息系统（GIS）和生物多样性和野生动物生态学研究中的空间方法的技术进步相结合。 模型的实现和验证将导致将创建的模型层次结构转换为互连编程模块的网络，其方式与过程建模类似。 这种实施最终应具有模拟和预测能力，可根据涉及不同复杂程度的具体情况进行调整。 将实施教育倡议，以建立具有这方面专门知识的人力资源基础设施。 现有的教育资源（REU和VIGRE赠款）正在用于开发跨学科课件和跨学科研究活动。 这些材料以及由孵化补助金支持的研讨会和讲习班为实施严格的研究生课程提供了基础，该课程旨在培养学生在生态学和环境科学中应用高等数学和科学计算。生态学和环境科学在生成具有管理和工业应用的预测模型方面落后于自然科学。 虽然有大量的理论是关于自然系统如何运作以及这些系统如何受到人类活动的影响，但我们对如何最好地恢复受损的生态系统或如何预测人类活动的长期后果没有很好的了解。 自然系统极其复杂，既受到季节变化等规律性的预测过程的影响，也受到风暴和火灾等罕见的严重事件的影响。 物种之间的相互作用也很复杂。 如果科学家要发展出一种合理的预测自然系统的能力，那么他们必须能够以越来越高的准确性和精确度来描述和建模自然系统。 这意味着他们必须能够开发这些系统的数学模型和描述以及分析它们的计算方法。 该项目将开展几项试点研究，开始生态学家、数学家和计算机科学家之间的跨学科合作。此外，该项目还将举办研讨会和研讨会，以启动数学和计算生态学研究生学位课程的创建，培养新一代研究人员，以更好地管理和恢复我们的自然系统。