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

当前的许多生态学理论是从经验拟合数据发展而来的，然而这些模型往往缺乏对本质上是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建立一个综合概念框架所需的广泛知识。这个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、拓扑、连续介质力学和计算逆问题等数学领域；科学计算和信息技术领域；以及野生动物生态学和生物多样性的空间方法领域。跨学科合作倡议可以将上述各个数学领域的最新突破与地理信息系统（GIS）的技术进步以及生物多样性和野生动物生态学研究中的空间方法结合起来。模型的实现和验证将导致以类似于流程建模的方式，将创建的模型的层次结构转换为相互连接的编程模块网络。这样的实现最终应该具有模拟和预测能力，这可以根据具体情况进行调整，涉及不同程度的复杂性。将实施教育倡议，建立具有这方面专门知识的人力资源基础结构。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。这些材料以及孵化基金支持的研讨会和讲习班为实施严格的研究生计划提供了基础，以培训学生在生态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产生具有管理和工业应用的预测模型方面落后于自然科学。尽管有很多关于自然系统如何运作以及这些系统如何受到人类活动影响的理论，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并没有很好的理解。自然系统极其复杂，既受到季节变化等规律的、可预测的过程的影响，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。如果科学家想要发展出一种合理的预测自然系统的能力，那么他们就必须能够越来越精确地描述和模拟自然系统。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。这个项目将发展几个试点研究努力，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，该项目将举办讲习班和研讨会，启动数学和计算生态学研究生学位课程的创建，以培养新一代研究人员更好地管理和恢复我们的自然系统。

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.