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

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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.