Mathematical Sciences: Nonlinear Self-focussing as a Deterministic Mechanism for Generating Spatial Complexity in Ecosystems

数学科学：非线性自聚焦作为生态系统中产生空间复杂性的确定性机制

• 批准号: 9505327
• 负责人: James Powell
• 金额: $ 6万
• 依托单位: Utah State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-15 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9505327&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Self; focussing

Powell The investigator and his colleagues study the spatial dynamics of populations, developing and analyzing models that incorporate biological data and investigating the way individuals of a population aggregate and disperse. Aggregation leads to spatial complexity through feedback. The feedback is nonlinear when the cues individuals use to aggregate depend on the number of individuals. In a population model that allows for movement, aggregative feedback causes nonlinear self-focussing, the organization or `focussing' of population groups on small scales. Decreases in the scale of spatial correlation make the dispersal pattern more complex, leading to complicated spatial structure. Mathematically, issues of pattern formation are related to the structure of invasion waves or `fronts' between ecological states. When the structure is known, stability analyses of states behind the front or along the front determine how complexity is generated. A body of mathematical work has focussed on predicting the speed and shape of invasion waves in biological problems. Unfortunately, known techniques only address the invasion problem in systems of low dimensionality (one or two dependent variables), and do not lend themselves to general ecological application. Techniques to predict front propagation in systems of many variables are therefore at the center of the research. Front solutions, or waves of invasion, are the basis for stability analyses at invasion boundaries, which predict how curvature instabilities produce complexity at the invasion boundaries. Results of these mathematical efforts are used to understand complexity generation in the mountain pine beetle/pine system. Results from the mathematical model are compared with data on size, shape, and structure of known infestations. In short, the idea is to determine how much focussing, or clumping, of a species determines the natural formation of patterns in ecosystems. Aggregation, or clumping, of spec ies occurs naturally, and can be predicted mathematically. The researchers examine how this mechanism creates complexity in ecosystems, and study how to determine how much of ecological complexity is self-generating, as opposed to being generated by the complexity of the environment. The Mountain Pine Beetle/Lodgepole Pine ecosystem is studied because elements of the spatial pattern (attacked and killed trees) are distinctive and easy to measure. Moreover, understanding the predictable aspects of the course of pine beetle infestations is important to understanding the role this pest plays in western forests, including the relationship between beetle-killed pines and forest fire.

鲍威尔 研究人员和他的同事研究种群的空间动态，开发和分析模型，结合生物数据和调查的方式，人口的个人聚集和分散。 聚合通过反馈导致空间复杂性。 当个体用来聚集的线索依赖于个体的数量时，反馈是非线性的。 在一个允许流动的人口模型中，聚合反馈导致非线性的自我聚焦，即人口群体在小规模上的组织或“聚焦”。 空间相关性尺度的减小使得扩散格局更加复杂，从而导致复杂的空间结构。 从数学上讲，格局形成的问题与生态状态之间的入侵波或“前沿”的结构有关。 当结构是已知的，稳定性分析的状态后，前或沿着前线确定如何产生的复杂性。 大量的数学工作集中在预测生物问题中入侵波的速度和形状。 不幸的是，已知的技术仅解决了低维系统（一个或两个因变量）中的入侵问题，并且不适合于一般的生态应用。 因此，预测多变量系统中的前沿传播的技术是研究的中心。 前沿解或侵入波是侵入边界稳定性分析的基础，它预测曲率不稳定性如何在侵入边界产生复杂性。 这些数学努力的结果被用来了解复杂的一代山松甲虫/松树系统。 从数学模型的结果进行比较的大小，形状和已知的虫害结构的数据。 简而言之，这个想法是为了确定一个物种的集中或聚集程度决定了生态系统中模式的自然形成。 物质的聚集或聚集是自然发生的，并且可以通过数学方法预测。 研究人员研究了这种机制如何在生态系统中创造复杂性，并研究如何确定有多少生态复杂性是自我生成的，而不是由环境的复杂性生成的。 山松甲虫/Lodgepole松生态系统的研究，因为元素的空间格局（攻击和杀害树木）是独特的，易于测量。 此外，了解松树甲虫侵扰过程中可预测的方面对于了解这种害虫在西部森林中的作用非常重要，包括甲虫杀死的松树和森林火灾之间的关系。