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.

研究人员鲍威尔和他的同事们研究种群的空间动态，开发和分析纳入生物数据的模型，并调查种群个体聚集和分散的方式。聚合通过反馈导致空间复杂性。当个体用来聚集的线索取决于个体的数量时，反馈是非线性的。在允许流动的人口模型中，聚合反馈导致了非线性的自我聚焦，即人口群体在小范围内的组织或“聚焦”。空间相关性尺度的降低使扩散格局更加复杂，导致空间结构复杂化。从数学上讲，模式形成的问题与入侵波或生态状态之间的“锋面”的结构有关。当结构已知时，对前线后面或沿前线的状态的稳定性分析确定复杂性是如何产生的。一系列数学研究集中于预测生物学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)的入侵问题，并不适合一般的生态学应用。因此，预测多变量系统中锋面传播的技术是研究的中心。前沿解，或入侵波，是入侵边界稳定性分析的基础，它预测曲率不稳定性如何在入侵边界产生复杂性。这些数学努力的结果被用来理解山松甲虫/松树系统中复杂性的产生。将数学模型的结果与已知虫害的大小、形状和结构的数据进行比较。简而言之，这个想法是为了确定一个物种的聚集性或聚集性在多大程度上决定了生态系统中模式的自然形成。规格的聚集或聚集是自然发生的，并且可以从数学上预测。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产生的。之所以对山松甲虫/罗奇松生态系统进行研究，是因为空间格局的元素(被攻击和被杀死的树木)是独特的，并且易于测量。此外，了解松树甲虫侵袭过程的可预测方面对于了解这种害虫在西部森林中所起的作用非常重要，包括甲虫死亡的松树和森林火灾之间的关系。