Mathematical modelling in ecology - A resource-based approach

生态学数学建模 - 基于资源的方法

• 批准号: 9358-2006
• 负责人: Wolkowicz, Gail
• 金额: $ 1.75万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=362517
• 关键词: Mathematical; modelling; ecology; resource; based

In my research I use a resource-based approach to study population dynamics.  In an attempt to better understand the structure of communities, and in particular, what factors promote or limit the diversity of natural ecosystems, I develop and analyze  mathematical models of  species interactions that make predictions that can be  tested in the laboratory. The goal is  to reconcile what were commonly   believed general principles, e.g., the  "Principle of Competitive Exclusion," that basically states that at most n species persist if competing for n niches (e.g., resources), with conflicting experimental observations e.g., the "Paradox of the Plankton," and hence  suggest new or modified principles. Whereas predation is generally considered to be one of the factors responsible for the diversity in natural ecosystems,  competition is usually thought of as limiting diversity.  However, in my research, I have found diverse examples of models that predict "Competitor-Mediated Coexistence" is possible, i.e. more species persist in the presence of a certain competitor than would persist if that competitor is eliminated. Whenever possible I try to do global analyses. Bifurcation theory helps one to determine the full spectrum of behaviour for all appropriate parameter ranges and initial states. It also identifies which key parameters need to be measured and how accurately, since only changes in their magnitude result in changes in the dynamics. Computer simulations are used to elucidate complicated dynamics, to test conjectures and to reveal properties of the models that are useful in developing analytic proofs. Symbolic computation is used for complicated calculations. Specialized software for obtaining bifurcation diagrams is especially useful when the attracting invariant sets are complicated and there are multiple attractors. The analyses often lead to interesting abstract mathematical problems in dynamical systems, ordinary, impulsive, integro- and functional differential equations, the qualitative theory of differential equations including bifurcation and stability theory.

在我的研究中，我使用基于资源的方法来研究种群动态。为了更好地了解群落的结构，特别是哪些因素促进或限制了自然生态系统的多样性，我开发和分析了各种物种相互作用的数学模型，这些模型做出了可以在实验室进行验证的预测。我们的目标是调和通常被认为是普遍接受的一般原则，例如，另一种名为“竞争排斥原则”的原则，该原则基本上规定，如果竞争n个利基(例如资源)，至多n个物种将持续存在，与相互冲突的实验观察结果(例如“浮游生物悖论”)相矛盾，因此可能会提出新的或修改后的原则。虽然捕食通常被认为是导致自然生态系统多样性的因素之一，但竞争通常被认为是限制多样性。然而，在我的研究中，我发现了各种模型的例子，这些模型预测了可能的“竞争者中介共存”，即更多的物种在某个竞争者的存在下坚持下来，而不是在那个竞争者被淘汰后继续存在。只要有可能，我都会尝试做全球分析。分叉理论有助于确定所有适当参数范围和初始状态的行为的全谱。它还确定了需要测量的关键参数以及测量的精确度，因为只有其大小的变化才会导致动力学的变化。计算机模拟被用来阐明复杂的动力学，检验猜想，并揭示模型的性质，这些性质对开发分析证明很有用。符号计算用于复杂的计算。当吸引不变集复杂且有多个吸引子时，获得分叉图的专用软件特别有用。这些分析往往导致有趣的抽象数学问题的动力系统，普通的，脉冲的，积分和泛函微分方程，微分方程的定性理论，包括分支和稳定性理论。