Patterns of interacting populations in heterogeneous environments

异质环境中群体相互作用的模式

• 批准号: 326416-2011
• 负责人: Lutscher, Frithjof
• 金额: $ 0.95万
• 依托单位: University of Ottawa
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=571836
• 关键词: Patterns; interacting; populations; heterogeneous; environments

The goal of my research program is to mechanistically understand the effects of temporal and spatial variation on the dynamics of interacting populations and to study the patterns emerging from this interplay. The approach is to derive a variety of mathematical models and to study their behavior using analytical and numerical methods. The models are dynamical systems, given by ordinary or partial differential equations, difference or integrodifference equations, or some combination thereof. The techniques include linear and non-linear analysis, homogenization, stability theory, traveling waves, and numerical analysis. The program consists of several interconnected research directions, strategic and tactical, that inform and benefit from one another. Strategic projects capture the essence of a certain mechanism or interaction and study the resulting patterns in general. These include the interplay of Hopf- and Turing-bifurcations in the diffusive Leslie-Gower-May model with spatial heterogeneity; simple food-web models in advective media; and traveling pulse solutions in integrodifference equations. Tactical models are specific to a particular situation and aim to understand a particular situation by connecting models and data. These include the dispersal behavior of the Emerald Ash borer and its impact on host trees; effects of dams and other migration barriers on fish in Southern Ontario streams; and effect of treatment on evolution of resistance in cancer. The research program offers a wide variety of excellent training opportunities for undergraduate and graduate students as well as for a postdoctoral fellow. Students learn mathematical analysis, numerical software packages, interdisciplinary collaboration, as well as communication and presentation skills.

我的研究计划的目标是机械地了解时间和空间变化对相互作用的种群动态的影响，并研究这种相互作用产生的模式。方法是推导出各种数学模型，并使用分析和数值方法研究它们的行为。这些模型是动力系统，由常微分方程式或偏微分方程式、差分方程式或积分差分方程式或它们的某种组合所给出。这些技术包括线性和非线性分析、齐次化、稳定性理论、行波和数值分析。该计划由几个相互关联的战略和战术研究方向组成，这些方向相互通报并从中受益。 战略项目捕捉特定机制或交互的本质，并研究总体上产生的模式。其中包括具有空间异质性的扩散Leslie-Gower-May模型中Hopf分支和Turing分支的相互作用；平流介质中的简单食物网模型；以及积分差分方程组中的行波脉冲解。 战术模型是特定于特定情况的，旨在通过连接模型和数据来了解特定情况。这些问题包括翡翠白蜡虫的扩散行为及其对寄主树木的影响；水坝和其他迁徙障碍对安大略省南部溪流中鱼类的影响；以及治疗对癌症耐药性演变的影响。 该研究计划为本科生和研究生以及博士后研究员提供了各种各样的极好的培训机会。学生学习数学分析、数值软件包、跨学科协作以及交流和演示技能。