Collaborative Research: Spatial Spread of Stage-Structured Populations

合作研究：阶段结构种群的空间扩散

• 批准号: 1225693
• 负责人: Bingtuan Li
• 金额: $ 25万
• 依托单位: University of Louisville Research Foundation Inc
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1225693&HistoricalAwards=false
• 关键词: Collaborative; Research; Spatial; Spread; Stage

Two significant challenges in ecology are to understand and accurately describe the spatial spread of species. Such spatial spread is important in a variety of ecological contexts, such as when non-native species invade new habitat and when species shift their spatial distributions in response to global change processes. Meeting these challenges requires population models that capture essential aspects of the dynamics of spatially spreading species, including demography and dispersal. Integro-difference equations will be used to describe the spread of populations with separate growth and dispersal stages wherein vital rates and dispersal abilities are determined by age, size, or developmental stage. Semi-discrete models (hybrid dynamical systems) involving reaction-diffusion equations and integro-differential equations will be employed to study the spread of populations in which different processes or different rates occur inside versus outside a species' reproductive period. Models with Allee effects will be developed for plant populations with pollination limitation, and for two-sex populations with reproductive asynchrony and imperfect mate-finding. Data from two well-studied field systems matching the structure of specific models will be used to parametrize key model components. The investigators will examine the existence of spreading speeds and traveling waves for the models, provide formulas for spreading speeds and traveling wave speeds, and calculate the sensitivity and elasticity of the speeds to changes in demographic and dispersal parameters. Methods from differential equations, integral equations, and dynamical systems will be used to investigate the spatial dynamics for the models. The outcomes of this research will also have broader impacts in other scientific disciplines where wave propagation is addressed. New rigorous mathematics will be integrated with extensive field and laboratory data to bridge the gulf between abstract mathematical results and ecological observations. To further broaden the impacts of this research, the investigators will also develop a MathBench module (.umd.edu) relating to ecological invasion dynamics. This module will feed into the larger, NSF-funded MathBench Initiative, which is designed to improve the quantitative literacy of undergraduate biology students and give them a deeper appreciation of the role of mathematics in understanding biological problems. Through new research at the interface of mathematics and biology, this project will contribute to the growing body of information on the spatial spread of species. Research on the dynamics of species spatial spread is essential to understanding when and where resource managers can act to limit the spread and impacts of non-native, invasive species. Likewise, better understanding of the dynamics of spatial spread is essential for forecasting species responses to global change processes. In this project the investigators will develop and analyze mathematical models incorporating species birth, growth, death, and movement to identify points in species? life-cycles that are critical to the rates of population spatial spread. Models for plant species limited by pollen supply and for populations featuring imperfect mate finding will be explored, with a focus on understanding the effects that particular population processes have on the rate and nature of species spatial spread. By focusing on two ecological case-studies in addition to novel mathematics, this project will help to point out specific targets and opportunities for natural resources management.

生态学上的两个重大挑战是了解并准确描述物种的空间传播。这种空间扩散在多种生态环境中很重要，例如当非本地物种入侵新栖息地以及物种以响应全球变化过程而移动其空间分布时。应对这些挑战需要人口模型，以捕捉空间传播物种动态的基本方面，包括人口统计学和分散。整数差异方程将用于描述人口的传播，并具有单独的增长和分散阶段，其中重要率和分散能力取决于年龄，大小或发育阶段。将采用涉及反应扩散方程和全差异方程的半混凝土模型（混合动力学系统）来研究种群的传播，在这种种群中，不同过程或不同的速率发生在物种的生殖时期。具有授粉限制的植物种群以及具有生殖性异步和不完美伴侣的两性种群的植物种群将开发具有合同作用的模型。来自两个符合特定模型结构的两个经过良好研究的现场系统的数据将用于参数化关键模型组件。研究人员将检查模型的扩展速度和行进波的存在，为扩张速度和行驶波速度提供公式，并计算速度对人口统计学和分散参数变化的敏感性和弹性。来自微分方程，积分方程和动力学系统的方法将用于研究模型的空间动力学。这项研究的结果还将在解决波传播的其他科学学科中产生更广泛的影响。新的严格数学将与广泛的领域和实验室数据集成，以弥合抽象数学结果和生态观察之间的海湾。为了进一步扩大这项研究的影响，研究人员还将开发与生态入侵动态有关的数学模块（.umd.edu）。该模块将融入由NSF资助的更大的数学培养基中，该计划旨在提高本科生物学学生的定量素养，并使他们对数学在理解生物学问题中的作用更深入地了解。通过在数学和生物学的界面上进行的新研究，该项目将有助于不断增长的有关物种空间传播的信息体系。对物种空间扩散动态的研究对于理解资源经理可以采取行动限制非本地，入侵物种的传播和影响至关重要。同样，更好地理解空间扩散的动力学对于预测物种对全球变化过程的反应至关重要。在这个项目中，研究人员将开发和分析结合物种出生，生长，死亡和运动以识别物种中观点的数学模型？生命周期对于人口空间扩散率至关重要。将探索受花粉供应限制的植物物种的模型和以不完美伴侣发现为特征的种群，重点是了解特定种群过程对物种空间扩散率和性质的影响。除了新的数学外，还要专注于两个生态案例研究，该项目将有助于指出自然资源管理的特定目标和机会。