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.

生态学中的两个重大挑战是理解和准确描述物种的空间分布。这种空间扩散在各种生态环境中都很重要，例如当非本地物种入侵新的栖息地时，以及当物种因全球变化过程而改变其空间分布时。应对这些挑战需要种群模型来捕捉空间传播物种动态的基本方面，包括人口统计学和扩散。积分-差分方程组将被用来描述具有不同生长和扩散阶段的种群的扩散，其中生命率和扩散能力由年龄、大小或发育阶段决定。半离散模型(混合动力系统)，包括反应扩散方程和积分-微分方程，将被用来研究种群的扩散，其中不同的过程或不同的速率发生在一个物种的繁殖期内和之外。对于有传粉限制的植物种群，以及具有生殖异步性和不完全交配的两性种群，将建立具有Allee效应的模型。来自两个经过充分研究并与特定模型结构相匹配的实地系统的数据将被用来对关键模型组件进行参数化。研究人员将为模型检查传播速度和行波的存在，提供传播速度和行波速度的公式，并计算速度对人口统计和扩散参数变化的敏感度和弹性。从微分方程组、积分方程组和动力系统的方法将被用来研究模型的空间动力学。这项研究的结果也将对研究波传播的其他科学学科产生更广泛的影响。新的严格数学将与广泛的野外和实验室数据相结合，以弥合抽象数学结果和生态观测之间的鸿沟。为了进一步扩大这项研究的影响，研究人员还将开发一个与生态入侵动力学有关的MathBitch模块(.umd.edu)。这一模块将纳入由美国国家科学基金会资助的更大的MathBtch倡议，该倡议旨在提高本科生生物学学生的量化素养，并让他们更深入地了解数学在理解生物问题中的作用。通过在数学和生物学的界面上进行新的研究，该项目将有助于增加有关物种空间传播的信息量。对物种空间传播动态的研究对于理解资源管理者何时何地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，更好地了解空间扩散的动态对于预测物种对全球变化过程的反应也是至关重要的。在这个项目中，研究人员将开发和分析包含物种出生、生长、死亡和运动的数学模型，以确定物种中的点？对种群空间扩散速度至关重要的生命周期。将探索受花粉供应限制的植物物种和具有不完美交配发现的种群的模型，重点是了解特定种群过程对物种空间传播的速度和性质的影响。除了新的数学外，该项目还侧重于两个生态案例研究，将有助于指出自然资源管理的具体目标和机会。