Spreading Speeds and Non-Spreading Solutions for Spatial Population Models with Allee Effects

具有 Allee 效应的空间种群模型的传播速度和非传播解

基本信息

批准号：
1951482
负责人：
Bingtuan Li
金额：
$ 18万
依托单位：
University of Louisville Research Foundation Inc
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-05-01 至 2024-04-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1951482&HistoricalAwards=false
关键词：
Spreading Speeds Non Solutions Spatial

项目摘要

Spatial dynamics of populations remain poorly understood when compared to what is known about fluctuations in population size. For example, we have very limited understanding of how variability is maintained when populations spread across landscapes, why populations are often patchily distributed in space, and how phenology (the timing of biological events) influences these processes and patterns. The Allee threshold or critical size for population growth plays a particular role in spread of many populations. This project develops and analyzes mathematical models to investigate how a combination of an Allee effect and over-compensatory growth can produce oscillations in spreading speeds and robust non-spreading solutions across regions of parameter space, and to determine biologically when these outcomes should be expected. The project aims to extend these results to address important questions such as how "invasion models" can yield growth and persistence of a species in multiple, spatially separated patches within an unbounded habitat, and how phenology, stage-structure, and barrier zones affect spatially spreading systems. The findings of this research are expected to have direct, critical implications for controlling the spread of invasive species or promoting the reintroduction of native species into areas of extirpation. Graduate students will be trained through involvement in research at the interface of mathematics and biology. This project will advance our understanding of spatial population dynamics through rigorous efforts in four mathematical areas. These are: (i) analysis of integro-difference equations to characterize oscillations in spreading speeds and existence of non-spreading solutions; (ii) development and analysis of spatial models where Allee effects and over-compensation are generated by phenology and where dispersal is critical to population persistence; (iii) construction and examination of stage-structured models with an Allee effect; and (iv) creation and exploration of spatial models with an Allee effect and a stationary or moving barrier zone. For the models, the existence and stability of traveling wave solutions with constant and oscillating speeds will be established, and the links between the Allee effect and population dispersal will be explored. The minimal width of a barrier zone needed to stop, slow, or reverse a population invasion will be determined. Methods from differential equations, integral equations, and dynamical systems will be employed to identify conditions under which solutions spread into open space or stop invading. Applications of the models to biology will be addressed through studies of spread of species such as the gypsy moth.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

与人口大小的波动相比，人口的空间动力学仍然很糟糕。例如，我们对种群分布在景观中时保持可变性的理解非常有限，为什么人口通常在太空中分布，以及物候学（生物事件的时机）如何影响这些过程和模式。人口增长的Allee阈值或临界大小在许多人群的传播中起着特殊的作用。该项目开发和分析了数学模型，以调查合同效应和过度补偿生长的组合如何在跨参数空间区域之间产生扩散速度和强大的非扩展解决方案的振荡，并在预期的结果时确定生物学上的振荡。该项目旨在扩展这些结果，以解决重要的问题，例如“入侵模型”如何在无限栖息地内的多个，空间分离的斑块中产生一个物种的生长和持久性，以及物候学，舞台结构和障碍区如何影响空间扩散的系统。这项研究的发现预计将对控制入侵物种的传播或促进本地物种重新引入灭绝地区具有直接的，关键的影响。研究生将通过参与数学和生物学界面的研究而接受培训。该项目将通过四个数学领域的严格努力来提高我们对空间人口动态的理解。这些是：（i）分析整数差异方程，以表征传播速度和非膨胀解决方案的存在中的振荡；（ii）对空间模型的开发和分析，在物候学产生的效果和过度补偿的情况下，分散对人口持久性至关重要；（iii）建造和检查具有效果的舞台结构模型；（iv）创建和探索具有合同作用以及固定或移动屏障区的空间模型。对于模型，将建立恒定和振荡速度的行驶波解决方案的存在和稳定性，并将探索Allee效应与人口散布之间的联系。将确定停止，缓慢或扭转人口入侵所需的屏障区的最小宽度。将采用来自微分方程，积分方程和动态系统的方法来确定解决方案扩散到开放空间或停止入侵的条件。该模型在生物学上的应用将通过对吉普赛蛾等物种的扩散进行研究。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛影响的评估评估的评估来支持的。