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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.

与对人口规模波动的了解相比，人们对人口的空间动态仍然知之甚少。例如，我们对当种群分布在不同景观中时如何保持变异性、为什么种群在空间中分布经常不均匀，以及物候（生物事件发生的时间）如何影响这些过程和模式等方面的了解非常有限。 Allee 阈值或人口增长的临界规模在许多人口的扩散中发挥着特殊作用。该项目开发并分析数学模型，以研究 Allee 效应和过度补偿性增长的组合如何在参数空间区域中产生传播速度振荡和稳健的非传播解决方案，并从生物学上确定何时应该预期这些结果。该项目旨在扩展这些结果以解决重要问题，例如“入侵模型”如何在无界栖息地内的多个空间分离斑块中产生物种的生长和持久性，以及物候、阶段结构和屏障区如何影响空间扩散系统。这项研究的结果预计将对控制入侵物种的传播或促进本土物种重新引入灭绝地区产生直接、关键的影响。研究生将通过参与数学和生物学交叉领域的研究来接受培训。该项目将通过四个数学领域的严格努力，增进我们对空间人口动态的理解。这些是： (i) 积分差分方程分析，以表征扩展速度的振荡和非扩展解的存在； (ii) 空间模型的开发和分析，其中 Allee 效应和过度补偿是由物候学产生的，并且扩散对于种群持续存在至关重要； (iii) 具有 Allee 效应的阶段结构模型的构建和检验； (iv) 创建和探索具有 Allee 效应和静止或移动障碍区的空间模型。对于模型，将建立具有恒定速度和振荡速度的行波解的存在性和稳定性，并探索阿利效应和种群扩散之间的联系。将确定阻止、减缓或扭转人口入侵所需的屏障区的最小宽度。将采用微分方程、积分方程和动力系统的方法来确定解扩散到开放空间或停止入侵的条件。这些模型在生物学中的应用将通过对吉普赛蛾等物种传播的研究来解决。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。