Collaborative Research: Population Dynamics in Random Environments: Theory and Approximation

合作研究：随机环境中的种群动态：理论与近似

• 批准号: 1853467
• 负责人: Hai Dang Nguyen
• 金额: $ 10.5万
• 依托单位: University of Alabama Tuscaloosa
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-07-01 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1853467&HistoricalAwards=false
• 关键词: Collaborative; Research; Population; Dynamics; Random

This project will formulate and analyze a general mathematical framework to facilitate understanding the persistence and extinction of species affected by random environmental fluctuations. Global climate change models predict increasing temporal variability in temperature, precipitation and storms in the next century. Random environmental fluctuations have been shown to drive populations extinct, promote persistence, change genetic diversity, and modify the spread of infectious diseases. It is therefore urgent to develop tools for understanding the effects of random temporal fluctuations in environmental conditions on species. The PIs will develop mathematical theory, in conjunction with analytical and numerical approximation methods, to help theoretical ecologists pinpoint how environmental fluctuations affect the long-term dynamics of ecological communities. In collaboration with the Gore lab at Massachusetts Institute of Technology the PIs will test theoretical results by comparison with microbial ecology experiments. The investigators plan to involve high school and undergraduate students in projects allowing them to develop programming skills and diversify their mathematical and ecological knowledge. For outreach, the investigatprs will organize seminars and conferences and promote the participation of women and members of traditionally underrepresented minorities within the sciences.The PIs will investigate continuous and discrete time models of interacting populations that experience random temporal environmental variations. In the continuous time setting the research will focus on Piecewise Deterministic Markov Processes - processes that switch between different systems of ordinary differential equations at random times. In the discrete time setting stochastic difference equations will be analyzed. New methods for checking when species persist and converge to their invariant probability measures (which describe the 'random equilibria' of subcommunities of species) will be developed, and conditions under which species go extinct exponentially fast determined. Since all theoretical models are merely approximations of natural systems, the PIs will study how the persistence/extinction results change under small, density-dependent, perturbations of the model parameters. The extinction/persistence criteria will involve Lyapunov exponents, which usually cannot be computed explicitly. In order to resolve this issue analytical and numerical approximation methods for estimating the Lyapunov exponents will be developed. Finally, together with the Gore lab at Massachusetts Institute of Technology, the PIs will run experiments in order to see how analytical results qualitatively compare with multi-species microbial systems under environmental fluctuations. This project is jointly funded by the Division of Mathematical Sciences Mathematical Biology Program the Established Program to Stimulate Competitive Research (EPSCoR).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.

该项目将制定和分析一个通用数学框架，以帮助理解受随机环境波动影响的物种的持续存在和灭绝。全球气候变化模型预测下个世纪温度、降水和风暴的时间变化将增加。随机环境波动已被证明会导致种群灭绝、促进持久性、改变遗传多样性并改变传染病的传播。因此，迫切需要开发工具来了解环境条件随机时间波动对物种的影响。 PI 将开发数学理论，结合分析和数值近似方法，帮助理论生态学家查明环境波动如何影响生态群落的长期动态。 PI 将与麻省理工学院戈尔实验室合作，通过与微生物生态学实验进行比较来测试理论结果。研究人员计划让高中生和本科生参与项目，使他们能够发展编程技能并使他们的数学和生态知识多样化。为了进行推广，研究人员将组织研讨会和会议，并促进妇女和传统上代表性不足的少数群体成员在科学领域的参与。研究人员将研究经历随机时间环境变化的相互作用人群的连续和离散时间模型。在连续时间设置中，研究将集中于分段确定性马尔可夫过程 - 随机时间在不同常微分方程组之间切换的过程。在离散时间设置中，将分析随机差分方程。将开发用于检查物种何时持续存在并收敛于其不变概率测量（描述物种子群落的“随机平衡”）的新方法，并快速确定物种灭绝的条件。 由于所有理论模型都只是自然系统的近似值，PI 将研究在模型参数受到较小的、依赖于密度的扰动下，持久性/灭绝结果如何变化。灭绝/持续标准将涉及李亚普诺夫指数，通常无法明确计算。为了解决这个问题，将开发用于估计李亚普诺夫指数的分析和数值近似方法。最后，PI 将与麻省理工学院的戈尔实验室一起进行实验，以了解分析结果如何与环境波动下的多物种微生物系统进行定性比较。该项目由数学科学部数学生物学计划和刺激竞争性研究既定计划 (EPSCoR) 联合资助。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。

项目成果

General nonlinear stochastic systems motivated by chemostat models: Complete characterization of long-time behavior, optimal controls, and applications to wastewater treatment

• DOI: 10.1016/j.spa.2020.01.010
• 发表时间: 2020-08-01
• 期刊: STOCHASTIC PROCESSES AND THEIR APPLICATIONS
• 影响因子: 1.4
• 作者: Nguyen, Dang H.;Nguyen, Nhu N.;Yin, George
• 通讯作者: Yin, George

Dynamics of a vector-host model under switching environments

• DOI: 10.3934/dcdsb.2021029
• 发表时间: 2021
• 期刊: Discrete & Continuous Dynamical Systems - B
• 作者: Harrison Watts;Arti Mishra;D. Nguyen;T. D. Tuong

A classification of the dynamics of three-dimensional stochastic ecological systems

三维随机生态系统动力学的分类

• DOI: 10.1214/21-aap1699
• 发表时间: 2022
• 期刊: The Annals of Applied Probability
• 作者: Hening, Alexandru;Nguyen, Dang H.;Schreiber, Sebastian J.
• 通讯作者: Schreiber, Sebastian J.

A general theory of coexistence and extinction for stochastic ecological communities

随机生态群落共存与灭绝的一般理论

• DOI: 10.1007/s00285-021-01606-1
• 发表时间: 2021
• 期刊: Journal of Mathematical Biology
• 影响因子: 1.9
• 作者: Hening, Alexandru;Nguyen, Dang H.;Chesson, Peter
• 通讯作者: Chesson, Peter

Stability in distribution and stabilization of switching jump diffusions

• DOI: 10.1051/cocv/2022062
• 发表时间: 2022-09
• 期刊: ESAIM: Control, Optimisation and Calculus of Variations
• 作者: K. Tran;D. Nguyen;G. Yin