Collaborative Research: RUI: Topological methods for analyzing shifting patterns and population collapse

合作研究：RUI：分析变化模式和人口崩溃的拓扑方法

• 批准号: 2327892
• 负责人: Laura Storch
• 金额: $ 16.94万
• 依托单位: Bates College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-02-01 至 2027-01-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2327892&HistoricalAwards=false
• 关键词: Collaborative; Research; RUI; Topological; methods

Profound and irreversible changes in ecosystems, such as population collapse, are occurring globally due to climate change, habitat destruction, and overuse of natural resources, and are only expected to become more frequent in the future. To prevent an impending collapse, we must recognize the early warning signs. This is particularly challenging in ecological systems due to their naturally complex behavior in both space and time, as well as noisy and/or poorly resolved data. In this project, the investigators will use a novel approach for early detection of impending population collapse, and apply the methodology to spatially distributed populations, for example, a grassland. They utilize a method called computational topology, which can quantify features of a population distribution pattern, such as the level of patchiness in the pattern. In previous work, the investigators used a spatial population model to quantify the changes in a population distribution pattern that occurred as the population went extinct and observed a "topological route to extinction". In this project, the investigators will develop and extend the methodology for use in stochastic population models and real-world data sets, which are expected to contain high levels of noise and/or missing/corrupted data. The developed methodology will serve as an additional tool for the prediction of impending population collapse. This tool can then be used by conservation biologists and natural resource managers in order to assist in preserving vulnerable species and ecosystems. The project also supports undergraduate research, and includes recruitment efforts directed at students from underrepresented groups.In previous work on data generated by a deterministic population model, the investigators measured changes in topological features (via cubical homology) of population distribution patterns en route to extinction, and observed clear topological signatures of impending collapse. Results with the deterministic model serve as a proof of concept, but in this project, the investigators will study dynamical changes in stochastic population models and real ecological data sets. Transitioning from deterministic to stochastic systems will require substantial development of the methodology, and will require the use of more sophisticated tools, e.g., multiparameter persistent homology. The developed methodology must be able to detect signal in noisy data, corrupted data, missing data, and data that is sparse in space and/or time. Because the topological approach can distinguish fine-scale stochastic noise from large-scale deterministic spatial patterns, it is a promising tool for the analysis of noisy ecological data, and preliminary work using multiparameter persistence shows that it is capable of recovering "true” dynamical signal (a population distribution pattern) from noise.This project is jointly funded by the Mathematical Biology program of the Division of Mathematical Sciences (DMS) in the Directorate for Mathematical and Physical Sciences (MPS), the Established Program to Stimulate Competitive Research (EPSCoR), and the Population and Community Ecology Cluster (PEC) of the Division of Environmental Biology (DEB) in the Directorate for Biological Sciences (BIO).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.

由于气候变化、栖息地破坏和自然资源的过度使用，生态系统正在发生深刻且不可逆转的变化，例如人口崩溃，并且预计未来只会变得更加频繁。为了防止即将发生的崩溃，我们必须认识到。由于生态系统在空间和时间上的自然复杂行为以及嘈杂和/或解析不佳的数据，这在生态系统中尤其具有挑战性。在这个项目中，研究人员将使用一种新颖的方法来早期检测。即将发生的人口崩溃，并应用该方法他们利用一种称为计算拓扑的方法来量化人口分布模式的特征，例如模式中的斑块程度。在之前的工作中，研究人员使用了空间人口模型。量化人口灭绝时发生的人口分布模式的变化，并观察到“灭绝的拓扑路线”。在这个项目中，研究人员将开发和扩展用于随机人口模型和现实世界数据集的方法。 ，预计其中含有高水平的所开发的方法将作为预测即将发生的人口崩溃的额外工具，然后可以由保护生物学家和自然资源管理者使用，以帮助保护脆弱的物种和生态系统。该项目还支持本科生研究，包括针对代表性不足群体的学生的招募工作。在之前对确定性种群模型生成的数据进行的研究中，研究人员测量了种群分布模式在走向灭绝过程中的拓扑特征（通过立方同源性）的变化，并观察到清晰的拓扑确定性模型的结果可以作为概念证明，但在这个项目中，研究人员将研究随机种群模型和真实生态数据集的动态变化，从确定性系统到随机系统的转变将需要大量的发展。方法，并且需要使用更复杂的工具，例如多参数持久同源性，所开发的方法必须能够检测噪声数据、损坏数据、丢失数据和空间稀疏数据中的信号。由于拓扑方法可以区分细尺度随机噪声和大规模确定性空间模式，因此它是分析噪声生态数据的有前途的工具，并且使用多参数持久性的初步工作表明它能够恢复。噪声中的“真实”动态信号（群体分布模式）。该项目由数学与物理科学理事会 (MPS) 数学科学部 (DMS) 的数学生物学项目联合资助，成立了刺激竞争性研究计划 (EPSCoR) 以及生物科学理事会 (BIO) 环境生物学部 (DEB) 的人口和社区生态集群 (PEC)。该奖项反映了 NSF 的法定使命，并被认为值得通过使用基金会的智力优势和更广泛的影响审查标准进行评估来提供支持。