eMB: Mathematical Classification of Complexity in Population Dynamics

eMB：人口动态复杂性的数学分类

• 批准号: 2325146
• 负责人: Yang Kuang
• 金额: $ 50万
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-09-01 至 2026-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2325146&HistoricalAwards=false
• 关键词: eMB; Mathematical; Classification; Complexity; Population

As Darwin famously observed, life is a struggle with various limiting resources constantly inhibiting its growth. With unlimited nutrients and space, a single E. coli cell can multiply into the size of planet Earth in two days. In reality, population growth is a complex nonlinear process influenced by environmental cues and constrained by numerous factors. All cell growth is dependent upon the availability of various essential nutrients and space. The complex dynamics of life is thus shaped by ubiquitous multiple resource limitation (MRL) from gene expression up to the global ecosystem level. Such dynamics may be described in the forms of nonlinear mathematical models based on laws of conservation that govern nutrient limitations. These models may embody rules of life that exhibit emerging systematic properties applicable to multiple temporal and spatial scales. Discovering such rules is the goal of this team of researchers. This project will generate a variety of biological and mathematical modeling resources for the scientific community. The project will produce uniquely trained graduate students and undergraduates with experiences in integrating studies across ecology, evolutionary biology, and applied mathematics fields. The research will further advance society's ability to predict, design and engineer controllable population dynamics in laboratory and natural settings. In addition, the project's intimate association of modeling with experimental work affords the scientific community an opportunity to develop both modeling and experimental approaches in synchrony to better understand the complexity observed in experiments.Motivated by and based on complex time series data sets from existing and ongoing experiments of flour beetle (Tribolium) populations, it is anticipated that this proposed work will address one specific and compelling question about how the MRL shapes the spatiotemporal organization of life. More specifically, the investigators seek to classify complex population dynamical patterns according to three main stages: 1) the transient and seemingly chaotic dynamics characteristic of the initial exponential growth stage that may be subject to influence by random factors to 2) the stable intermediate growth stage, and 3) final or asymptotical growth stage. It is expected that new hidden interactions will emerge between organisms and these stages due to competition for shared limiting resources, leading to complex and highly nonlinear properties that are rare under a single resource limitation concept but could lead to catastrophic problems in real-world ecosystems. Understanding the rules of behavior of these emergent properties consisting of the nutrient state of living individual, living systems, their environments and interactions will help the society to identify early-warning signals and formulate control strategies to address the issues of resilience and sustainability in evolving environments. The main objective of this proposal is to formulate a family of MRL population growth models, validate them via experimental data and understand their complex dynamics with the help of emergent mathematical theories.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.

正如达尔文（Darwin）著名地观察到的那样，生活是一场斗争，各种限制资源不断抑制其增长。有了无限的营养和空间，单个大肠杆菌细胞可以在两天内繁殖到地球的大小。实际上，人口增长是一个复杂的非线性过程，受环境线索的影响，受众多因素的限制。所有细胞生长都取决于各种必需营养物质和空间的可用性。因此，生命的复杂动力学是由从基因表达到全球生态系统层面的普遍多重资源限制（MRL）塑造的。这种动态可以基于控制营养限制的保护定律的非线性数学模型形式来描述。这些模型可能会体现出适用于多个时间和空间尺度的新兴系统特性的生命规则。发现这样的规则是该研究人员团队的目标。该项目将为科学界创造各种生物学和数学建模资源。该项目将在跨生态学，进化生物学和应用数学领域的研究中生产出唯一培训的研究生和本科生。这项研究将进一步提高社会在实验室和自然环境中预测，设计和设计可控制人群动态的能力。此外，该项目的建模与实验工作的紧密关联为科学界提供了一个机会，可以在同步中开发建模和实验方法，以更好地了解实验中观察到的复杂性。基于和基于复杂的时间序列数据集，来自现有和正在进行的实验的复杂时间序列数据集。时空生活组织。更具体地说，研究人员试图根据三个主要阶段对复杂的种群动力学模式进行分类：1）最初指数增长阶段的短暂和看似混乱的动力学特征，可能会受到随机因素的影响2）稳定中间生长阶段，以及3）最终或不良生长阶段。预计，由于共享限制资源的竞争，生物体和这些阶段之间的新隐藏相互作用将出现，从而导致复杂且高度非线性的特性在单个资源限制概念下很少见，但可能导致现实世界中的灾难性问题。了解这些新兴属性的行为规则，这些属性由生命个人，生活系统，它们的环境和互动的营养状态组成，将有助于社会确定早期的信号并制定控制策略，以解决在不断发展的环境中的弹性和可持续性问题。该提案的主要目的是建立MRL人口增长模型的家族，通过实验数据对其进行验证，并在新兴的数学理论的帮助下了解其复杂的动态。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的审查标准通过评估来通过评估来支持的。