eMB: Mathematical Classification of Complexity in Population Dynamics

正如达尔文的著名观察，生命是一场与各种限制资源的斗争，这些资源不断地抑制着它的生长。有了无限的营养和空间，一个E。大肠杆菌细胞可以在两天内繁殖成地球大小。实际上，种群增长是一个受环境因素影响和众多因素制约的复杂的非线性过程。所有的细胞生长都依赖于各种必需营养素和空间的可用性。因此，从基因表达到全球生态系统水平，无处不在的多种资源限制（MRL）塑造了生命的复杂动态。这种动力学可以以非线性数学模型的形式来描述，这些模型基于管理营养限制的守恒定律。这些模型可能体现了生命的规则，表现出适用于多个时间和空间尺度的新兴系统属性。发现这样的规则是这个研究小组的目标。该项目将为科学界提供各种生物和数学建模资源。该项目将培养出受过独特训练的研究生和本科生，他们在整合生态学、进化生物学和应用数学领域的研究方面有经验。这项研究将进一步提高社会在实验室和自然环境中预测、设计和设计可控种群动态的能力。此外，该项目将建模与实验工作紧密联系在一起，为科学界提供了一个同步开发建模和实验方法的机会，以更好地理解实验中观察到的复杂性。（赤拟谷盗）种群，预计这项拟议的工作将解决一个具体的和令人信服的问题，如何MRL形状的时空组织的生活。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）可能受到随机因素影响的初始指数增长阶段的瞬态和看似混沌的动力学特征，2）稳定的中间增长阶段，以及3）最终或渐近增长阶段。预计由于对共享有限资源的竞争，生物体和这些阶段之间将出现新的隐藏相互作用，导致在单一资源限制概念下罕见的复杂和高度非线性特性，但可能导致现实世界生态系统中的灾难性问题。了解这些由生物个体、生物系统、其环境和相互作用的营养状态组成的新兴属性的行为规则，将有助于社会识别预警信号并制定控制策略，以解决不断变化的环境中的弹性和可持续性问题。该项目的主要目标是建立一系列MRL人口增长模型，通过实验数据验证这些模型，并借助新兴数学理论了解其复杂的动态。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.