eMB: Mathematical Classification of Complexity in Population Dynamics

正如达尔文的著名观察，生命是一场斗争，各种有限的资源不断地抑制着它的增长。有了无限的营养和空间，一个大肠杆菌细胞可以在两天内繁殖成地球的大小。现实中，人口增长是一个受环境因素影响、受多种因素制约的复杂的非线性过程。所有细胞的生长都依赖于各种必需营养物质和空间的供应。因此，从基因表达到全球生态系统层面，无处不在的多重资源限制(MRL)塑造了生命的复杂动态。这种动态可以用基于控制养分限制的守恒定律的非线性数学模型的形式来描述。这些模型可能体现了生命规律，展现了适用于多个时间和空间尺度的新出现的系统特性。发现这样的规律是这组研究人员的目标。该项目将为科学界产生各种生物和数学建模资源。该项目将培养出受过独特培训的研究生和本科生，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具有经验。这项研究将进一步提高社会在实验室和自然环境中预测、设计和设计可控人口动态的能力。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。受现有和正在进行的面粉甲虫(Tribolium)种群实验的复杂时间序列数据集的激励和基于，预计这项拟议的工作将解决一个具体而引人注目的问题，即MRL如何塑造生命的时空组织。更具体地说，研究人员试图将复杂的种群动态模式分为三个主要阶段：1)初始指数增长阶段的瞬时和看似混沌的动力学特征，可能受到随机因素的影响；2)稳定的中期增长阶段；3)最终或渐近增长阶段。由于对共享限制资源的竞争，预计生物体和这些阶段之间将出现新的隐藏相互作用，导致复杂和高度非线性的性质，这些性质在单一资源限制概念下是罕见的，但可能导致现实世界生态系统中的灾难性问题。了解这些新出现的特性的行为规则，包括生物个体、生命系统、它们的环境和相互作用的营养状态，将有助于社会识别早期预警信号，并制定控制策略，以解决不断演变的环境中的弹性和可持续性问题。这项建议的主要目标是制定一系列MRL人口增长模型，通过实验数据验证它们，并在新兴数学理论的帮助下了解它们的复杂动态。这一奖项反映了NSF的法定使命，并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，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.