Collaborative Research: RUI: Structured Population Dynamics Subject to Stoichiometric Constraints

随着人类活动继续改变环境平衡和营养循环，了解这些变化如何影响环境变得至关重要。生态过程依赖于碳、氮和磷等基本元素的流动和平衡。这些基本要素对青少年消费者的影响可能不同于成年消费者。这种特定年龄/阶段的影响影响人口动态，这表明需要年龄/阶段结构的数学模型来准确地捕捉和理解人口动态。几十年来，年龄/阶段结构种群模型的发展为理解生态系统的能量流动和种群动态做出了重要贡献。然而，当肥力和成熟度在养分循环和生态系统功能中发挥重要作用时，当前的模型就失效了。在这里，研究人员将设计和进行实验室实验，并开发数学模型，将年龄/阶段特定的营养限制纳入对生长、成熟时间和生殖的限制。这将导致生态学中新的理论应用的发展，研究不同的营养水平如何帮助塑造生态群落。该项目是德克萨斯理工大学、哈弗福德学院和加州州立大学北岭分校的合作项目，提供了宝贵的教育、培训和外展机会。具体来说，本科生和研究生将接受数学和生态学领域的跨学科培训和指导，以获得询问、回答和实现对科学问题的广泛理解的能力，这是跨学科有效交流所必需的。调查人员和学生将参与K-12外展活动。这个项目试图了解化学计量限制和种群动态的相互作用，特别是生物体阶段结构和生态系统功能如何相互影响。为此，研究人员将开发和分析一系列在生态化学计量学框架下构建的可经经验检验的稳健的种群动力学数学模型。生态化学计量学理论强调生态相互作用中各要素之间的平衡。将开发常微分方程组和延迟积分-微分方程组，以解决特定阶段的营养限制及其对成熟和生殖产量的影响等复杂问题。将使用动力系统理论和工具对模型进行解释和分析，包括分析、数值和分叉分析。模型和实验的综合将把结构种群数学建模领域与生态化学计量学理论结合起来。由此产生的理论框架和他们的发现将有助于阐明生态系统中基本约束和阶段结构之间的相互作用，并拓宽模型可以回答的生态问题的类型。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 human activities continue to alter environmental balances and nutrient cycles, it is becoming vital to understand how these changes can impact the environment. Ecological processes depend on the flow and balance of essential elements such as carbon, nitrogen, and phosphorus. These essential elements can affect juvenile consumers differently than adult consumers. Such age/stage-specific effects affect population dynamics, suggesting age/stage-structured mathematical models are needed to accurately capture and understand population dynamics. The development of age/stage-structured population models over the decades has significantly contributed to understanding energy flow and population dynamics of ecological systems. However, current models fail when fertility and maturation play important roles in nutrient recycling and ecosystem function. Here, investigators will design and conduct laboratory experiments in conjunction with developing mathematical models that incorporate age/stage-specific nutritional constraints on growth, time to maturation, and reproduction. This will result in the development of new theoretical applications in ecology that investigate how varying nutrient levels help shape ecological communities. The project is a collaboration between Texas Tech University, Haverford College, and California State University Northridge, and offers valuable educational, training, and outreach opportunities. Specifically, undergraduate and graduate students will receive interdisciplinary training and mentorship in the fields of mathematics and ecology to gain the ability to ask, answer, and achieve broad understandings of scientific problems, that is necessary to communicate effectively across disciplines. Investigators and students will be involved in K-12 outreach initiatives. This project seeks to understand the interactive effects of stoichiometric constraints and population dynamics, particularly, how organismal stage structures and ecosystem function influence each other. To this end, the investigators will develop and analyze a series of empirically testable and robust mathematical models of population dynamics structured under the framework of Ecological Stoichiometry. The theory of Ecological Stoichiometry emphasizes the balance of essential elements throughout ecological interactions. Compartmental systems of ordinary differential equations and delayed integro-differential equations will be developed to address complex questions about stage-specific nutritional constraints, and their consequences on maturation and reproductive output. Dynamical systems theory and tools will be used to interpret and analyze the models including analytical, numerical, as well as bifurcation analysis. The synthesis of the models and experiments will integrate the field of structured population mathematical modeling with the theory of Ecological Stoichiometry. The resulting theoretical frameworks and their findings will help shed light on the interplay between elemental constraints and stage-structures within ecological systems and broaden the types of ecological questions that models can answer.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.