Robust Theoretical Frameworks for Ecological Dynamics Subject to Stoichiometric Constraints

生物体是由碳、氢、氧、氮和磷等化学元素组成的。生态化学计量学（ES）领域的研究强调了化学成分相对丰度的生态重要性，已知化学成分在物种和营养水平之间存在很大差异。ES研究生态系统中能量和元素的平衡如何影响和被生物体影响，以及它们之间的相互作用。它已被证明是一个重要的新视角，通过它来观察和理解生态相互作用，并通过明确地将生物的基本生理与其食物网相互作用和生态系统功能联系起来而获得了动力。因此，ES理论涵盖了多个生物尺度，并允许通过严格的物理和化学约束，构建强大的机械和预测数学模型。虽然生物学的研究传统本质上是经验性的，通常只与正式的定量分析有微弱的联系，但另一方面，数学和理论生物学的研究议程往往与主流的经验生物学有一定的距离。在将实证结果与理论发现相结合方面没有足够的努力和关注。研究人员将扩展和推广现有的基于化学计量学的数学模型，以涵盖更广泛的生态情况，包括细胞配额动力学、消费者年龄或大小结构、可变消费者化学计量学和延迟营养循环。一旦建立了这样一个广义的理论框架，研究人员将根据ES中最近的经验发现来构建和评估模型，其中包括考虑食品营养含量不足和过量对消费者动态的影响的模型，以及考虑化学计量膳食混合的影响的模型。最后，研究人员将对这些参数化的化学计量模型进行定性和定量的挑战，以观察到的种群增长动态。在这样做的过程中，研究人员希望以新的理论应用的形式实现模型和实验之间的深远综合，这可能允许对化学计量限制对生态系统过程的影响进行直接和定量的预测。研究人员将研究的模型可能会在非线性微分方程和延迟微分方程的定性和计算研究领域激发具有挑战性但易于处理的问题。这个项目将对当地和全球环境产生广泛的影响。该项目的生物学发现可能在诸如富营养化、生物燃料生产、全球变化和生物多样性等问题上有许多实际应用。它的理论成果将提供一个坚实的和用户友好的框架，以建立数学模型，允许定量预测生态相互作用。此外，它将在癌症和其他宿主疾病动力学和治疗建模中找到许多现成的应用，因为人们可以将癌细胞和病原体视为宿主生态系统中的入侵物种。研究人员的合作努力将为不同民族/种族背景的本科生和研究生提供跨学科交流和探索的第一手教育经验。最后，研究人员正在与亚利桑那州立大学生命科学学院的获奖ask - a - biology项目合作，开发与该项目相关的文章和虚拟实验，以增强初高中学生对生物学和数学概念的学习。

Organisms are composed of chemical elements such as carbon, hydrogen, oxygen, nitrogen, and phosphorus. Research in the area known as ecological stoichiometry (ES) has highlighted the ecological importance of the relative abundance of chemical constituents, known to vary considerably among species and across trophic levels. ES deals with how the balance of energy and elements affect and are affected by organisms and their interactions in ecosystems. It has proven to be an important new lens through which to view and understand ecological interactions and has gained momentum by explicitly linking the elemental physiology of organisms to their food web interactions and ecosystem function. Thus, ES theory covers multiple biological scales and allows, via rigid physical and chemical constraints, the construction of robust mechanistic and predictive mathematical models. While biology has a research tradition that is empirical in nature and often only weakly connected to formal quantitative analyses, mathematical and theoretical biology on the other hand has had a research agenda that has often been somewhat distanced from mainstream empirical biology. There is not enough effort and attention on marrying empirical results with theoretical findings. The investigators will extend and generalize existing well-received stoichiometry-based mathematical models to encompass a broader range of ecological situations, including cell quota dynamics, consumer age- or size-structures, variable consumer stoichiometry, and delayed nutrient cycling. Once such a generalized theoretical framework is established, the investigators will construct and evaluate models inspired by recent empirical discoveries in ES, including one considering the effects on consumer dynamics of not only insufficient food nutrient content but also of excess food nutrient content, and another considering the effects of stoichiometric dietary mixing. Finally, the investigators will challenge these parameterized stoichiometric models against observed population growth dynamics qualitatively and quantitatively. In doing so, the investigators hope to achieve a far-reaching synthesis between model and experiment in the form of new theoretical applications that may allow for direct and quantitative predictions of the effects of stoichiometric constraints on ecosystem processes. The models the investigators will investigate may motivate challenging but tractable problems in areas of qualitative and computational studies of nonlinear differential equations and delay differential equations. This project will have a broad impact in both local and global environs. The biological findings of this project may have a number of practical applications to issues such as eutrophication, biofuel production, global change, and biodiversity. Its theoretical outcomes will provide a solid and user-friendly framework to build mathematical models that allow quantitative prediction of ecological interactions. Moreover, it will find many ready applications in cancer and other within host diseases dynamics and treatment modeling since one can view cancer cells and pathogens as invading species in a host ecosystem. The investigators' collaborative efforts will provide undergraduate and graduate students of diverse ethnic/racial backgrounds with first-hand educational experience in cross-disciplinary communication and exploration. Finally, the investigators are partnering with Arizona State University's School of Life Sciences award-winning Ask-A-Biologist program to develop articles and virtual experiments related to this project to enhance middle- and high school student learning of biological and mathematical concepts.