Multiscale Multistage Ecological and Evolutionary Modeling with Applications to Social Insect Colonies

群居昆虫群落，如蜜蜂、蚂蚁、黄蜂，是在复杂的适应性社会中模拟组织挑战的优秀系统。社会昆虫生物学家面临的挑战是整合个体和群体水平的给定组织。本研究旨在发展和研究生态和进化模型，这些模型不仅充分整合了群体中不同层次的相互作用，而且还捕捉了社会群体内部动态的复杂性，以及它们的进化结果。该项目是应用数学和生命科学交叉领域跨学科研究和教育的理想载体。本研究中开发的方法和理论可以应用于生物学以外的许多领域，包括流行病学（例如正在进行的Covid-19大流行）、优化理论、免疫系统和机器人。该研究继续通过本科生和/或研究生的共享研究项目，为应用数学和生命科学的学生开发一个整合跨学科学习和教学的模板。该基金还将支持研究生在暑期学习应用数学。夏季研究项目为代表性不足的少数民族本科生提供第一手的研究经验。与本研究相关的讲座和简单项目将提供给参加亚利桑那州立大学科学与工程体验（SCENE）的高中二年级，三年级和四年级学生，其中SCENE为参与的高中生提供尖端的科学研究体验。亚利桑那州立大学应用数学和生物学的这项合作研究促进了理论-实验合作的文化，旨在开发新颖而复杂的建模方法，以理解社会动态过程和多层次选择之间的接口。这种跨学科合作将(a)跨生态尺度和阶段整合；(b)结合自然选择和进化效应；(c)纳入可直接测量的参数，包括代谢成本、能量流效率、个体质量和群体大小。新的分析技术和理论将被发展并添加到现有的动力学理论和进化博弈论中。提出的综合多尺度模型将解决行为生态学和社会生物学的中心主题，包括：1。社会群体如何平衡信息流的好处和病原体通过促进交流的相同机制传播的代价？2. 复杂社会群体的等级结构是如何形成的，相对于环境条件和约束的规模？3. 不同群体阶段的社会互动模式如何影响适合度？它们是如何通过选择形成的？严谨的数学将与广泛的野外和实验室数据相结合，以研究在个体和群体水平上具有多阶段结构的进化环境中的社会性昆虫社会的复杂适应系统。非线性、非自治微分方程以及空间随机过程，结合现有的经验数据，将被用于模拟不同生态尺度和阶段的生态和进化动力学。该奖项反映了美国国家科学基金会的法定使命，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。

Social insect colonies, such as bees, ants, wasps are excellent systems for which to model organizational challenges in complex adaptive societies. Social insect biologists face the challenge of integrating both the individual and colony levels of a given organization. This research aims to develop and study ecological and evolutionary models that not only adequately integrate the different levels of interaction in a colony but also capture the complexity of the internal dynamics within social groups, as well as their evolutionary outcomes. The project serves as an ideal vehicle for interdisciplinary research and education at the intersection of applied mathematics and life sciences. The methods and theories developed in this research may be applied to many domains outside of biology, including epidemiology (for example in the ongoing Covid-19 pandemic), optimization theory, the immune system and robotics. The research continues to develop a template integrating interdisciplinary learning and teaching for students from applied mathematics and life sciences through shared research projects at both the undergraduate and/or graduate levels. The funding will also support graduate students in applied mathematics during summer studies. Summer research projects provide underrepresented, minority undergraduate students with first-hand research experience. Lectures and simple projects related to this research will be given to high school sophomores, juniors and seniors who are participating in The SCience and ENgineering Experience (SCENE) at ASU where SCENE provides cutting-edge science research experience to the participating high school students. This collaborative research between Applied Mathematics and Biology at Arizona State University fosters a culture of theory-experiment collaboration which aims to develop novel and sophisticated modeling approaches to understand the interface between social dynamical processes and multilevel selections. This interdisciplinary collaboration will (a). integrate across ecological scales and stages; (b). incorporate selection and thus evolutionary effects; and (c). incorporate directly measurable parameters, including metabolic costs, efficiency of energy flow, individual mass and group size. The new analytical techniques and theories will be developed and added to current dynamical theory and evolutionary game theory. The proposed integrated multiscale models will address central themes in Behavior Ecology and Sociobiology, including: 1. How do social groups balance the benefits of information flow against the costs of pathogens that spread via the same mechanisms that foster communication? 2. How does hierarchy formation of complex social groups, scale relative to environmental conditions and constraints? 3. How do patterns of social interactions at different colony stages influence fitness and how are they shaped by selection? Rigorous mathematics will be integrated with extensive field and laboratory data to study complex adaptive systems of social insect societies in the evolutionary settings with multistage structures in both individual and colony levels. Nonlinear, non-autonomous differential equations as well as spatial stochastic processes, combined with available empirical data, will be used to model ecological and evolutionary dynamics at different ecological scales and stages.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.