REU Site: Mathematical Biology at the University of North Carolina at Greensboro

许多动物生活在其内部结构反映多种因素的种群中，例如，共同种之间的领土行为与物理环境的空间安排之间的相互作用，或在由支配地位或亲属关系建立的社会等级背景下表现出来的其他相互作用。该项目将为动物领地和社会互动的结构化模型开发一个统一的数学框架。使用进化图理论，学生研究人员将研究和分类在不同交互模式下在不同站点网络中移动和交互的有限种群的分布。在将要探讨的几个问题中，参与者将试图了解现有的种群结构对同类之间的攻击性水平的影响。本项目将为自然出现的动物种群和社会群体组织和划分为合作或对抗派别的方式提供理解。参与者将努力创建一个可概括的框架，该框架可以在生态学、进化论和行为科学等多个领域提供见解。作为跨学科互动的结果，许多STEM领域正在经历动态变化，该项目将培养一支多样化的新科学家队伍，能够跨越传统的学术和科学边界工作。这个REU网站项目训练本科生在数学和生物科学的交界处工作。每年，八名本科生将参加为期十周的暑期项目，并将被整合到由教职员工领导的研究团队中。参与者将接受相关数学技术和生物学概念的培训，他们将从事原创研究。这一REU经验将提高参与者的定量、分析和科学沟通技能，并为他们进入研究生院和科学职业生涯做好准备。

Many animals live in populations whose internal structure reflects multiple factors, for example, the interplay between territorial behavior between conspecifics and the spatial arrangement of the physical environment or other interactions demonstrated within the context of a social hierarchy established by dominance or kinship. This project will develop a unified mathematical framework for structured models of animal territoriality and social interactions. Using evolutionary graph theory, student researchers will study and classify the distribution of finite populations moving and interacting across a network of distinct sites under different models of interaction. Among several questions that will be explored, the participants will seek to understand the effect that the existing population structure has on the level of aggressiveness between conspecifics.This project will provide an understanding for the natural emergence of the ways in which animal populations and social groups organize and partition themselves into cooperative or antagonistic factions. The participants will endeavor to create a generalizable framework which could provide insight in multiple fields such as ecology, evolution, and the behavioral sciences. Many STEM fields are undergoing dynamic changes as a consequence of cross-disciplinary interactions, and this project will develop a diverse cadre of new scientists capable of working across traditional academic and scientific boundaries. This REU Site project trains undergraduate students to work at the interface of mathematics and the biological sciences. Each year, eight undergraduate students will participate in a ten week summer program and will be integrated into research teams lead by faculty members. The participants will be trained in pertinent mathematical techniques and biological concepts and they will engage in original research. This REU experience will improve participants' quantitative, analytical, and scientific communication skills and will prepare them for graduate school and scientific careers.