Connecting Empirical and Mathematical Approaches to Collective Behaviour

跨越尺度，生物聚集体形成引人注目的模式，通过自组织原则显示协调，内聚运动和功能，但群体层面的复杂性可能会模糊潜在的机制。要确定这种群体行为是如何产生和维持的，既需要对这些群体进行直接观察，也需要建立数学模型来检验假设的行为机制。我的研究项目就在这个界面上。我设计并实施从鸟类到人类的集体观察和实验研究。我开发算法来处理和分析这些数据，总结重要的相互作用统计标记，并提供跨物种和条件比较的测试。我开发、测试和模拟基于个体的微分方程模型，以评估个体相互作用如何解释观察到的群体层次结构的假设。通过通过经验数据告知这些模型的构建和验证，我将模型预测直接与自然现象联系起来。我使用这种经验-理论方法来研究现场的大群冲浪滑板，从重建的轨迹中推断出个体的相互作用规则。进一步的分析揭示了有序/无序转换的动力学，捕食避免模式和对环境的集体反应。我将把我的分析方法扩展到集体运动的新数据集。与澳大利亚悉尼的一位新合作者一起，我将在实地和实验室中分析一系列基于轨迹的鱼类数据集。这些数据集包括大堡礁雀鲷对风险的集体防御反应，鱼间熟悉度对食蚊鱼集体行为的影响，以及彩虹鱼家族的物种和环境如何塑造行为参数。实验室数据允许的控制程度将允许开发一种更新的逐步建模方法，从个体到成对，再到大型集体。在第二个主要方向上，我将通过听觉互动研究人类的集体行为。本研究在已经完成的试点工作的基础上，通过一个耦合振荡器建模框架，使用一个人类同步鼓掌的实验系统（2到数百人的群体）来研究什么类型的相互作用可以产生同步鼓掌，以及在实现同步后，顺序参数（群体频率、群体同步）是如何演变的。这项研究将人类感觉运动同步的工作从个人扩展到集体。此外，还将研究群体大小、节奏初始化和空间信息传递等影响。这些举措有助于我测量和解释有组织集体模式的总体研究目标。

Across scales, biological aggregates form striking patterns, display coordinated, cohesive motion, and function via principles of self-organization, yet complexity at the group level can obscure the underlying mechanisms. Determining how such group behaviour emerges and is sustained involves both direct observation of such groups, and mathematical models to test hypothetical behaviour regimes. My research program lies at this interface. I design and implement observational and experimental studies of collectives, from birds to humans. I develop algorithms to process and analyze these data, to summarize important statistical markers of interaction, and provide tests for comparison across species and condition. I develop, test, and simulate individual based differential-equation models to evaluate hypotheses of what individual interactions explain the observed group-level structure. By informing the construction and validation of these models via empirical data, I tie model predictions directly to the natural phenomena. I have used this empirical-theoretical approach to study large flocks of surf scoters in the field, to infer individual rules of interaction from reconstructed trajectories. Further analysis has revealed insights into the dynamics of order/disorder transitions, patterns of predation avoidance, and collective response to the environment.I will extend my analytical methods to new datasets of collective motion. With a new collaborator in Sydney, Australia, I will analyze a collection of trajectory-based datasets of fish, both in the field and in the lab. These datasets include the collective defensive response to risk in damselfish in the Great Barrier Reef, the effects of inter-fish familiarity on collective behaviour of mosquitofish, and how behavioural parameters are shaped by speciation and environment within the family of Rainbowfish. The degree of control permitted by the laboratory data will allow for the development of an updated, stepwise modelling approach from individuals, to pairs, up to large collectives.In the second main direction, I will study human collective behaviour via aural interactions. This research, based on pilot work already completed, uses an experimental system of humans clapping synchronously (groups of 2 to hundreds) to study what type of interactions allow synchronous clapping to arise, and how order parameters (group frequency, group synchrony) evolve after synchrony is achieved, via a coupled-oscillator modelling framework. This research extends work on human sensorimotor synchronization from the individual to the collective. Furthermore, effects such as group size, rhythmic initialization, and spatial information transfer will be studied.These initiatives contribute to my overall research goal of measuring, and explaining pattern in organized collectives.