Event-based spatiotemporal networks for modelling emergent phenomena in complex systems

Complex systems display emergent phenomena that vary significantly across spatial and temporal scales. These variations originate from fine-grained system processes, yet arriving at macroscopic dynamics from micro-level data — particularly when large, high-resolution datasets are available — remains a persistent challenge. Here we develop event-based spatiotemporal networks, a computational modelling framework that encodes system processes as discrete events anchored in space and time. Event-based spatiotemporal networks offer a unified, flexible and efficient approach to generate emergent behaviour in complex systems across space and time from these events. We demonstrate the effectiveness of event-based spatiotemporal networks through two illustrative real-world applications. First, following a local outbreak of a novel respiratory pathogen in the Netherlands, spatiotemporal networks enable fine-grained tracking of transmission routes, infection patterns, superspreaders and superspreading events through space and time. Second, we use spatiotemporal networks to model propagation of delays in a public transportation system (Sihltal-Zürich-Uetliberg-bahn) around Zürich, Switzerland. We also discuss broader uses of event-based spatiotemporal networks in fields like developmental biology and community ecology, where focusing on events rather than static system states can improve data analysis, simulation, and collection strategies. Emergent phenomena are a defining feature of complex systems, yet predicting their dynamics across space and time remains challenging. Here, the authors trace how individual events - where and when actors interact and carry out system processes - shape the spatiotemporal dynamics of emergent phenomena.