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.