Coordinated development between metropolitan areas and regional express rail: an empirical study in Paris and Tokyo

Regional express rail can reshape metropolitan spatial structure by changing core–suburb accessibility and travel costs. Measuring the long-term co-evolution of rail and metropolitan systems, and the drivers of stage transitions, is crucial for TOD planning decisions. Using multi-source data for Paris (1937–2020) and Tokyo (1920–2020), we employ synergetics to model a composite system with a regional express rail subsystem and a metropolitan subsystem. We compute subsystem order and overall synergy, identify coordination stages, and compare them with historical periodization. Order parameters are measurable variables that drive changes in order and synergy. Candidates are derived from mechanism hypotheses and prior studies, and validated by correlation thresholds, robustness across model specifications, and cross-period consistency. Both cases show three coordination stages, but with different transition timing and drivers. In Paris, synergy increases mainly with network structure and connectivity, supported by social variables. Tokyo reaches high coordination earlier and remains more stable, driven by network structure and transport capacity together with social and economic variables. Ecological variables also contribute, but early data gaps limit their estimated effects. This study provides quantitative evidence for integrated regional express rail networks and spatial development decisions in metropolitan regions across countries.