Calculation Model for the Scale of Planning Urban Rail Transit Network Based on the Lotka–Volterra Model

There is a typical coopetition relationship between the urban rail transit (URT) network scale and the urban development (UD) level. A reasonable URT network scale is essential for promoting sustainable UD. Currently, the determination of the URT network scale for planning primarily relies on qualitative approaches such as static estimation and analogical methods, which fail to dynamically reflect the coopetition relationship between URT and UD. An improved time-varying parameter Lotka–Volterra (LV) model derived from ecological theory is employed to describe the coopetition relationship between the URT network scale and the UD level. The sliding-window least squares method is applied to estimate parameters of the model. Based on the improved LV model, the lower bound of the URT network scale is obtained by solving for the minimum network scale required to promote sustainable UD under a cooperative relationship; the upper bound of the URT network scale is obtained by solving for the maximum network scale that urban resources can support under competitive conditions. The proposed model is validated using eight Chinese cities with different UD levels. The study offers quantitative theoretical insights for determining the reasonable URT network scale for planning.