The Stability of Population Distribution in Moscow: Analysis Based on Mobile Operators' Data

This study investigates the spatial and temporal characteristics of population distribution in the city of Moscow, with a focus on the constancy of these dynamics over time, using high-frequency data from mobile network operators. The primary unit of analysis is a 500 × 500 meter grid cell covering the city's territory. The analysis spans the period from 2018 to 2020. The stability of population distribution is assessed along two dimensions: the spatial distribution of the permanent population and the interannual variation of daily population gradients across grid cells. The hypothesis of distributional constancy is tested through the construction of regression models, followed by a residual analysis using Geographic Information Systems (GIS). Spatial heterogeneities identified in the residuals are further examined. The findings indicate that, for a number of Moscow districts, the spatial population distribution closely follows a pattern consistent with the Zipf – Mandelbrot law, while other districts deviate significantly from this model. This pattern was further validated using Rosstat data for Moscow districts covering the years 2013–2022, confirming both the functional form and the classification of districts into two distinct groups. The first group primarily includes areas within Moscow's 2012 administrative boundaries and high-density zones in New Moscow, whereas the second group comprises the remaining, less densely populated areas. The proposed methodology demonstrates that the distribution of the permanent population across Moscow remained generally stable in both spatial and temporal terms over the study period. Conversely, the hypothesis of temporal constancy in daily population gradients is rejected, likely due to the influence of complex factors such as the evolving urban transportation infrastructure and cumulative measurement errors.