Diversity of individual mobility patterns and emergence of aggregated scaling laws

TL;DR

This paper reveals that individual human mobility does not follow scaling laws, but aggregated displacement data follow a power law with an exponential cutoff, shaped by travel costs and the mixture of transportation modes.

Contribution

It analytically links the aggregated displacement distribution to travel costs and mode mixture, providing a theoretical explanation for observed scaling laws in human mobility.

Findings

Individual displacement distributions lack scaling properties.

Aggregated displacement follows a power law with exponential cutoff.

Travel cost constrains and shapes the aggregated mobility patterns.

Abstract

Uncovering human mobility patterns is of fundamental importance to the understanding of epidemic spreading, urban transportation and other socioeconomic dynamics embodying spatiality and human travel. According to the direct travel diaries of volunteers, we show the absence of scaling properties in the displacement distribution at the individual level,while the aggregated displacement distribution follows a power law with an exponential cutoff. Given the constraint on total travelling cost, this aggregated scaling law can be analytically predicted by the mixture nature of human travel under the principle of maximum entropy. A direct corollary of such theory is that the displacement distribution of a single mode of transportation should follow an exponential law, which also gets supportive evidences in known data. We thus conclude that the travelling cost shapes the displacement distribution at the aggregated level.