Evidence for a Conserved Quantity in Human Mobility (1609.03526v3)

Abstract: Recent seminal works on human mobility have shown that individuals constantly exploit a small set of repeatedly visited locations. A concurrent literature has emphasized the explorative nature of human behavior, showing that the number of visited places grows steadily over time. How to reconcile these seemingly contradicting facts remains an open question. Here, we analyze high-resolution multi-year traces of $\sim$40,000 individuals from 4 datasets and show that this tension vanishes when the long-term evolution of mobility patterns is considered. We reveal that mobility patterns evolve significantly yet smoothly, and that the number of familiar locations an individual visits at any point is a conserved quantity with a typical size of $\sim$25 locations. We use this finding to improve state-of-the-art modeling of human mobility. Furthermore, shifting the attention from aggregated quantities to individual behavior, we show that the size of an individual's set of preferred locations correlates with the number of her social interactions. This result suggests a connection between the conserved quantity we identify, which as we show can not be understood purely on the basis of time constraints, and the `Dunbar number' describing a cognitive upper limit to an individual's number of social relations. We anticipate that our work will spark further research linking the study of Human Mobility and the Cognitive and Behavioral Sciences.

Analysis of Conserved Quantities in Human Mobility

The paper on the dynamics of human mobility presented in this paper challenges the prevailing views about the balance between exploration and exploitation in how individuals navigate their environments. Conducted on high-resolution, multi-year data gathered from approximately 40,000 individuals across four distinct datasets, the research aims to resolve the apparent contradiction between the stability of human mobility patterns and the explorative tendencies observed over time.

Key Findings and Methodology

This analysis utilizes datasets that span varied durations, capturing granular movements of individual subjects through GPS, GSM, Wi-Fi, and cell tower data. The comprehensive nature and longitudinal aspect of the data facilitate examination beyond the regular, predictable patterns of human movement, such as commuting between home and work. By including detailed social interaction data through phone calls, SMS, and Facebook interactions, the paper is able to link spatial behavior with social dynamics—a crucial element in unveiling the broader socio-behavioral implications.

Key Findings Include:

• Conserved Location Capacity: The investigation finds that despite dynamic movement patterns, the number of familiar locations visited regularly by individuals tends to stabilize around a specific value—approximately 25 locations. This conserved location capacity exists independently of temporal variations or the specific definition of these locations.
• Sub-linear Growth in Exploration: Individuals explore new locations at a sub-linear growth rate, which mirrors Heaps' law, suggesting that novelty discovery is more restrictive than previously assumed.
• Correlation Between Location and Social Network Size: A notable correlation is observed between the size of an individual's activity set and their social network size, hinting at a cognitive limit aligning with Dunbar’s Number—a theoretical cognitive ceiling for maintaining social connections.

Implications for Human Mobility Modeling

These findings carry significant implications for computational models predicting human movement. Existing models, such as the Exploration and Preferential Return (EPR) model, show limitations in accounting for the evolution of mobility over extended periods. The introduction of finite memory within these models stands out as a promising modification, capturing the empirical nuances of human mobility more accurately than the purely recency-based techniques.

The conserved quantity in the location capacity requires adjustments in these models to reflect both the fixed nature of individual space utilization and the continuous evolution observed in the data. This work encourages integrating cognitive constraints into mobility models, reshaping urban planning and epidemiological simulation frameworks which rely heavily on understanding population movement dynamics and social interaction patterns.

Future Directions and Speculations

The insights from this research make a case for deeper explorations into the cognitive and psychological factors influencing spatial behavior. Future studies may benefit from investigating not just the external socio-demographic factors but also innate cognitive aspects governing both spatial and social domain behaviors. Such holistic understanding will enhance multi-disciplinary applications, particularly in designing smart cities and managing public health emergencies.

The paper casts light on how inherent limits within human cognition translate into spatial behaviors, paving the path for enriched models that factor in the dynamic interplay between cognitive boundaries and technological interventions. Further exploration into these cognitive-social interactions could transform both theoretical frameworks and practical applications within the realms of urban studies, transportation, and social network analysis.