Density-functional fluctuation theory of crowds

J Felipe Méndez-Valderrama,Jeffrey Silver,T A Arias,Yunus A Kinkhabwala,Itai Cohen

doi:10.1038/s41467-018-05750-z

Abstract

A primary goal of collective population behavior studies is to determine the rules governing crowd distributions in order to predict future behaviors in new environments. Current top-down modeling approaches describe, instead of predict, specific emergent behaviors, whereas bottom-up approaches must postulate, instead of directly determine, rules for individual behaviors. Here, we employ classical density functional theory (DFT) to quantify, directly from observations of local crowd density, the rules that predict mass behaviors under new circumstances. To demonstrate our theory-based, data-driven approach, we use a model crowd consisting of walking fruit flies and extract two functions that separately describe spatial and social preferences. The resulting theory accurately predicts experimental fly distributions in new environments and provides quantification of the crowd “mood”. Should this approach generalize beyond milling crowds, it may find powerful applications in fields ranging from spatial ecology and active matter to demography and economics.

Highlights

A primary goal of collective population behavior studies is to determine the rules governing crowd distributions in order to predict future behaviors in new environments
One of the central tenants of statistical physics is that generic thermodynamic behaviors emerge from underlying interaction rules among large numbers of particles[16,17]
Not because we are interested directly in individual behaviors, but rather because we are interested in the generic “macroscopic” behaviors that emerge in crowds en masse

Summary

Introduction

A primary goal of collective population behavior studies is to determine the rules governing crowd distributions in order to predict future behaviors in new environments. We introduce a general class of plausible agent-based models in which two different functions,“vexation” and “frustration,” quantify location and social preferences, respectively For this class of models, we develop a coarse-grained approach stemming from classical density-functional theory (DFT) that allows us to determine the general mathematical form of the probability distributions describing a crowd. We discuss the conditions a system must possess to be describable by our theory and test our approach using a living system consisting of walking fruit flies (Drosophila melanogaster), which we confine to a variety of two-dimensional environments For this fruit-fly system, we successfully extract the vexation and frustration functions corresponding to a variety of different physical settings. By exposing the fly system to conditions that elicit distinct social motivations, we are able to identify changes in the overall behavior of the crowd, i.e., its “mood,” by tracking the evolution of the social preference function

Methods

Results

Conclusion