SCIENCE sciencemag.orgPHOTO: MARCO MEGA/ALAMY STOCK PHOTO
By Nicholas T. OuelletteC
ollective behavior of social animals,
particularly coordinated group move-
ments, is one of the most striking
phenomena in the natural world, as
anyone who has been enthralled by
flocks of starlings or schools of sar-
dines can attest. Research in this broad, in-
terdisciplinary field has recently exploded,
with motivations ranging from understand-
ing the biological basis of social behavior
( 1 ) to developing algorithms for designing
and controlling swarms of robots ( 2 ). There
is good reason to think that the behavior
of human crowds is quite similar to these
animal groups and that studying humans
might help elucidate the origins of crowd
panic and other dangerous instabilities that
can lead to injury or loss of life ( 3 ). All these
goals require modeling, both as a check on
our understanding and as a predictive tool
for analyzing new situations. On p. 46 of this
issue, Bain and Bartolo ( 4 ) describe a pow-
erful new way to model human crowds. In-
stead of focusing on individuals, they builda continuum “hydrodynamic” model of the
crowd as a whole and then constrain it with
observational data collected from marathon
runners. This approach circumvents many
of the sometimes-questionable assumptions
that have previously been made and provides
a roadmap for constructing an empirically
grounded theory of collective behavior.
The dominant paradigm for describing
collective behavior is agent-based model-
ing. Each individual in a group is treated as
an “agent” that follows a set of rules to de-
termine its behavior. Most commonly, these
rules include instructions to not stray too
far from the group, to avoid collisions, and,
for directed motion, to move in the same
direction as nearby agents ( 5 ). Agent-based
models have succeeded in qualitatively re-
producing patterns observed in real animal
groups ( 1 ), providing strong evidence that lo-
cal interaction alone is sufficient to drive the
formation of group-level coherent behavior.
However, pattern isn’t everything, and just
because a model’s output qualitatively looks
acceptable does not mean that the model is
right. There is also reason to be skeptical of
this approach because it requires a priori as-
sumptions about animal behavior that are at
least oversimplified if not incorrect. In recentyears, researchers have attempted to con-
strain these assumed rules by measuring real
animal groups ( 6 – 9 ). However, this approach
is fraught. Data can be hard to come by for
many reasons—including, in the case of hu-
mans, substantial ethical considerations.
More fundamentally, extracting individual
interaction rules from observations of group
behavior is a complex, nonlinear inverse
problem, so drawing reliable conclusions in a
model-free way is often impossible.
Rather than thinking about a group as a
composite of individual agents with their
own rules, a group can instead be considered
as an entity itself. The properties of the group
certainly emerge from interactions between
the individuals, but to model these properties,
it is not necessary to know where they come
from. In this sense, collective behavior can
be treated analogously to how the mechan-
ics of materials are modeled. To describe how
water flows, one does not need to consider
molecular interactions; rather, one can apply
conservation laws for a macroscopic amount
of water and constrain them with empirical
observations (in the case of hydrodynamics, a
linear constitutive law that relates stress and
strain rate). Such an approach cannot cap-
ture the behavior of water molecules, but if
the goal is to formulate a predictive theory of
hydrodynamics, they are not necessary.
Bain and Bartolo have essentially followed
this approach for human crowds. They be-
gin with generic equations of motion for theCROWD DYNAMICSFlowing crowds
Modeling human crowds as a fluid allows
prediction of group behavior
Department of Civil and Environmental Engineering, Stanford
University, Stanford, CA 94305, USA. Email: [email protected]PERSPECTIVES
A human crowd supports a wave-like transmission
of information when the crowd is modeled as a single
entity rather than a composite of individuals.4 JANUARY 2019 • VOL 363 ISSUE 6422 27
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