The origin of heavy tails in honeybee and human interaction times
Burstiness
of an inter-event time distribution has been much studied because of
its relation to information or disease spreading. On the other hand,
the distribution of contact duration has received less attention. We
measured the duration of honeybee trophallaxis, or mouth-to-mouth
liquid food transfer, and face-to-face encounters by using
high-resolution tracking in collaboration with Robinson Lab
in the University of Illinois and found out that the distribution of
event durations is heavy-tailed. Human data recorded by the
SocioPatterns
collaboration show that human face-to-face interactions in
various settings also exhibit a heavy-tailed interaction time
distribution. Such similarity across different systems suggests
unexpected universality in social interactions. We have derived the
power-law form by building a minimal model that treats the termination
of an interaction as a particle escaping over an energy barrier; the
variability in the population leads to a distribution of energy
barriers which is determined by the extreme value theory and is a key
to achieving the final power-law form. Honeybees indeed exhibit
individual differences in interactivity although they are less
different than humans. Our work demonstrates how individual differences
can lead to universal patterns of social interaction that transcend
species, context and specific mechanisms.