  Online communities, which have become an integral part of the day-to-day life
of people and organizations, exhibit much diversity in both size and activity
level; some communities grow to a massive scale and thrive, whereas others
remain small, and even wither. In spite of the important role of these
proliferating communities, there is limited empirical evidence that identifies
the dominant factors underlying their dynamics. Using data collected from seven
large online platforms, we observe a universal relationship between online
community size and its activity: First, three distinct activity regimes exist,
one of low-activity and two of high-activity. Further, we find a sharp activity
phase transition at a critical community size that marks the shift between the
first and the second regime. Essentially, it is around this critical size that
sustainable interactive communities emerge. Finally, above a higher
characteristic size, community activity reaches and remains at a constant and
high level to form the third regime. We propose that the sharp activity phase
transition and the regime structure stem from the branching property of online
interactions. Branching results in the emergence of multiplicative growth of
the interactions above certain community sizes.
