  Research teams are the fundamental social unit of science, and yet there is
currently no model that describes their basic property: size. In most fields
teams have grown significantly in recent decades. We show that this is partly
due to the change in the character of team-size distribution. We explain these
changes with a comprehensive yet straightforward model of how teams of
different sizes emerge and grow. This model accurately reproduces the evolution
of empirical team-size distribution over the period of 50 years. The modeling
reveals that there are two modes of knowledge production. The first and more
fundamental mode employs relatively small, core teams. Core teams form by a
Poisson process and produce a Poisson distribution of team sizes in which
larger teams are exceedingly rare. The second mode employs extended teams,
which started as core teams, but subsequently accumulated new members
proportional to the past productivity of their members. Given time, this mode
gives rise to a power-law tail of large teams (10-1000 members), which features
in many fields today. Based on this model we construct an analytical functional
form that allows the contribution of different modes of authorship to be
determined directly from the data and is applicable to any field. The model
also offers a solid foundation for studying other social aspects of science,
such as productivity and collaboration.
