  Research institutions provide the infrastructure for scientific discovery,
yet their role in the production of knowledge is not well characterized. To
address this gap, we analyze interactions of researchers within and between
institutions from millions of scientific papers. Our analysis reveals that the
number of collaborations scales superlinearly with institution size, though at
different rates (heterogeneous densification). We also find that the number of
institutions scales with the number of researchers as a power law (Heaps' law)
and institution sizes approximate Zipf's law. These patterns can be reproduced
by a simple model with three mechanisms: (i) researchers collaborate with
friends-of-friends, (ii) new institutions trigger more potential institutions,
and (iii) researchers are preferentially hired by large institutions. This
model reveals an economy of scale in research: larger institutions grow faster
and amplify collaborations. Our work provides a new understanding of emergent
behavior in research institutions and how they facilitate innovation.
