We study coagulation-fragmentation equations inspired by a simple model
proposed in fisheries science to explain data for the size distribution of
schools of pelagic fish. Although the equations lack detailed balance and admit
no $H$-theorem, we are able to develop a rather complete description of
equilibrium profiles and large-time behavior, based on recent developments in
complex function theory for Bernstein and Pick functions. In the
large-population continuum limit, a scaling-invariant regime is reached in
which all equilibria are determined by a single scaling profile. This universal
profile exhibits power-law behavior crossing over from exponent $-\frac23$ for
small size to $-\frac32$ for large size, with an exponential cut-off.