  Data from the LIGO and Virgo detectors has confirmed that stellar-mass black
holes can merge within a Hubble time, leaving behind massive remnant black
holes. In some astrophysical environments such as globular clusters and AGN
disks, it may be possible for these remnants to take part in further
compact-object mergers, producing a population of hierarchically formed black
holes. In this work, we present a parameterized framework for describing the
population of binary black hole mergers, while self-consistently accounting for
hierarchical mergers. The framework casts black holes as particles in a box
which can collide based on an effective cross-section, but allows inputs from
more detailed astrophysical simulations. Our approach is relevant to any
population which is comprised of second or higher generation black holes, such
as primordial black holes or dense cluster environments. We describe some
possible inputs to this generic model and their effects on the black hole
merger populations, and use the model to perform Bayesian inference on the
catalog of black holes from LIGO and Virgo's first two observing runs. We find
that models with a high rate of hierarchical mergers are disfavored, consistent
with previous population analyses. Future gravitational-wave events will
further constrain the inputs to this generic hierarchical merger model,
enabling a deeper look into the formation environments of binary black holes.
