  The second LIGO-Virgo catalog of gravitational wave transients has more than
quadrupled the observational sample of binary black holes. We analyze this
catalog using a suite of five state-of-the-art binary black hole population
models covering a range of isolated and dynamical formation channels and infer
branching fractions between channels as well as constraints on uncertain
physical processes that impact the observational properties of mergers. Given
our set of formation models, we find significant differences between the
branching fractions of the underlying and detectable populations, and that the
diversity of detections suggests that multiple formation channels are at play.
A mixture of channels is strongly preferred over any single channel dominating
the detected population: an individual channel does not contribute to more than
$\simeq 70\%$ of the observational sample of binary black holes. We calculate
the preference between the natal spin assumptions and common envelope
efficiencies in our models, favoring natal spins of isolated black holes of
$\lesssim 0.1$, and marginally preferring common envelope efficiencies of
$\gtrsim 2.0$ while strongly disfavoring highly inefficient common envelopes.
We show that it is essential to consider multiple channels when interpreting
gravitational wave catalogs, as inference on branching fractions and physical
prescriptions becomes biased when contributing formation scenarios are not
considered or incorrect physical prescriptions are assumed. Although our
quantitative results can be affected by uncertain assumptions in model
predictions, our methodology is capable of including models with updated
theoretical considerations and additional formation channels.
