  We report on the results of a systematic search for associated asteroid
families for all active asteroids known to date. We find that 10 out of 12
main-belt comets (MBCs) and 5 out of 7 disrupted asteroids are linked with
known or candidate families, rates that have ~0.1% and ~6% probabilities,
respectively, of occurring by chance, given an overall family association rate
of 37% for asteroids in the inner solar system. We find previously unidentified
family associations between 238P/Read and the candidate Gorchakov family,
311P/PANSTARRS and the candidate Behrens family, 324P/La Sagra and the Alauda
family, 354P/LINEAR and the Baptistina family, P/2013 R3-B (Catalina-PANSTARRS)
and the Mandragora family, P/2015 X6 (PANSTARRS) and the Aeolia family, P/2016
G1 (PANSTARRS) and the Adeona family, and P/2016 J1-A/B (PANSTARRS) and the
Theobalda family. All MBCs with family associations belong to families that
contain asteroids with primitive taxonomic classifications and low average
reported albedos (pV_avg < 0.10), while disrupted asteroids with family
associations belong to families that contain asteroids that span wider ranges
of taxonomic types and average reported albedos (0.06 < pV_avg < 0.25). These
findings are consistent with MBC activity being closely correlated to
composition (i.e., whether an object is likely to contain ice), while disrupted
asteroid activity is not as sensitive to composition. Given our results, we
describe a sequence of processes by which the formation of young asteroid
families could lead to the production of present-day MBCs.
