  It has been suggested for quite a long time that galaxy mergers trigger
activities of supermassive black holes (SMBHs) on the grounds of imaging
observations of individual galaxies. To quantitatively examine this hypothesis,
we calculate quasar luminosity functions (LFs) by manipulating the observed
galaxy LFs ($z\lesssim 2$) and theoretical merger rates from semi-analytical
formulations. We find that the model reproduces the observed quasar LFs
provided that the mass ratio ($q$) of the secondary galaxy to the newly formed
one changes with cosmic time. The results show that the fraction of major
mergers decreases from $f_{\rm maj}\sim 0.2$ at $z\sim 2$ to $f_{\rm maj}\to 0$
at $z\sim 0$. As a consequence, the newly formed SMBHs from major mergers at
$z\sim 2$ may acquire a maximal spin due to the orbital angular momentum of the
merging holes. Subsequently, random accretion led by minor mergers rapidly
drives the SMBHs to spin down. Such an evolutionary trend of the SMBH spins is
consistent with that radiative efficiency of accreting SMBHs strongly declines
with cosmic time, reported by Wang et al. (2009). This suggests that minor
mergers are important in triggering activities of SMBHs at low redshift while
major mergers may dominate at high redshift.
