  One key problem in astrophysics is understanding how and why galaxies switch
off their star formation, building the quiescent population that we observe in
the local Universe. From the GAMA and VIPERS surveys, we use spectroscopic
indices to select quiescent and candidate transition galaxies. We identify
potentially rapidly transitioning post-starburst galaxies, and slower
transitioning green-valley galaxies. Over the last 8 Gyrs the quiescent
population has grown more slowly in number density at high masses
(M$_*>10^{11}$M$_\odot$) than at intermediate masses
(M$_*>10^{10.6}$M$_\odot$). There is evolution in both the post-starburst and
green valley stellar mass functions, consistent with higher mass galaxies
quenching at earlier cosmic times. At intermediate masses
(M$_*>10^{10.6}$M$_\odot$) we find a green valley transition timescale of 2.6
Gyr. Alternatively, at $z\sim0.7$ the entire growth rate could be explained by
fast-quenching post-starburst galaxies, with a visibility timescale of 0.5 Gyr.
At lower redshift, the number density of post-starbursts is so low that an
unphysically short visibility window would be required for them to contribute
significantly to the quiescent population growth. The importance of the
fast-quenching route may rapidly diminish at $z<1$. However, at high masses
(M$_*>10^{11}$M$_\odot$), there is tension between the large number of
candidate transition galaxies compared to the slow growth of the quiescent
population. This could be resolved if not all high mass post-starburst and
green-valley galaxies are transitioning from star-forming to quiescent, for
example if they rejuvenate out of the quiescent population following the
accretion of gas and triggering of star formation, or if they fail to
completely quench their star formation.
