Reconciling the observed star-forming sequence with the observed stellar
  mass function
  We examine the connection between the observed star-forming sequence (SFR
$\propto$ $M^{\alpha}$) and the observed evolution of the stellar mass function
between $0.2 < z < 2.5$. We find the star-forming sequence cannot have a slope
$\alpha$ $\lesssim$ 0.9 at all masses and redshifts, as this would result in a
much higher number density at $10 < \log(\mathrm{M/M_{\odot}}) < 11$ by $z=1$
than is observed. We show that a transition in the slope of the star-forming
sequence, such that $\alpha=1$ at $\log(\mathrm{M/M_{\odot}})<10.5$ and
$\alpha=0.7-0.13z$ ({Whitaker} {et~al.} 2012) at
$\log(\mathrm{M/M_{\odot}})>10.5$, greatly improves agreement with the
evolution of the stellar mass function. We then derive a star-forming sequence
which reproduces the evolution of the mass function by design. This
star-forming sequence is also well-described by a broken-power law, with a
shallow slope at high masses and a steep slope at low masses. At $z=2$, it is
offset by $\sim$0.3 dex from the observed star-forming sequence, consistent
with the mild disagreement between the cosmic SFR and recent observations of
the growth of the stellar mass density. It is unclear whether this problem
stems from errors in stellar mass estimates, errors in SFRs, or other effects.
We show that a mass-dependent slope is also seen in other self-consistent
models of galaxy evolution, including semi-analytical, hydrodynamical, and
abundance-matching models. As part of the analysis, we demonstrate that neither
mergers nor hidden low-mass quiescent galaxies are likely to reconcile the
evolution of the mass function and the star-forming sequence. These results are
supported by observations from {Whitaker} {et~al.} (2014).
