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 can not 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 - 0.13 z ( 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 ) .