  We analyze star formation (SF) as a function of stellar mass (M*) and
redshift z in the All Wavelength Extended Groth Strip International Survey
(AEGIS). For 2905 field galaxies, complete to 10^10(10^10.8) Msun at z<0.7(1),
with Keck spectroscopic redshifts out to z=1.1, we compile SF rates (SFR) from
emission lines, GALEX, and Spitzer MIPS 24 micron photometry, optical-NIR M*
measurements, and HST morphologies. Galaxies with reliable signs of SF form a
distinct "main sequence (MS)", with a limited range of SFR at a given M* and z
(1 sigma < +-0.3 dex), and log(SFR) approximately proportional to log(M*). The
range of log(SFR) remains constant to z>1, while the MS as a whole moves to
higher SFR as z increases. The range of SFR along the MS constrains the
amplitude of episodic variations of SF, and the effect of mergers on SFR.
Typical galaxies spend ~67(95)% of their lifetime since z=1 within a factor of
<~ 2(4) of their average SFR at a given M* and z. The dominant mode of the
evolution of SF since z~1 is apparently a gradual decline of the average SFR in
most individual galaxies, not a decreasing frequency of starburst episodes, or
a decreasing factor by which SFR are enhanced in starbursts. LIRGs at z~1 seem
to mostly reflect the high SFR typical for massive galaxies at that epoch. The
smooth MS may reflect that the same set of few physical processes governs star
formation prior to additional quenching processes. A gradual process like gas
exhaustion may play a dominant role.
