  We show that the ratio of galaxies' specific star formation rates (SSFRs) to
their host halos' specific mass accretion rates (SMARs) strongly constrains how
the galaxies' stellar masses, specific star formation rates, and host halo
masses evolve over cosmic time. This evolutionary constraint provides a simple
way to probe z>8 galaxy populations without direct observations. Tests of the
method with galaxy properties at z=4 successfully reproduce the known evolution
of the stellar mass--halo mass (SMHM) relation, galaxy SSFRs, and the cosmic
star formation rate (CSFR) for 5<z<8. We then predict the continued evolution
of these properties for 8<z<15. In contrast to the non-evolution in the SMHM
relation at z<4, the median galaxy mass at fixed halo mass increases strongly
at z>4. We show that this result is closely linked to the flattening in galaxy
SSFRs at z>2 compared to halo specific mass accretion rates; we expect that
average galaxy SSFRs at fixed stellar mass will continue their mild evolution
to z~15. The expected CSFR shows no breaks or features at z>8.5; this
constrains both reionization and the possibility of a steep falloff in the CSFR
at z=9-10. Finally, we make predictions for stellar mass and luminosity
functions for the James Webb Space Telescope (JWST), which should be able to
observe one galaxy with M* > ~10^8 Msun per 10^3 Mpc^3 at z=9.6 and one such
galaxy per 10^4 Mpc^3 at z=15.
