  We employ high-resolution dissipationless simulations of the concordance LCDM
cosmology to model the observed luminosity dependence and evolution of galaxy
clustering through most of the age of the universe, from z~5 to z~0. We use a
simple, non-parametric model which monotonically relates galaxy luminosities to
the maximum circular velocity of dark matter halos (V_max) by preserving the
observed galaxy luminosity function in order to match the halos in simulations
with observed galaxies. The novel feature of the model is the use of the
maximum circular velocity at the time of accretion, V_max,acc, for subhalos,
the halos located within virial regions of larger halos. We argue that for
subhalos in dissipationless simulations, V_max,acc reflects the luminosity and
stellar mass of the associated galaxies better than the circular velocity at
the epoch of observation, V_max,now. The simulations and our model L-V_max
relation predict the shape, amplitude, and luminosity dependence of the
two-point correlation function in excellent agreement with the observed galaxy
clustering in the SDSS data at z~0 and in the DEEP2 samples at z~1 over the
entire probed range of projected separations, 0.1<r_p/(Mpc/h)<10.0. In
particular, the small-scale upturn of the correlation function from the
power-law form in the SDSS and DEEP2 luminosity-selected samples is reproduced
very well. At z~3-5, our predictions also match the observed shape and
amplitude of the angular two-point correlation function of Lyman-break galaxies
(LBGs) on both large and small scales, including the small-scale upturn.
