  We examine the effects of magnitude, colour, and Ly-alpha equivalent width
(EW) on the spatial distribution of z~3 Lyman break galaxies (LBGs) and report
significant differences in their auto-correlation functions (ACFs). The results
are obtained using samples of ~10,000-57,000 LBGs from the Canada-France-Hawaii
Telescope Legacy Survey. We find that magnitude has a larger effect on the ACF
amplitude on small scales (<~1 Mpc) and that colour is more influential on
large scales (>~1 Mpc). We find the most significant differences between ACFs
for LBGs with dominant net Ly-alpha EW in absorption (aLBGs) and dominant net
Ly-alpha EW in emission (eLBGs) determined from >~95% pure samples of each
population using a photometric technique calibrated from ~1000 spectra. The
aLBG ACF one-halo term departs from a power law fit near ~1 Mpc, corresponding
to the virial radii of M_DM ~10^13 M_solar haloes, and shows a strong two-halo
term amplitude. In contrast, the eLBG ACF one-halo term departs at ~0.12 Mpc,
suggesting parent haloes of M_DM ~10^11 M_solar, and a two-halo term that
exhibits a `hump' on intermediate scales that we localize to the faintest,
bluest members. We find that the `hump' can be well fit with a model in which a
significant fraction of eLBGs reside on shells. The auto- and cross-correlation
functions indicate that aLBGs are found in massive, group-like haloes and that
eLBGs are found largely on group outskirts and in the field. Ly-alpha is a
tracer of several intrinsic LBG properties, including morphology, implying that
the mechanisms behind the morphology-density relation are in place at z~3 and
that Ly-alpha EW may be a key environment diagnostic. Finally, our results show
that the mass of LBGs has been underestimated because the LBG ACF amplitude is
lower than the true average as a result of the spatial anti-correlation of the
spectral sub-types (abridged).
