  We study the enrichment histories for nine elements, C, four alpha-elements
of Mg, Si, Ca, and Ti, Sc, and three iron-peak elements of Co, Ni, and Zn, by
using a large number of stellar data, collected by the Stellar Abundances for
Galactic Archaeology (SAGA) database. We find statistically significant
changes, or breaks, of the mean abundance ratios to iron at three metallicities
of [Fe/H]-1.8, -2.2, and -3.3. Across the first one, the mean abundance ratios
decrease with the metallicity by similar extents for all the elements with the
sufficient data. Across the latter two, downward trends with the metallicity
are also detected but for limited elements, C, Co, Zn, and possibly Sc, and for
two of Co and Zn, respectively. The breaks define four stellar populations with
the different abundance patters which are dominant in each metallicity range
divided by the breaks, Pop IIa, IIb, IIc, and IId in order of increasing
metallicity. We also explore their spatial distributions with the spectroscopic
distances to demonstrate that Pops IIa and IIb spread over the Galactic halo
while Pops IIc and IId are observed near the Galactic plane. In particular, Pop
IIc stars emerge around [Fe/H] -2.6 and coexist with Pop IIb stars, segregated
by the spatial distributions. Our results reveal two distinct modes of star
formation during the early stages of Galaxy formation, which are associated
with the variations of IMF and the spatial distribution of remnant low-mass
stars. For the two lower-metallicity populations, the enhancements of Zn and Co
indicate a high-mass and top-heavy IMF together with the statistics on the
carbon-enhanced stars. We discuss the relevance to the kinematically resolved
structures of the Galactic halo and the possible sites of these populations
within the framework of hierarchical structure formation scenario.
