In this paper we study the very early phases of the evolution of our Galaxy by means of a chemical evolution model which reproduces most of the observational constraints in the solar vicinity and in the disk . We have restricted our analysis to the solar neighborhood and present the predicted abundances of several elements ( C , N , O , Mg , Si , S , Ca , Fe ) over an extended range of metallicities { [ Fe / H ] } = -4.0 to { [ Fe / H ] } = 0.0 compared to previous models . We adopted the most recent yield calculations for massive stars taken from different authors ( Woosley & Weaver 1995 and Thielemann et al . 1996 ) and compared the results with a very large sample of data , one of the largest ever used to this purpose . We have obtained this by selecting the most recent and higher quality abundance data from a number of sources and renormalizing them to the same solar abundances . These data have been analysed with a new and powerful statistical method which allows us to quantify the observational spread in measured elemental abundances and obtain a more meaningful comparison with the predictions from our chemical evolution model . Our analysis shows that the “ plateau ” observed for the [ \alpha /Fe ] ratios at low metallicities ( -3.0 < [ Fe / H ] < -1.0 ) is not perfectly constant but it shows a slope , especially for oxygen . This slope is very well reproduced by our model with both sets of yields . This is not surprising since realistic chemical evolution models , taking into account in detail stellar lifetimes , never predicted a completely flat plateau . This is due either to the fact that massive stars of different mass produce a slightly different O/Fe ratio or to the often forgotten fact that supernovae of type Ia , originating from white dwarfs , start appearing already at a galactic age of 30 million years and reach their maximum at 1 Gyr . For lower metallicities ( -4.0 < [ Fe / H ] < -3.0 ) the two sets of adopted yields differ , especially for iron . In this range the “ plateau ” is almost constant since at such low metallicities there is almost no contribution from type Ia supernovae . However , there are not enough data in this domain to significantly test this point . Finally , we show the evolution with redshift of the [ O/Fe ] ratio for different cosmologies and conclude that a sharp rise of this ratio should be observed at high redshift , irrespective of the adopted yields . The same behaviour is expected for the [ O/Zn ] ratio which should be easier to compare with the abundances observed in high redshift Damped Lyman- \alpha systems , as these elements are likely not to be affected by dust . Future measurements of either [ \alpha /Fe ] or [ \alpha /Zn ] ratios in very metal poor stars will be very useful to infer the nature and the age of high-redshift objects .