  We have extended our chemical and cosmological galaxy evolution model to
calculate the abundance evolution for altogether 16 different elements in
spiral galaxies in a chemically consistent way which is a considerable step
towards a more realistic galaxy modeling. Our models well reproduce observed
average HII region abundances in all spiral types. All observed element
abundances in DLA systems have been compiled. The conformity between observed
and calculated abundances over the redshift range from z=4.5 through z=0.4
indicates that DLA galaxies may well evolve into the full range of present- day
spiral galaxies from Sa through Sd.
  Comparison of our chemically consistent models with models using only solar
metallicity input physics shows that differences in the redshift evolution are
small for some elements but large for others. For those elements with large
differences the chemically consistent models provide significant better
agreement with observed DLA abundances.
  For typical spiral galaxies the star formation histories of our models
clearly bridge the gap between high redshift DLA systems and the nearby spiral
galaxy population. The slow redshift evolution of DLA abundances is understood
in terms of the long star formation timescales in galactic and proto-galactic
disks. Towards lower redshift z < 1.5 our models indicate that early type
spirals drop out of the DLA samples as their gas content falls below ~50%.
Implications for optical identification are discussed.
