  We analyse a sample of 24 damped Lyman-alpha (DLA)/moderate DLA systems at
0.3<z<2.2, all with measurement of the weak MnII absorption lines, to
investigate which elemental ratios could possibly be used as tracers of either
dust depletion or nucleosynthesis effects. We applied a component-by-component
analysis and show that the standard method which uses column densities
integrated over the whole absorption profiles could substantially underestimate
the abundance of rare elements relative to Fe. The apparent correlation we
found between [Mn/Fe] and [Zn/Fe] cannot be accounted for by any dust depletion
sequence: it implies either variations of the intrinsic Mn abundance relative
to Fe from -0.3 to +0.1 dex and/or a relation between depletion level and
metallicity. The correlation between [Mn/Fe] and metallicity strengthens the
assumption of intrinsic variations of [Mn/Fe] although some marginal
correlation between [Zn or Si/Fe] and [Zn/H] is present as well. The variations
of [Ti/Fe] vs. [Zn/Fe] cannot be fitted by a single dust depletion sequence
either. At high metallicity, [Fe/H]dc>~-0.5, the intrinsic (dust-corrected)
abundance pattern of Si, Ti, Cr and Mn in DLA absorbers closely follows the
trends observed in Galactic stars and these absorbers should thus have a
chemical evolution similar to that of our Galaxy. At lower metallicity, some
absorbers do follow the trends present in Galactic stars but a substantial
fraction of them have elemental ratios (in particular [Si/Fe]dc and [Mn/Fe]dc)
closer to the solar values than Galactic stars. This could be explained by a
larger contribution of type Ia supernovae to the chemical enrichment of these
DLA absorbers than in Galactic stars of similar metallicity. This metal-poor
DLA absorber population could trace HI-rich dwarf galaxies. (Abridged)
