Redshift distribution of {\bf Ly-$\alpha$} lines and metal systems

The observed redshift distribution of Ly-$\alpha$ lines and metal systems is examined in order to discriminate and to trace the evolution of structure elements observed in the galaxy distribution, at small redshifts, and to test the theoretical description of structure evolution. We show that the expected evolution of filamentary component of structure describes quite well the redshift distribution of metal systems and stronger Ly-$\alpha$ lines with $\log(N_{HI})\geq$14, at $z\leq$ 3. The redshift distribution of weaker Ly-$\alpha$ lines can be attributed to the population of poorer structure elements (Zel'dovich pancakes), which were formed at high redshifts from the invisible DM and non luminous baryonic matter, and at lower redshifts they mainly merged and dispersed.