 Solution

Hydrogen is the most abundant element, and its Lyman-alpha line is a strong resonance from the ground state. Very small neutral fractions in an otherwise ionized intergalactic medium therefore produce detectable Lyman-alpha absorption. A long quasar sightline samples a great many modest density enhancements in the cosmic gas, with a much larger covering area than the compact high-column regions that produce damped Lyman-alpha systems.

Heavy-element absorption additionally requires metal enrichment and enough ions in the relevant ionization state. Many weak Lyman-alpha forest absorbers contain too few such ions to produce detectable metal lines at the same sensitivity, while high-column Lyman limit systems and damped Lyman-alpha systems are intrinsically rarer. Thus abundant hydrogen, a sensitive resonance and the large interception area of diffuse gas together explain the forest's numerical dominance. The comparison is between absorber classes at specified observational sensitivity; it does not mean that a metal-rich system has only one spectral transition.