= Solution
For a fixed <column density> or rest-equivalent-width threshold, the number of ordinary <Lyman-alpha forest> features per unit <redshift> generally increases towards higher redshift. Over much of $z\sim1$–$4$, a rough description is $d\mathcal N/dz\propto(1+z)^\gamma$ with an index of order $2$–$3$, dependent on selection; the evolution is much slower at low redshift. Near <reionization>, blending and widespread opacity make a decomposition into individually detected lines increasingly inappropriate.
First separate physical evolution from geometrical path length. For comoving absorber density $n_c$ and proper interception area $\sigma_p$, <absorber incidence and comoving number density> gives
$$
\frac{d\mathcal N}{dz}=n_c\sigma_p\frac{c(1+z)^2}{H(z)}.
$$
Even a non-evolving population is not constant per unit redshift. Using <absorption distance> removes this particular geometrical effect.
The remaining <redshift evolution of the Lyman-alpha forest> reflects several competing processes. <Cosmic expansion> dilutes the gas; at fixed overdensity, <photoionization equilibrium> gives $n_{\rm HI}\propto\alpha(T)(1+z)^6/\Gamma$, so dilution can move many features below a fixed threshold. The <cosmic ionizing background> evolves as <quasars>, stellar sources and ionizing-photon absorption evolve; a decline of its intensity at late times partly offsets dilution. Photoheating changes <temperature> and <radiative recombination>, while <gravitational instability> redistributes gas into denser structures and hot shocked phases and changes its velocity field. Thus evolving line counts are not a direct count of conserved clouds; the density, thermal state, radiation field, geometry and observational selection must all be accounted for. The high-redshift increase and its physical interpretation are documented in https://arxiv.org/abs/astro-ph/9806286[the forest observations and models].
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