Mean line number density evolution of the combined sample as a function of redshift using the high-order Lyman-series sample for column density intervals of log  N_H i = [12.75,14.0] and log  N_H i = [14,17]. The sample is binned in redshift with Δz = 0.26, starting from z = 1.90. The vertical error bars indicate 1σ Poisson errors, while the x-axis error bars show the redshift range covered by each data point. For comparison, the results of the Lyα-only fits (grey open circles) are shown for the log  N_H i = [14,17] interval. The straight solid lines denote results from a linear regression to the binned data. Two dashed lines represent the mean number density evolution of the Lyα-only fit sample for log  N_H i = [14,17] (log  dn/dz = (−0.41 ± 0.35) + (4.14 ± 0.63) × log  (1 + z)) and for log  N_H i = [12.75,14] (log  dn/dz = (1.96 ± 0.13) + (1.12 ± 0.24) × log  (1 + z)), respectively. Exactly same redshift range was used for both fit samples. The data are tabulated in Table A.2. The parameters of the fits are given in Table 2.