Line number density evolution derived on a quasar by quasar analysis using the high-order Lyman sample for column density intervals of log  N_H i = [12.75,14.0] and log  N_H i = [14,17]. The vertical error bars indicate 1σ Poisson errors, while the x-axis error bars show the redshift range covered by each sightline. The straight lines denote results from a linear regression to the data with parameters given in Table 2. The data are tabulated in Table A.1.