Redshift density l(z) of LLSs (τ >  1) per unit redshift at z <  1.5 from Ribaudo et al. (2011) (blue solid circle) and Songaila & Cowie (2010) (red open square). Blue solid line is the redshift evolution law that Ribaudo et al. (2011) deduced from their data and used as reference in our simulation. Overdensities of LLSs resulting from the simulation are shown as black dotted lines in the range 0.45 <  z <  1.35 for α_ν = −2: bottom line, over–density of 1.5 (β₁ = −1.7, β₂ = −1.7); top line, overdensity of 1.7 (β₁ = −1.7, β₂ = −1.5). For comparison with the spectroscopic measurements these lines are shown after correction for a 10% contribution from Proximate LLSs resulting in overdensities of 1.35 and 1.54 respectively in the plot.