Variation of the linking length parameters as a function of redshift. The left panel shows the transversely linking length for volume-limited samples, D₀, the middle panel shows the scale factor R_s, while the right panel shows the transverse linking length for flux-limited samples, D_l (see equations in Sect. 3.2). The solid blue lines show the parameters using a LF that varies with redshift (see Fig. 3) while dashed red lines show the parameters when a fixed LF at redshift close to zero is adopted.