Temporal evolution of the relationship between the IGL mass fraction, f_IGL(t), and the mass-weighted velocity dispersion of group galaxies, σ_gal(t). Thin solid orange lines represent linear fits to the secular evolution of these quantities in individual groups, while the dotted black line shows the global trend. Dashed lines indicate the best linear fits of this relationship at four specific redshifts: z = 1.2 (red, diamonds), z = 0.7 (green, triangles), z = 0.3 (blue, stars), and z = 0 (purple, crosses), with line colours matching the corresponding data symbols. Each cosmic epoch-specific fit is annotated with its Pearson r correlation coefficient and p-value. For clarity, only data corresponding to the projection onto the XY plane are displayed, although the reported fit statistics take into account all three Cartesian projections.