Observed fraction of galaxy groups as a function of their magnitude gap (black points with error bars) compared to the predictions of semi-analytic galaxy formation models, B06 (solid and dash-dotted blue histograms), DLB07 (solid and dotted green histograms) and G11 (solid and dashed red histograms) for S–I (top left panel), S–II (top right panel), S–III (bottom left panel) and S–IV (bottom right panel). We find that the fraction of groups declines with magnitude gap at all redshifts. Magnitude gap bin sizes are equal to one magnitude for ΔM_1,2< 2. ΔM_1,2 ≥ 2 systems are plotted as a 2 mag wide bin.