Evolution of with redshift as predicted by Eq. (1)(solid lines). The red curve is determined using ULAS J1120+0641 data alone and assumes a fixed normalization at z = 5.5. The uncertainty in ξ for z> 5.5 is indicated by the red dashed lines. The black dashed curve indicates the expected optical depth if the low-redshift case were to continue indefinitely. Points indicate direct measurements of along different lines of sight.