Evolution of the IRRC found when using (i) the real spectral index, where it is known, otherwise using α = − 0.7 (magenta; 1σ uncertainty region shaded); (ii) a spectral index of α = − 0.7 for all sources (black); and (iii) a spectral index of α = − 0.8 for all sources (cyan). The green points and line show the result of sampling α (where it is unknown) from a Gaussian distribution with μ = − 0.7 and σ = 0.35. The red dashed line shows the use of α = − 0.7 (at z< 2) and − 0.8 (at z> 2) where it is unknown.