Number of sources (starting from the highest percentage contributor) that provide at least 50% of the total flux, N_50%, as a function E_min, the minimum event energy. In panel a), N_50% is shown for a mixed-composition model with source densities of n_s = 10^-4,10^-5,and   10^-6   Mpc^-3. Panel b) shows N_50% for a source density of n_s = 10^-5   Mpc^-3 for each model and, in addition, a mixed-composition model with source luminosities distributed according to a log₁₀-normal distribution with σ = 1. The shaded contours show the region in which 68% of all realizations lie; it is omitted in the second figure for clarity.