Figure 5.

Ordered integer-valued frequencies j, plotted on a log-log scale, of the C_* distinct (A) alpha and (B) beta chains drawn using OLGA. The index 1 ≤ i ≤ C_* < N_* labels the distinct sequences drawn while b_j is defined as the number these sequences that exhibit the specific frequency j [b ₁ and b ₂ are explicitly indicated in (B)]. The highest frequency clone appears J times such that b_j>J = 0. Since C_* is comparable to N_* , the drawn sequences are dominated by the low probability ones that appear only once. The insets display the frequencies on a linear scale and indicate the long-tailed behavior of the frequencies. The shape of the frequency spectra is self-similar once N_* ≳ 10⁷, allowing us to use this sampling procedure to reliably estimate ${\pi }_{\alpha }\left(\alpha |\overline{\alpha }\right)$ .