Schematic illustration of a statistical test based on coalescent theory to explore the possibility that the high degree of sequence identity observed could be explained merely by rounds of viral replication in which no mutation occurred. The left side of the figure represents the sample from participant 03 as analyzed by sequencing of the env gene in supernatant HIV-1 RNA from clonal p24⁺ wells (see Fig. 3). A total of 31 independent isolates were obtained, including one set with eight isolates (dark blue cells), six smaller sets (other colors), and eight unique isolates (singletons). The right side imagines a sample of the same size that would have been collected had no clonal proliferation occurred. The large clone is reduced to the size that maximizes likelihood under a neutral coalescent, and singletons are added to keep the total sample the same size. Because reducing the large clone essentially adds a parameter, a likelihood ratio test can be done. As shown in Table 1, p-values for all subjects tested in this manner were <0.05, indicating that mutation-free viral replication is an insufficient explanation for the data.