(A) Distribution of overlapping sites when two sets of sites are drawn at random along the full length of the indicated gene or genes, matching the number of unique variable sites empirically observed in each patient and in the global influenza population (see Materials and methods). These simulations test a simple null model in which each site is equally like to mutate. We calculated the overlap between the two sets of sites in each simulation as a metric of parallelism: greater overlap means that more parallelism has occurred. The p-value indicates the proportion of 100,000 simulations in which the number of overlapping sites is greater than or equal to what is empirically observed. (B) Distribution of overlapping sites for simulations as described in (A), performed with a constrained null model in which the fraction of sites considered mutable is the fraction that shows at least two instances of nonsynonymous mutation in the global H3N2 influenza population between 2000 and 2015 (see Materials and methods) to account for constraints on protein evolution. For HA, but not NA or the other influenza genes in aggregate, the observed overlap of mutations at the within-host and global scales is statistically significant under this set of constraints. (C) p-values as described in (A), calculated across a range of constraints on the fraction of mutable sites. The constrained null model indicated in (B) is indicated with a red arrow. For HA, the observed parallelism is statistically significant at a threshold of 0.05 unless it is assumed that fewer than half the sites in the protein are mutable.