The range of selection coefficient (s) for a beneficial allele

To find the reasonable range of the strength of positive selection acting on H3N2 viruses, we inferred selection coefficient (s) from how rapidly the frequencies of antigen-changing mutations increase. Namely, we fit an allele frequency change to

[49] where u₀ and u_t are the ratio of derived (q) to ancestral (p) allele frequency in time 0 and t (in generation), respectively. For each trajectory, we chose two time points approximately corresponding to q = 0.1 and 0.9. Since sampling was sparse and information for the month of collection was usually absent before the 1990s, we estimated s only from mutations that occurred later than 1990 out of 17 mutations in Koel et al. [19]. The frequencies of antigenic changing mutations through time were obtained from sliding windows of 6 months with a step size of 1 month. Time in months estimated to be taken for frequency to increase from 0.1 to 0.9 was then converted to time in generations. Estimated s ranged between 0.05 and 0.11. Changing window and step sizes did not affect our estimation of s. In the trajectories of mutations from which relatively low selection coefficients were estimated, allele frequencies were often observed to fluctuate even after they reach higher than 0.3 and maintained intermediate values for several months. This is probably due to clonal interference and would lead to underestimating their fitness effects. We confirmed that selection coefficients are underestimated from frequency trajectories generated in our simulation (Model A), where the rate of adaptive substitutions is sufficiently high enough to cause clonal interference. Considering these results, we choose s = 0.1 as a reasonable parameter for our further investigation.