Fig. 3 shows the fits to the observed values for mel-yak of the predicted values of ?ln(?S). The fits are clearly far better than with BGS alone. The goodness of fit was assessed from the Pearson correlation coefficient (r) between the observed and expected values across the 49 bins used for the fit. The r values were 0.924 and 0.918 for the low and high gene conversion rates, respectively; the corresponding minimum SSDs were 0.193 and 0.296. These two measures show that the low gene conversion rate gives a better fit than the high gene conversion rate. The corresponding estimates for UTR sites of ?u were 213 and 260, respectively; the values of pu were very similar for each bin, with means of 9.03 ? 10 ?4 and 8.41 ? 10 ?4 .
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Fig. 4 shows estimates of ?a, pa, and the ratio of synonymous diversity relative to neutral expectation (?rel = ?S/?0) for each bin of KA values, assuming either low or high gene conversion rates. ?a and pa increase with increasing KA, and ?rel declines. The mean values of ?a and pa over bins were 249 and 2.21 ? 10 ?4 , respectively, for the low gene conversion rates, and 508 and 8.41 ? 10 ?4 for the high gene conversion rates. The estimated values of ?0 were 0.019 and 0.017 for the low and high gene conversion rates, with corresponding ?rel values of 0.758 and 0.843, respectively.
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The black circles are the predicted values of ?S relative to its expected value in the absence of hitchhiking; the red diamonds are the estimates of ?a (multiplied by 10 ?3 ); the blue crosses are the estimates of pa (multiplied by 10 3 ). The other parameters are as in Fig. 3, assuming effects of BGS and SSWs at both NS and UTR sites.
Corresponding results were obtained for the mel data (SI Appendix, Fig. S2), which yielded somewhat lower estimates of mean ?a of 119 and 434 for the low and high gene conversion rates, respectively; the corresponding ?u values were 97.5 and 260. 31 ? 10 ?4 and 1.23 ? 10 ?4 for NS sites, and 3.80 ? 10 ?3 and 7.17 ? 10 ?4 for UTR sites. The r values were substantially lower than for mel-yak: 0.812 and 0.820 for the low and high gene conversion rates, respectively, implying poorer fits to the data. This difference probably arises from the fact that the underlying rate of adaptive protein sequence evolution (obtained from ?KA: SI Appendix, Eq. S17) for individual bins of KA, which was used in the sweep analyses, was less accurately estimated from the mel than the mel-yak data; the mean over all bins of the coefficient of variation of ?KA from the bootstrap analyses described below was 18.5% for mel compared with 14.4% for mel-yak, a 22% lower value for mel-yak relative to mel. Given the higher relative errors in the estimates of ?KA, this result is not surprising. We have accordingly focused attention on the mel-yak results.
We explored the question of the effects of BGS and gene conversion on the parameter estimates for adaptive mutations, by obtaining estimates from the original mel-yak data with/without BGS, gene conversion, and UTRs; these are shown in Table 1. Ignoring BGS causes an overestimation of ?a, although the relative size of the effect is smaller than that of gene conversion. It seems that fairly accurate estimates of ?a can thus be obtained if BGS is ignored, but not if gene conversion is ignored. The effects on pa are in the opposite direction, as would be expected. Ignoring UTRs has only a slight effect on the estimates of ?a and pa for NS sites, but causes a considerable overestimation of ?rel.