A for ?ln(?S) and mean E for a bin. For the data used in Fig. 3, the regression coefficient for ?ln(?S) was 3.81 ± 0.21 (the SE was obtained from normal distribution regression theory). The regression coefficients (b) for mean E for the low and high rates of gene conversion were 0.236 ± 0.039 and 0.0935 ± 0.0208, respectively, indicating a significant difference between the two regression coefficients in each case. Similar results were obtained with the mel data. 3, which assumed that 15% of the total number of mutations had strongly deleterious effects (tl = 0.044), and cases without any major effect mutations. In the absence of major effect mutations, there was a weakening of the BGS effects for a given bin of KA; b for mean E was barely affected with the low gene conversion rate and decreased to 0.0574 ± 0.0122 with the high gene conversion rate.
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The sensitivity of the results to variation in the mutation and crossing-over parameters was explored by using rates of mutation and crossing over with the mel-yak data that were either one-half or twice the “standard” values used above (SI Appendix, Table S7). As expected, higher mutation rates and lower crossing-over rates were associated with larger b values for E. The results were much more sensitive to the mutation rate than the crossing-over rate, especially with the high gene conversion rate. In no case, however, did the b values approach that for –ln(?S).
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To provide a more rigorous test of the ability of BGS to explain the relation between ?S and KA, we generated 500 bootstrap values of all of the variables for each bin separately (Materials and Methods), reran the regression analyses for each bootstrap replicate, and determined the proportion of cases in which the regression coefficient for –ln(?S) was less than that for E, as well as upper and lower percentiles of the distributions of both regression coefficients, and of the difference between them. For the low gene conversion rate and other parameters used in Fig. 3 for the mel-yak data, 100% of the bootstraps had a larger regression coefficient for –ln(?S) than for mean E, with upper and lower 2.5 percentiles of Fort Wayne escort the difference of (3.18, 4.04). The upper and lower 2.5 percentiles for the regression coefficients were (3.42, 4.25) for –ln(?S) and (0.14, 0.32) for mean E. As would be expected, with the high gene conversion rate, the difference between the two regression coefficients was more pronounced, with upper and lower 2.5 percentiles of (0.05, 0.14) for the mean E regression, and (3.34, 4.18) for the difference. There is thus good evidence that the BGS model cannot fully account for the relation between ?S and KA. Similar results were obtained for the mel data.
The only obvious alternative explanation is that a higher incidence of SSWs is occurring in genes with higher KA values, resulting in greater reductions in ?S than in genes with low KA. This hypothesis is qualitatively consistent with the fact that bins with higher KA have larger ?a values (SI Appendix, Table S2). We explore this possibility quantitatively in the next section.
We now describe the estimates of the parameters for beneficial mutations, obtained using the procedures described in Materials and Methods, Expected Effects of SSWs on a Single Gene and Estimating Positive-Selection Parameters. These are based on the standard equations for the effects of a SSW (32), which can be used to predict the effects of sweeps of favorable NS and UTR mutations on the mean ?S of genes in a given bin (SI Appendix, section 4). In addition, the contribution of BGS to the reduction in ?S for the bin was estimated as described above; the net predicted value of ?S/?0 with both BGS and SSWs was then found using SI Appendix, Eq. S16c.