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Using a direct numerical simulation (DNS) data set, the statistical properties of two important parameters, the scalar dissipation and chemical source term, are analyzed in details.
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Separate analysis conducted for dN and dS yielded significant results for dN (data set 2: XN = 0.079, P = 0.005; data set 3: XN = 0.084, P = 0.029; supplementary table S7, Supplementary Material online) but not for dS (data set 2: XS = 1.983, P = 0.872; data set 3: XS = 1.316, P = 0.703; supplementary table S7, Supplementary Material online).
Moreover, this analysis showed a significant association between pathway position and ω and dN for data set 3 when O. anatinus was not considered.
In addition, the path analysis revealed a significant association between pathway position and dN for data set 1 (standardized path coefficient, β = −0.246; P = 0.041; supplementary table S13, Supplementary Material online).
When the correlation was analyzed in each phylogenetic branch separately (fig. 5), the correlation coefficient is negative in a number of branches significantly greater than the number expected by chance (i.e., 50%), independent of the data set used for dN and for data sets 2 and 3 for ω.
Furthermore, the correlation between pathway position and ω is significant for two branches regardless of the data set, whereas for dN, the correlation is significant for either two (data sets 1 and 3) or four branches (data set 2).
Furthermore, after removing O. anatinus sequences from the analysis, the correlation between the pathway position and the overall dN values is significantly negative for data set 2 (table 2).
A threshold of <5 on dN, dS, and ω reduced the final data set to 826 estimates.
We did not find any association between clade size and any of the measures of substitution rate (T, dN, dS) estimated from our nuclear gene data set for 32 mammalian sister pairs (Table 5).
Furthermore, the correlation between pathway position and dN is negative for all seven branches in each data set (binomial test, P = 0.008; supplementary table S12, Supplementary Material online) and significant for either two (data sets 1 and 3) or six phylogenetic branches (data set 2).
The mean rates of synonymous (dS) and non-synonymous (dN) substitutions are the means for all sequence comparisons in each data set.
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