_{S} and K_{An excellent} using the R function “pcor.test,” available at yilab.gatech.edu/pcor.R, with 95% CIs obtained by bootstrapping across genes. We used the following statistics for each gene as covariates: codon use bias, measured as the proportion of optimal codons (Fop); synonymous divergence (K_{S}), a proxy for the mutation rate of each gene; gene expression, measured using RNAseq (average log_{dos} reads per kilobase of transcript per million mapped reads across all developmental stages of D. melanogaster); smoothed effective rates of crossing over (centimorgan per megabase) from Loess regression fits to the rates of crossing over from the D. melanogaster data of ref. 22, multiplied by one-half to correct for the absence of recombination in males; GC content of short introns (<80 bp); the coding sequence (CDS) length of each gene. For further details concerning these measures, see refs. 18, 20, and 58.

For the analyses of NS sites, we applied DFE-? (24) to each of 52 (mel-yak) or 53 (mel) sets of genes binned by K_{A}, to estimate the following parameters: ?, the shape parameter of a gamma distribution of the heterozygous fitness effects of deleterious NS mutations (the DFE); ?, the proportion of adaptive substitutions; ?_{a} = ? K_{A}/K_{S}, the rate of adaptive substitutions for NS mutations relative to the neutral rate; ?_{na} = (1 – ?) K_{A}/K_{S}, the rate of nonadaptive substitutions (due to fixations of neutral or slightly deleterious mutations) relative to the neutral rate (26). Binning was necessary, because DFE-? parameter estimates for single genes are very imprecise.

## S family (hill = –0

We ensured that each bin included at least 50 genes (SI Appendix, Table S2) and removed bins with negative estimates of ? (the bin with the lowest K_{A} in each case). We also excluded the last bin of mel-yak and the last two bins of mel, which contained genes with a broad range of very high K_{A} values that yielded anomalous estimates of ? and/or ?; this excluded only 74 and 81 genes for the mel-yak and mel datasets, respectively. This left a total of 50 bins for each NS dataset: 6,748 genes for mel-yak, and 5,397 genes for mel (SI Appendix, Table S2). The binned data gave similar linear regression coefficients for the relation between ?_{S} and mean K_{A} for a bin (–0.026, mel-yak; –0.179, mel) to those for the unbinned K_{A} ? ?_{028, mel-yak; –0.177, mel).}

_{KYou}

_{To run DFE-?, we used a demographic model where the population at initial size N1 (set to 100) experienced a step change to N2 at n generations in the past. We also generated replicate bootstrap estimates of all of the variables for each bin pling genes 1,000 times within a given bin and running DFE-? for each bootstrap.}

We also applied DFE-? to UTRs for genes binned by K_{A}, for both the mel-yak and mel data (SI Appendix, Table S3). (Note that these bins do not contain exactly the same genes as in the NS site analyses.) Least-squares quadratic regressions gave little evidence for significant relations between K_{A} and the prieters, ? and ?, for the two types of UTR. The linear regression coefficient on K_{A} for ? for 5?-UTRs for mel-yak had P = 0.041; no other escort services Jacksonville coefficient approached significance. Given the number of tests, and the fact that normal distribution tests are likely to exaggerate significance, it seems safe to treat ? and ? for UTRs as independent of K_{A}, which reduces the complexity of the models used in the data analyses.

values were, however, strongly related to K_{A} for the binned data. For mel-yak, the quadratic regressions of on K_{A} were y = 0.068 + 1.54x – 6.08x 2 for 3?-UTRs and y = 0.0087 + 0.641x – 1.901x 2 for 5?-UTRs. For mel, the regressions were y = 0.016 + 1.12x – 27.4x 2 for 3?-UTRs, and y = 0.019 + 0.330x for 5?-UTRs (there was no evidence for a significant quadratic term in this case). For all coefficients shown, P < 0.005. These were used to obtain values of for the K_{A} bins used in the BGS and SSW models in the final data analyses described below.