Genome Sequences and Annotation

Genome sequences for the human [46] (version hg18), chimpanzee [45] (version panTro2), and rhesus macaque [52] (version rheMac2) genomes, and human genome annotation files were obtained from the University of California at Santa Cruz Genomic Informatics (UCSC) web site [53]. Human protein-coding sequences and exons were identified using UCSC ‘known gene’ files [54] (downloaded Sept. 2007). Repetitive regions were identified using the UCSC lower-case markup (which is based on RepeatMasker [55] and Tandem Repeats Finder [56] analysis). Simple repeats identified by Tandem Repeats Finder were also downloaded from the UCSC simpleRepeats track so that they could be used independently.

Recombination Rates

Files indicating map distance per nucleotide for deCODE [26] and Myers et al. [25] recombination maps were downloaded Feb 2007 (we used snpRecombRateHapmap files for the Myers et al. map), and transferred from hg17 using the UCSC liftOver tool. X chromosome values were multiplied by 2/3 to correct for non-recombination in males. Chromosome regions missing from the recombination maps were ignored for most analyses; however for use in calculating background selection values, we assigned each base in missing regions a recombination rate equal to that of the nearest defined base (for terminal regions of chromosomes) or the mean of the nearest defined bases from each side (for internal regions).

Human–Chimp–Macaque Whole-Genome Alignments

We downloaded ‘chained and netted’ pairwise whole genome alignments from UCSC [57]–[59] for human (hg18), chimp (panTro2) and macaque (rheMac2). We converted these ‘best’ alignments to be best-reciprocal by splitting alignment blocks to omit portions that were non-reciprocal between forward (e.g. hg18 vs. panTro2) and reverse (e.g. panTro2 vs. hg18) alignments. Next, blocks aligning parts of non-orthologous chromosomes or unassigned to a chromosome region were discarded. Human and macaque chromosome regions were considered orthologous if their pairing was consistent with the synteny map of Rogers et al. [60] and for the sex chromosomes, only X to X and Y to Y alignment blocks were kept, in accordance with the synteny map of Murphy et al. [61].

We filtered out putative copy number variants and segmental duplications since these are likely to be enriched for non-orthologous alignments. Alignment blocks were omitted if more than 50% of a block overlapped regions identified as having an excessive depth of shotgun sequence reads (WSSD regions). WSSD features generated from Celera, Venter, and Watson human genome sequences as well as chimpanzee and orangutan sequencing projects were combined in order to create the set used for filtering [62],[63]. Additionally, human-chimp alignment blocks were excluded if the chimp sequence overlapped WSSD features identified by aligning chimp reads to the chimp genome, and human-macaque alignment blocks were excluded if they overlapped WSSD features identified by aligning macaque reads to the macaque genome [63].

We then grouped remaining alignment blocks into ‘chains’. Blocks were chained when their chromosomal ordering was consistent for both species. We eliminated chains with fewer than 250 kb in the human-chimp alignment, or 50 kb in the human-macaque alignment. We further excluded blocks with lengths less than 2 kb from both alignments.

The remaining pairwise human-chimp and human-macaque alignments were then used to define a three-species alignment. We applied a set of site filters to individual alignment columns. We used only sequence with high-confidence base calls, requiring that each site was flanked by five sites with minimum quality scores 25 (in both chimp and macaque), and that the site itself had a quality score of at least 40. We ignored columns in the alignment that included gap characters, were adjacent to mismatches, gaps or undefined bases, or that overlapped a CpG dinucleotide in any of the three species. We also imposed a ‘symmetry’ filter to eliminate potential non-orthologous alignments by using macaque as an outgroup to assign (where possible) human-chimpanzee sequence differences to either the human or chimp branch, and eliminating regions in which more than 16 out of 20 successive substitutions were on the same branch.

Human–Dog Whole-Genome Alignments

We downloaded pairwise human (hg18) and dog (canFam2) [64] alignments, converted these to best-reciprocal alignments as described above, and discarded blocks of length<100 bp and blocks that were unassigned to a chromosome region. Chains of blocks that had a combined length of <5000 bp were then discarded in a subsequent pass.

Regional human/dog divergence was estimated by counting alignment columns in putative neutral sites (defined below) in 1 Mb sliding windows that were advanced by 1 bp at a time. Only transversion substitutions were used in divergence calculations because they gave better correlations to human/macaque divergence than transition substitutions or Kimura-corrected divergence (presumably because many sites have multiple transition substitutions). Sites were excluded from the analysis if they were in a potential CpG context (following a C or preceding a G) or if they were adjacent to a gap or N. Windows were discarded if they contained fewer than 200,000 sites post-filtering.

For comparison of H/C, H/M and H/D divergence (Figures 3, 7C, S2 and S6) we constructed the implied human-dog-macaque alignment and applied the same filtering criteria used to calculate regional H/D divergence, again using only transversion substitutions. The same alignment was used to calculate levels of divergence in several site classes relative to the neutral rate (Figure 5). In this case, less stringent filtering was applied (sites in a potential CpG context were still excluded), and all four species were required to have an aligned base at each site.

5-Species Primate Data

We downloaded HCGOM alignments utilized in [21] from http://genepath.med.harvard.edu/~reich, and extracted columns identified as used in that study (these all have at least one nucleotide difference among species). We eliminated columns that overlapped a CpG dinucleotide in any species or that were not flanked by invariant columns (i.e. columns for which all species shared the same nucleotide). In addition, we identified all invariant columns, and selected at random a subset of these equivalent to the number reported in [21].

We augmented these data with a smaller dataset generated in our own laboratory as follows. We chose primer pairs to amplify 591 human genome loci of size 1 to 2 kb spaced roughly every 5 Mb on the autosomes and 2.5 Mb on the X. Primers were chosen to avoid repetitive regions, positions where human, chimp, or macaque differed, and the dinucleotide CpG, and trinucleotides ACA, or TGT which we have found to have higher than average mutability in primate sequences (data not shown). DNA samples from a male chimpanzee (Pan troglodytes), a male bonobo (Pan paniscus), a female gorilla (Gorilla gorilla), a female Sumatran orangutan (Pongo pygmaeus) and a female rhesus monkey (Macaca mulatta), purchased from the Coriell Institute (Camden, NJ), were PCR amplified and sequenced in both directions, using standard protocols and an ABI Prism 3100 Genetic Analyzer. After basecalling with phred [65],[66], we searched each read against the human genome and eliminated reads for which the best match was to a non-target location. The remaining 4759 reads were aligned to the human sequence using a banded Smith-Waterman algorithm (cross_match; www.phrap.org). Analyzed data were required to pass quality and alignment filters similar to those described [21]. Traces have been deposited in the NCBI trace archive (http://www.ncbi.nlm.nih.gov/Traces).

A total of 8.5 million alignment columns passing these filters in the combined 5-species dataset were analyzed.

Human Diversity Data

Human single nucleotide polymorphism (SNP) data was obtained from Perlegen Sciences [19], HapMap phase II (non-redundant October 2008 update) [67], the SeattleSNPs NHLBI Program for Genomic Applications (PGA) [68] and the NIEHS Environmental Genome Project (EGP) [20],[69] (downloaded July 2008).

To estimate nucleotide diversity we averaged combined-population heterozygosity for all di-allelic polymorphisms in scanned regions (assuming heterozygosity of 0 for monomorphic sites). For the HapMap data the CEU panel was used instead of combined-population heterozygosity. As with divergence calculations, we required the presence of an aligned macaque base (necessary for normalization) and excluded sites in a CpG context, sites with poor quality scores, and sites adjacent to a gap or N in the human/macaque alignment. For both HapMap and Perlegen datasets we omitted sites that fell within annotated repeats.

Diversity for a given class of genomic sites (e.g. putative neutral sites having a specified background selection value) was estimated by summing the estimated heterozygosities (computed from observed allele frequencies in the samples) of SNPs in that class and dividing by the total number of scanned sites in the class.

To avoid ascertainment bias in the Perlegen data we only used class A SNPs, which had been identified using array-based resequencing [19]. We converted the NCBI34/hg16 coordinates of the Perlegen SNPs to NCBI36/hg18 coordinates using the UCSC-annotated positions of the associated dbSNP identifiers. The following sites were considered unscanned in order to correct for biases in Perlegen array-based detection: sites within 25 bases of an annotated repetitive region; sites with <6 or >13 G or C nucleotides among the 24 bases (12 to each side) flanking the site (our unpublished analyses indicate that class A SNPs are strongly depleted at such positions); regions >100 kb that completely lacked class A SNPs; and regions present in the NCBI36 assembly but not the NCBI34 assembly (as identified by mapping non-overlapping 1 kb segments from NCBI36 to NCBI34 using liftOver).

To address the possibility that Perlegen or HapMap SNP ascertainment strategies could bias our estimates of human diversity [70], we employed an ascertainment correction that takes into account the size of the discovery sample [71]. The discovery sample size of the Perlegen data is 20–50 chromosomes (see supplemental data for [19]). We were unable to obtain per-SNP discovery sample sizes so we calculated corrected nucleotide diversity values assuming uniform discovery sample sizes of either 20 or 50. Note that this ascertainment correction does not account for failure of the array technology to identify SNPs during the discovery process, but it should not bias our Figure 3 analyses (which compare regions near and far from conserved segments) provided discovery sample size and technology failures are not themselves biased with respect to distance from conserved segments. As expected, our ascertainment corrected nucleotide diversity estimates are higher than our uncorrected estimates, but our diversity ratios from regions near-to and far-from conserved sites are essentially unchanged (Table S5). Moreover, consistent with this expectation, we obtained similar results from HapMap phase II data, which used different ascertainment methodologies, and from SeattleSNPs EGP/PGA data derived from complete resequencing.

Gcons Conservation Model

We implemented a program, gcons, to identify evolutionarily conserved segments from aligned genomic sequences. Gcons extends the two-state phylogenetic Hidden Markov Model (phylo-HMM) approach used by phastCons [23] by incorporating alignment gap information. We define separate substitution models for nucleotide and gap evolution, and estimate substitution probability matrices on each branch of the phylogenetic tree without assuming a common rate matrix (phastCons uses a single rate matrix). Our probability matrices are constrained to be strand-symmetric (e.g. A→G substitutions must occur at the same rate as complementary T→C substitutions) but may be non-reversible. Our gap substitution model is a simple site-independent deletion model with three symbols representing defined bases (b), sites in short gaps of length≤10 bp (-), and sites in long gaps or unaligned regions (D). Because we consider only ‘ancient’ sites present in the root and assume that orthologous nucleotides are aligned, it is unnecessary to model insertions. Thus the only non-zero substitution rates are b→-, b→D, and -→D. In high coverage genomes, the absence of long gaps is indicative of functional constraint [72], but in low-coverage genomes, long gaps may simply represent coverage gaps and are therefore less informative [24]. Because our model uses separate long and short gap symbols and allows rates to vary on different branches, it can be applied effectively to a mixture of high and low sequence coverage genomes.

From a set of alignment columns we obtain maximum likelihood estimates of the substitution probability matrices on each branch of a phylogenetic tree using an EM algorithm [73]. For our purposes, it is sufficient to estimate substitution probabilities directly, rather than the underlying substitution rate matrices and branch lengths.

We downloaded a multiple alignment of 28 vertebrate genomes from UCSC in August 2007 [24] and extracted from this the alignment of placental mammal species. To avoid biasing our primate sequence analyses we excluded chimpanzee and rhesus macaque sequences from the alignments, leaving a total of 15 sequences plus human and we treated the human sequence as missing data for the likelihood calculations described below. For these sequences we assume the following fixed phylogenetic tree topology obtained from UCSC (http://hgdownload.cse.ucsc.edu/goldenPath/hg18/multiz28way/28way.nh): ((((hg18,otoGar1),tupBel1),(((rn4,mm8),cavPor2),oryCun1)),((sorAra1,eriEur1),(((canFam2,felCat3),equCab1),bosTau3))).

We restrict our analysis to ‘ancient’ sites defined as those present in at least one species on either side of the internal node ((((hg18,otoGar1),tupBel1),(((rn4,mm8),cavPor2),oryCun1)),((sorAra1,eriEur1),(((canFam2,felCat3),equCab1),bosTau3))). This node is used instead of the root because the three species on one side of the root (armadillo, elephant, tenrec) have low-coverage (2×) assemblies with many gaps.

We estimate neutral substitution probabilities using multiple alignment columns from ancient repeats. Repeats were identified using the lower-case markup in the UCSC human hg18 sequence; to allow for repeat alignment ambiguity we excluded the 5 bp at each end of the repeat. Ancient sites that fulfilled these criteria were considered to be ancient repeats. Similarly, we used first and second codon positions in annotated coding sequences to estimate the conserved region substitution probabilities. Alignments from odd-numbered autosomes were used as a ‘training set’ input for the EM algorithm, and data from even-numbered autosomes were used as a ‘test’ set. Substitution probabilities for the X chromosome were estimated using the full set of alignment data (i.e. no test set was held out).

To approximate flanking nucleotide context effects on substitution rates [74] we categorized sites by their inferred ancestral context and trained separate models for each category. Specifically, for each ‘ancient’ alignment column we designated an ancestral nucleotide by choosing the nucleotide with the highest posterior root probability, as calculated using our initial (context-free) neutral evolutionary model. We then grouped alignment columns into categories based upon their ancestral purine and pyrimidine contexts because these contexts have previously been shown to capture a substantial proportion of mutation rate variation [74]. The four possible context categories are RRR, RRY, YRR, YRY, where the center symbol is the ancestral state at the site of interest and R and Y denote purine and pyrimidine, respectively (note that reverse-complement pairs of contexts, e.g. RRY and YYR, are equivalent by virtue of the strand symmetry condition on our substitution matrices). After grouping columns by their ancestral contexts we trained separate conserved and neutral evolutionary models for each possible context as described above, retaining the initial context-free model for sites where one of the flanking ancestral states is unknown.

We then computed a conserved/neutral log-likelihood ratio (LLR) for each ancient site in the human genome using these models. The LLR for non-ancient and unaligned sites was taken as the log of the rate of occurrence of such sites in conserved regions (first and second codon positions) divided by the rate of such sites in neutral regions (ancient repeats). To avoid biasing our primate sequence analyses, human sites were treated as missing data in LLR calculations.

The sum of the nucleotide substitution and gap LLRs at each site may be interpreted as the log of the ratio of the emission probabilities of the corresponding alignment column by a Hidden Markov Model having two states, ‘conserved’ and ‘neutral’. We assigned state transition probabilities of 1/7 (conserved→neutral) and 0.0075 (neutral→conserved), implying an expected conserved segment length of 7 bp and an expected conserved portion of the genome of 5%, and computed a score, S, for each site which is related to the posterior probability, PP, of being in the conserved state by PP = e^s/(e^s+1).

To identify potentially incorrect portions of the multiple alignment we used a similar procedure, defining an HMM with a neutral and a ‘high substitution’ state. Emission probabilities for the neutral state used the context-free substitution probability matrices from ancient regions, whereas those matrices raised to the 5^th power defined emission probabilities for the high substitution state. State transition probabilities were chosen such that high substitution segments were expected to be of length 25 bp and span 10% of the genome. We then computed scores as above, and defined contiguous regions with scores greater than 0.0 (posterior probability 0.5) as high substitution segments; these comprise 8% of aligned ancient repeats, 2% of aligned intergenic bases and 0.2% of aligned first and second codon positions. These segments likely reflect misalignments, and we excluded them before re-extracting alignment columns and re-performing the training of the conserved and neutral models described above (i.e. the columns were omitted for training, but retained in other analyses).

Conserved Segment and Neutral Site Identification

We defined conserved segments to be contiguous sets of bases in the human genome having gcons score≥10; these are the bases with the strongest evidence for being under purifying selection. Note however that because the gcons model is designed to detect segments of a given minimal length rather than individual conserved bases, some bases within a conserved segment may be under little or no selection pressure (e.g. synonymous bases within coding exons), and short evolutionarily constrained segments may have low gcons scores. Approximately 39% of annotated exonic bases and 4.3% of non-exonic bases meet our gcons score threshold. We classified conserved segments as ‘exonic’ if they contain any annotated exonic base, and as ‘non-exonic’ otherwise. Exonic and non-exonic conserved segments comprise 1.1% and 4.2% of all genomic bases respectively.

Except where indicated, all analyses use putative neutral sites, which are required to be ≥10 bases away from any annotated exon, have gcons score<−10, and to pass the additional filters indicated above.

Gcons score thresholds of −10 and 10 were chosen to designate neutral and conserved sites because we found that they provide good separation between putative functional sites (e.g. known protein coding sequences) and putative non-functional sites (e.g. ancient repeats) (data not shown).

Following filtering, our primary datasets consisted of the following numbers of neutral sites: 1.2 billion autosomal and 48 million X chromosome human/chimp/macaque alignment columns; 550 million autosomal human/macaque/dog autosomal alignment columns; 5.3 million 5-species autosomal alignment columns; 6.5 million autosomal and 0.23 million X chromosome SeattleSNPs PGA and EGP scanned sites. Additional filtering steps were performed for the maximum likelihood analysis described below (regional H/D divergence was required to be defined, and some column types e.g. HGO, were not used). In total, 4.7 million alignment columns were retained for the 5-species autosomal dataset and 27 million alignment columns were retained for the chromosome X human/chimp dataset.

Background Selection

We applied the model of Nordborg et al. [5] and Hudson and Kaplan [4], which estimates the expected reduction in nucleotide diversity at a neutral site due to purifying selection at other sites as a function of deleterious mutation rate, selection strength, and recombination rate, under the assumptions that selection acts multiplicatively over loci and is strong enough that allele frequencies of deleterious mutations remain low (so that homozygotes for the deleterious allele may be ignored). Specifically, the background selection coefficient B = B^(ν) at a neutral site ν is given bywhere

1. π_e is the expected diversity at ν.
2. π₀ is the expected neutral diversity in the absence of background selection.
3. is the effective population size at ν.
4. is the effective population size in the absence of background selection.
5. x ranges over selected sites.
6. u_x is the (haploid) deleterious mutation rate per generation at x.
7. r_x,ν is the recombination rate per generation between ν and x.
8. t is the strength of selection on heterozygotes: (1−t) represents the fitness of an individual heterozygous for a deleterious allele at x, relative to an individual homozygous for the normal allele. For a site on the X chromosome, which spends 1/3 of its time in males and 2/3 in females, t = t_m/3+2 t_f/3, where t_m, t_f are the selection strengths in hemizygous males and heterozygous females carrying the deleterious allele.
9. f_x(t) specifies a probability density for alleles of varying selection strengths at x.

We distinguish two different classes of selected sites x, exonic and non-exonic, and allow them to have different u and f. Accordingly B may be expressed as a product B = B_ex B_nex where

Using the above formulae we computed B_ex and B_nex values for each site ν in the human genome, for various selection densities f, and u_x fixed (initially) to a value of 1.2×10⁻⁸. The selected sites x are taken to be the bases in exonic or non-exonic conserved segments as defined above, and r_x,ν is taken to be the recombination map distance between ν and x (this slightly overestimates the actual recombination rate). For f we use truncated exponential distributions: f(t) = 0 for t>1 and t<10⁻⁵, and f(t) = C e^−ct for 10⁻⁵≤t≤1 where c and C are constants. We considered f having mean values of the form a10^b, (or (4/3) a10^b in the case of the X chromosome) where a = 5.0, 2.5, or 1.0, and b = −2, −3, −4, or −5. As alternative possibilities for f we also considered point distributions, and truncated gamma distributions with shape parameters 0.25, 0.75 and 2.0 (using the same grid of mean values). The gamma distribution with shape parameter 0.75 gave a slightly higher likelihood for the 5-species autosomal dataset, but not significantly so given the additional degree of freedom (Table S2). For the human/chimp chromosome X dataset a point distribution gave a slightly better likelihood (Table S2), but for consistency with the autosomal analysis we use the exponential distribution results. Classifying conserved segments as coding or non-coding rather than exonic or non-exonic, or using the deCODE [26] instead of a finescale recombination map [25], gave somewhat lower likelihoods in our preliminary analyses (data not shown).

To accelerate calculations of B_ex and B_nex we employed several approximations. We constructed a lookup table giving, for a range of values of r and the length of the conserved segment, values of the integral (evaluated numerically) over f. Integrals were then estimated by performing bilinear interpolation between the nearest values stored in the table. Summations over x were done segment-by-segment, approximating the sum over the segment by a continuous integral. To make this approximation more accurate, segments were broken at points where the recombination map rate per nucleotide changed. The summations over segments were then performed by starting with segments nearest to ν and moving progressively farther away on the chromosome, calculating at each step the maximum possible remainder of the summation for the entire chromosome, and stopping the summation when this maximum remainder fell below a target value (0.001). Values for the first and second derivatives of the B's (with respect to the position of ν) were computed by summing the term-by-term derivatives. Finally, we carried out summations only for a subset of ν's on the chromosome, with B values for other sites estimated by quadratic interpolation using the derivatives.

Our B value estimates are available for download from http://www.phrap.org.

Likelihood Model

We model the probability of the observed 5-species alignment data as a function of species divergence times, ancestral effective population sizes, and background selection on exonic and non-exonic conserved segments, in order to estimate these parameters by maximum likelihood. Our model allows for the fact that the gene tree varies along the sequence, such that at a given site any two of human, chimp, or gorilla may share the most recent common ancestor (Figure S1). Following [21] we ignore alignment columns having more than two distinct nucleotides (implying two or more mutation events at the same position), and we label those with exactly two distinct nucleotides by indicating which species share the same nucleotide; thus an HG (or equivalently COM) column, or ‘site’, is one such that human (H) and gorilla (G) share one nucleotide, while chimp (C), orang (O) and macaque (M) share a different nucleotide. We ignore most site types such as HGO which represent obligate double mutation events, however we use HO and CO counts to help estimate rates of double mutation (described below). We assume each site involves a mutational change along at most two branches of the gene tree at that position; because all branches are short, multiple events are rare.

The probabilities that the sequences at the beginning and end of branch i differ by a transition (I) or transversion (V) substitution are given by Kimura's formulae [75]:where μ_I and μ_V are the per-generation per-nucleotide transition and transversion mutation rates (so that the combined mutation rate is μ = μ_I+2μ_v), and β_i is the branch length (in generations). The probability of an observed column of type k is thenif the column has two distinct nucleotides differing by a transition;if the column has two distinct nucleotides differing by a transversion; andif the column is invariant.

Here S and D denote sets of branches that can give rise to the observed column type via a single or double substitution, respectively. Distinct alignment columns are treated as independent observations. The parameters λ_I and λ_V are used to scale the rates of double substitution events, which are higher than predicted by the site-independent Kimura substitution model because of mutational hotspots and flanking nucleotide contexts. Patterson et al. [21] observed that it is particularly important to take recurrent mutation into account for HG and CG columns, a significant fraction of which are the result of substitutions on multiple branches. We calculated the expected number of sites that are due to recurrent substitutions under our fitted model and compared the results to those from Patterson et al. Our estimates are in close agreement for the column types that are most frequently due to double substitution (HC, HG, and CG) (Table S6). We estimate lower rates of double substitution for some of the other column types, but since only a small fraction of these are due to double substitutions, differences in these rates should not affect our overall results.

To illustrate these issues consider the alignment column GAGAA, where human and gorilla both have a G nucleotide and the other three species have an A. This column could be the result of a single A→G transition substitution on the HG branch (assuming a gene tree that differs from the species tree) but could also be due to A→G transitions on both H and G branches, or an A→G transition on the HCG branch and a back substitution (G→A) on the C branch. In this case S is (HG), and D is either (H,G) or (HCG,C).

Expected branch lengths β [21],[29],[76] for each site type are given by:where is the probability that the human-chimpanzee coalescent predates the gorilla speciation, the ' represent inter-speciation intervals (measured in generations), the represent ancestral effective population sizes (corresponding to in the formula for B in the Background selection section above, and as depicted in Figure 1), and B = B_exB_nex is the background selection value. The factor 1.4 in the β_M formula corrects for the estimated mutation rate excess in old world monkeys relative to hominids [77]. Note that in contrast to the other parameters, B depends on the sequence position. B also depends on the choice of recombination map, and on u_ex, u_nex, f_ex, and f_nex.

We assume the human-estimated B values apply to the orthologous bases in the other species, which is only approximately true because local recombination rates vary over time [27],[28]. Selection strengths may also vary, and even if they do not, differences in effective population size imply that deleterious mutations eliminated by selection in some populations may become fixed in others.

For the 3-species (human/chimpanzee/macaque whole genome alignment) analyses we developed a similar model, but ignoring the macaque branch and using .

To accelerate the probability calculations, we binned sites by their B values and column types. The log-probability of the data is thenwhere n_B,k is the number of filtered columns of type k in bin B, and π_k is the probability associated to column type k as given above.

For each maximum likelihood analysis, the distribution functions f_ex and f_nex are held fixed to compute B across the genome for a particular u_x, and estimates for the remaining parameters are obtained by searching the likelihood surface with the GNU Scientific Library's [78] implementation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method [79] (with slight modifications to prevent stalling at ridges), using analytically computed first partial derivatives. We varied u_ex and u_nex by rescaling B values (computed initially with a fixed u) as follows (where i denotes ex or nex, and and denote the updated values):

Because μ is confounded with the and parameters, a calibration is required to infer individual parameter values; we fix to 240,000 generations (assuming a species divergence time of 6 MYA and a 25 year generation time), and adjust the other and values proportionately. Note also that μ is distinct from u_x (deleterious mutation rate per selected site, for calculating B): in particular μ reflects alignment filtering whereas u_x does not, and the estimate of u_x is influenced by background selection arising from deleterious mutations at sites outside the identified conserved segments.

Regional variation in neutral substitution rates [80] has the potential to bias our parameter estimates. In particular, a higher average neutral substitution rate in regions which are distant from conserved segments (potentially due to a mutational effect associated with recombination [11],[17] or insertions and deletions [81]), could be misinterpreted as evidence for selection in the ancestral population. To incorporate regional substitution rate variation into our model, we allowed mutation rates to depend upon regional human/dog divergence. Alignment column counts used for maximum likelihood estimation were binned by the regional human/dog divergence D in addition to B_ex and B_nex. Rather than estimating the transition and transversion mutation rate parameters (μ_I and μ_V) directly we instead estimate parameters μ_A and μ_B and define the transition and transversion rates in each bin as μ_I = μ_AD and μ_V = μ_BD. This correction may not fully accommodate substitution rate variation if the effect is very local or has changed substantially over time.

Confidence Intervals

Confidence intervals in Figures 3, 4, 5, 6, S2 and S5 were calculated using 1000 bootstrap iterations. Correlation confidence intervals (Figures 7 and S6) were calculated by resampling windows; intervals for the other analyses were calculated by resampling counts of sites in bins, which were assumed to be binomially distributed.

Confidence intervals for maximum likelihood parameter estimates were also calculated by a bootstrap procedure. In each bootstrap iteration, alignment columns were resampled with replacement. As before, columns were binned by their associated exonic and non-exonic B values (which differ for each pair of selection coefficients tried), and the local human/dog divergence. Maximum likelihood parameter estimation was done using the binned column counts and a new set of parameter estimates was obtained for each iteration. Confidence intervals for each parameter correspond to the central 90% of the ordered set of estimated values. Confidence intervals for mean autosomal and chromosome X B values were calculated using parameter estimates from the same bootstrap iterations. We performed 100 bootstrap iterations, which required approximately six days for the 5-species analysis using a 96-node computer cluster.