The Positive Correlation between dN/dS and dS in Mammals
Is Due to Runs of Adjacent Substitutions
Nina Stoletzki*,1 and Adam Eyre-Walker1
1
Centre for the Study of Evolution, School of Life Sciences, University of Sussex, Brighton, United Kingdom
*Corresponding author: E-mail: nstoletzki@googlemail.com.
Associate editor: John H McDonald
Abstract
Key words: positive correlation, dN/dS, dS, adjacent aubstitutions, bias dN/dS.
Introduction
In protein-coding sequences, we can differentiate between
synonymous and nonsynonymous substitutions. If we assume that nonsynonymous mutations are either neutral
or deleterious, then the rate of nonsynonymous substitutions, dN, is fu, where u is the nucleotide mutation rate and
f is the proportion of nonsynonymous mutations that are
neutral. Although it is known that selection can operate on
synonymous sites, even in mammals (Chamary et al. 2006;
Resch et al. 2007), their evolution is often assumed to be
neutral and their rate, dS, would then become a measure of
the mutation rate (dS 5 u). Under this assumption, the ratio
of the nonsynonymous over the synonymous substitution
rate (x) is a measure of the proportion of mutations that
are neutral, f. Because both, dN and dS, depend upon the
mutation rate, they are expected to be positively correlated.
However, it has been known for some time that the correlation between dN and dS is stronger than one would
expect under this simple evolutionary model (Ohta and
Ina 1995; Smith and Hurst 1999; Smith et al. 2003). Furthermore, Wyckoff et al. (2005) and Vallender and Lahn (2007)
have recently shown that their ratio, x, is positively correlated to dS between several species pairs. Although the correlation is not always very strong between some species
pairs (Liao and Zhang 2006), may be negative (Studer
et al. 2008; Li et al. 2009), and can depend upon the method
used to estimate x and dS (Li et al. 2009), the cause of the
correlation remains unclear. The positive correlation between x and dS in mammals is quite unexpected under
simple evolutionary models because it would appear to imply that the strength of natural selection acting upon a protein, which is measured by x, is correlated to the mutation
rate, as measured by dS.
Wyckoff et al. (2005) suggest a number of explanations
by which such a correlation between the strength of selection upon a protein and the mutation rate could arise. First,
an increase in the mutation rate might decrease the effective population size of a genomic region through genetic
hitchhiking and background selection. This reduction in
the effective population size would allow more slightly deleterious mutations to fix, increasing x. Second, the correlation could arise through compensatory evolution because
under such a model, the rate of intragenic compensatory
substitutions would depend on the square of the gene’s
mutation rate (Kimura 1985). Third, and most intriguingly,
the mutation rate of a gene might be adapted to the characteristics of that gene; for example, if a gene is very important, then there may be selection to reduce the
mutation rate of that gene; although it should be noted
that such selection would be very weak and may not be
effective in the face of genetic drift.
We consider two other potential explanations for the
correlation between x and dS. First, there is a yet unconsidered statistical concern: when DNA sequences are very
similar, the rates of nonsynonymous and synonymous substitutions will be small and noisy and their ratio, x, will
hence be difficult to estimate without bias. Such a bias
may induce an artifactual positive correlation between
x and dS. Second, we note that if the correlation is genuine
and not a statistical artifact, it does not necessarily imply
that the rate of mutation is correlated to the selective constraint of the protein as suggested by Wyckoff et al. (2005).
The positive correlation may be due to any connection between the processes affecting synonymous and nonsynonymous sites. Adjacent substitutions may represent the
most obvious connection. As adjacent substitutions will
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Mol. Biol. Evol. 28(4):1371–1380. 2011 doi:10.1093/molbev/msq320
Advance Access publication November 29, 2010
1371
Research article
A positive correlation between x, the ratio of the nonsynonymous and synonymous substitution rates, and dS, the
synonymous substitution rate has recently been reported. This correlation is unexpected under simple evolutionary
models. Here, we investigate two explanations for this correlation: first, whether it is a consequence of a statistical bias in
the estimation of x and second, whether it is due to substitutions at adjacent sites. Using simulations, we show that
estimates of x are biased when levels of divergence are low. This is true using the methods of Yang and Nielsen, Nei and
Gojobori, and Muse and Gaut. Although the bias could generate a positive correlation between x and dS, we show that it
is unlikely to be the main determinant. Instead we show that the correlation is reduced when genes that are high quality in
sequence, annotation, and alignment are used. The remaining—likely genuine—positive correlation appears to be due to
adjacent tandem substitutions; single substitutions, though far more numerous, do not contribute to the correlation.
Genuine adjacent substitutions may be due to mutation or selection.
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Stoletzki and Eyre-Walker · doi:10.1093/molbev/msq320
affect proportionally higher numbers of nonsynonymous
sites than single substitutions (unless evolution is neutral),
sufficient variation of their relative numbers across the genome may cause a positive correlation between x and dS.
In particular, there is evidence that adjacent nucleotides
can mutate simultaneously (Averof et al. 2000). This will
generate a correlation between x and dS because some
synonymous mutations will be effectively selected by their
linkage to a nonsynonymous mutation.
We show in this study, first that x estimates are generally biased when sequence divergence is low. This bias can
cause a positive correlation between x and dS. However, by
restricting our analyses to genes in which the statistical bias
is minimal, we show that this bias is not the primary reason
for the correlation. Second, we show that the positive correlation between x and dS is entirely dependent upon runs
of two and more adjacent substitutions, whereas single
substitutions do not contribute. This indicates that the
correlation is not between the mutation rate of single point
mutations and selective constraint as suggested by Wyckoff
et al. (2005). Adjacent substitutions may be due to errors in
sequencing, alignment, and exon assignment but also due to
mutational processes (i.e., doublet mutations) or selection.
Material and Methods
Data
We used human–chimp–macaque–mouse–rat–dog alignments kindly provided by Schneider et al. (2009). To investigate the potential effect of errors in sequencing,
alignment, and annotation, we investigated the correlation
between x and dS in the whole data set of Schneider et al.
(2009; 9,942 genes), and in two restricted data sets, they
provide: first, the 2,890 genes that are longer than 200
codons and with less than 5% length difference between
homologues) and second, genes within the first group that
additionally had high trace sequencing coverage (excluding
humans for which this information was not available), known
annotation status, and 100% alignment HoT scores; this
yielded 1,514, 137, and 49 genes for mouse–rat, human–
macaque, and human–chimp, respectively.
Substitution Rates
In general, rates of synonymous and nonsynonymous substitutions (dS and dN) are estimated by dividing the observed number of synonymous and nonsynonymous
substitutions per gene (DS and DN) by the number of synonymous and nonsynonymous sites (S and N), that is, dS 5
DS/S and dN 5 DN/N. Many different methods exist to
estimate substitution rates. They can be divided into heuristic counting methods, such as Nei and Gojobori (1986;
NG) and maximum likelihood (ML) methods, such as the
methods of Goldman and Yang (1994, GY) and Muse and
Gaut (1994, MG); they can also be divided into those that
define the number of synonymous sites as ‘‘mutational
opportunities’’ and those that define sites ‘‘physically’’
(for discussion on the definition of sites, see Bierne and
Eyre-Walker 2003 and Yang 2006).
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The effect of the method used to estimate dS, particularly with respect to the correlation between dS and GC
content, has been extensively discussed before (Smith
and Hurst 1999; Bielawski et al. 2000; Williams and Hurst
2002; Bierne and Eyre-Walker 2003; Tzeng et al. 2004; Yang
2006). Furthermore, Li et al. (2009) highlight a large effect of
the method used to estimate substitution rates on the correlation between x and dS; they show that the correlation
is generally positive for most methods but less positive for
GY94 and even negative for those methods based upon the
method of Yang and Nielsen (2000). Li et al. (2009) suggest
that the negative correlation may be affected by the numerical computation of the later method. Because Yang
and Nielsen recommend the use of the GY method, that
is what we adopt here. We estimate dS using three different
methods. Using the PAML software (Yang 1997), we estimated pairwise substitution rates using the NG and Yang
and Nielsen (1998) methods, the latter being a variant of
GY method; we refer to the method as the GY method.
Both methods are mutational opportunity methods. Using
the HyPhy software (Pond et al. 2004), we estimated pairwise substitution rates using the MG method, a physical
site method. We performed PAML ML estimates using
the following parameters: pairwise comparison (i.e., runmode 5 1), x, and the transition–transversion ratio,
j, estimated from sequence data using codon frequencies
estimated from the nucleotide frequencies at the three codon positions (F3x4 model). The parameterization for MG,
using the MG94custom.mdl file, is similar to that of GY
without considering transition–transversion bias or varying
nucleotide frequencies between positions in a codon. Additionally, we used PAML to estimate the synonymous distance at 4-fold degenerate sites (d4) using the physical
definition of a site.
In heuristic counting methods, x is undefined if genes
do not have any synonymous substitutions (i.e., DS 5 0).
We adopted two strategies to overcome this problem. In
the first, we did what is commonly done and simply removed genes with DS 5 0; in the second, we calculated
x 5 dN/((DS þ 1)/S) for all genes. To add one to the denominator is a standard correction for ratios that has been
applied to odds ratios (e.g., see Jewell 1986). Note that the
GY ML method estimates x even if there is no apparent
synonymous substitution as it first estimates x and other
parameters and then calculates dN and dS from those parameters according to their definitions (Yang 2006). Similarly, the MG ML method can estimate x without any
apparent synonymous substitution.
Simulations
To investigate the bias in the estimation x when sequence
divergence is low, we simulated evolving sequences under
a simple evolutionary model using the Evolver software
from PAML (Yang 1997). For simplicity, we generated pairs
of sequences (900 bp and 1,800 bp) under the codon substitution model, using MCcodon.dat, with equal codon
frequencies, and j 5 1. This is most similar to the
Jukes–Cantor model which assumes equal base frequencies
Positive Correlation between dN/dS and dS in Mammals · doi:10.1093/molbev/msq320
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Table 1. Table Shows the Correlation between x and dS for Three Different Species Pairs Using Different Methods to Estimate the Number of
Substitutions.
Method Used to Estimate Substitution
Rates for v and dS
GYv–GYdS
GYv–GY d4
NGv–NGdS
NGvmod–NGdS
MGv–MGdS
Species Pairs
Mouse–Rat
10.0546***
10.1690***
10.1397***
10.1457***
10.0544***
Human–Macaque
10.0358***
10.1211***
10.2074***
10.2232***
10.0577***
Human–Chimp
20.2919***
20.2523***
20.1501***
20.0739***
20.3311***
NOTE.–All 9,942 genes from Schneider et al. (2009) were considered.
*P , 0.05, **P , 0.001, ***P , 0.0005.
and that all substitutions are equally likely (Jukes and
Cantor 1969). We used the model option 6, also known
as PAML Model M0 and we fixed x to 0.2 or 0.5 for all
sites in the gene. We varied the divergence from 0.0005
to 0.0500 in steps of 0.001. For each divergence level, we
simulated 1,000 sequences and estimated substitution
rates as described above.
Adjacent Substitutions
To investigate the effect of adjacent substitutions, we classified substitutions into those affecting a single site and
those affecting one or more adjacent sites. We further classified lineage-specific tandem substitutions affecting two
adjacent sites using parsimony and outgroups (mouse
for human–macaque and human for mouse–rat comparisons). For the analysis of the best quality mouse–rat genes
(i.e., those Schneider et al. (2009) selected because of trace
quality, annotation, and alignment), we used dog as the
outgroup as this species is of higher quality. We then excluded single, adjacent, and tandem substitutions to investigate their effect on the positive correlation between x
and dS. To test for correlations, we used two-tailed Spearman rank correlations.
Results
We began our analysis by confirming that a correlation exists between x and dS for three pairs of mammalian species: mouse–rat, human–macaque, and human–chimp.
We first estimated substitution rates using the popular
method of Yang and Nielsen (1998), which is a variant
of the method of Goldman and Yang (1994) and which
we hence refer to as the GY method. As Wyckoff et al.
(2005) observed, there is a positive correlation for
mouse–rat, and as Vallender and Lahn (2007) found, there
is a negative correlation in human–chimp (table 1). In contrast to Vallender and Lahn (2007), we find a positive correlation for human–macaque using the data of Schneider
et al. (2009; table 1); this is due to differences in the data
sets because we observe a negative correlation using the
data of Vallender and Lahn (2007; results not shown).
It has been shown previously that the direction and
strength of the correlation between dN and dS and between dS and the third-position GC content can depend
upon the method used to estimate the synonymous substitution rate (e.g., see Smith and Hurst 1999; Bielawski et al.
2000; Williams and Hurst 2002; Bierne and Eyre-Walker
2003; Tzeng et al. 2004; Li et al. 2009). In particular, the mutation rate is not always very well estimated by methods
that employ a mutational opportunity definition of a site
(Bierne and Eyre-Walker 2003; Yang 2006). We therefore
considered the rate of synonymous substitution at 4-fold
degenerate sites (d4). Finally, we investigated whether the
correlation between x and dS was restricted to the GY
method by estimating dN and dS using the NG and MG
methods. Under the NG method, there is a problem in estimating x when dS 5 0; we adopted two strategies: in the
first, we removed genes with dS 5 0 and in the second, we
calculated x 5 dN/((DS þ 1)/S) for all genes. The different
methods give qualitatively similar results to those obtained
with the GY method suggesting that the correlations are
not a product of the methodology used (table 1).
However, x and dS are not independent of each other
and one might expect them to be negatively correlated
through sampling error in dS (Wyckoff et al. 2005; Vallender
and Lahn 2007). The nonindependence between x and dS
arises because x 5 dN/dS; hence, sampling error in dS will
tend to generate a negative correlation between x and dS.
It seems possible this is why Li et al. (2009) observed negative correlations between x and dS in some of their simulated data. To remove this nonindependence, we divided
our genes into even and odd codons (Smith and EyreWalker 2003) and considered the correlation between
xODD and dSEVEN and the converse, xEVEN and dSODD.
When we do this, the correlation between x and dS is positive for all three species pairs when using d4 and NG methods (table 2). This is similar to results obtained by Vallender
and Lahn (2007) when they combined genes to reduce
sampling error. Independent of the method used to estimate substitution rate, x is significantly and positively correlated to dS (and d4) in mouse–rat and human–macaque
(table 2). For human–chimp, all the correlations are positive and most are significant; the exceptions are the correlations using the MG method, in which one correlation is
negative and the other positive but neither is significant.
The nonindependence of x and dS may explain the lack
of a strong positive correlation between human and mouse
observed by Liao and Zhang (2006); if we analyze the
human–mouse data of Schneider et al. (2009), we observe,
as Liao and Zhang (2006) did, a very weak positive correlation using the GY method (r 5 0.048, P , 0.0001); if we
use odd and even codons, the correlation becomes substantially stronger (r 5 0.086 and 0.087, P , 0.0001 in both
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Table 2. Table Shows the Correlation between x and dS When Genes Are Divided into Odd and Even Codons.
Method Used to Estimate Substitution
Rates for v and dS
GYv–GYdS
GYv–GYd4
NG–NGdS
NGvmod–NGdS
MGv–MGdS
Species Pairs
Mouse–Rat
10.1101***, 10.1103***
10.2062***, 10.2000***
10.1805***, 10.1841***
10.1880***, 10.1919***
10.0707***, 10.0755***
Human–Macaque
10.1216***, 10.1179***
10.2012***, 10.1897***
10.2748***, 10.2641***
10.2793***, 10.2889***
10.1144***, 10.1181***
Human–Chimp
10.0198 NS, 10.0306 **
10.0497***, 10.0322**
10.0339**, 10.0377**
10.1054***, 10.1126***
20.0019 NS, 10.0044 NS
NOTE.–All 9,942 genes from Schneider et al. (2009) were considered.
*P , 0.05, **P , 0.001, ***P , 0.0005, NS, not significant.
cases), but it is, nevertheless, weaker than the correlation
we observe in most other species pairs; this may be due to
the large divergence between human and mouse. Unless
otherwise specified, all subsequent analyses were performed splitting the data into odd and even codons.
Simulation Results
Estimates of ratios are typically biased because when the
denominator is small, the ratio becomes disproportionally
large. To investigate how the three methods perform in estimating x at low levels of divergence, we ran a series of
simulations; for each level of divergence, which varied between 0.0005 and 0.05, we simulated 1,000 sequences 900
bp in length. For each set of simulations (e.g., 1,000 replicates at a divergence of 0.0005), we calculated the mean DS
and the mean of x; the results are shown in figures 1–3
when x and dS are estimated using the GY, NG, and
MG methods, respectively. Our results show that all methods are statistically biased when sequence divergence is
low. Although the true x value should be 0.2, the mean
values for GY, NG, and MG have maximum mean values
of approximately 17, 0.26, and 1.1, respectively. The extreme overestimation of x by the GY method appears
to be largely due to genes with very low DS values (i.e.,
DS , 0.5) for which PAML often assigns a x value of
þ99. If we exclude those simulated sequence pairs that
have a DS , 0.5, we find that the bias in the GY x value
is very reduced and more similar to the NG method (figs. 1b
and 2a).
Note that the mean value of x is greater than the expected value even when DS is quite large (e.g., DS 5 8) for
all methods (figs. 1a, 2a, and 3a; expected x 5 0.2). This is
due to the fact that ratios tend to be overestimated. If we
modify x by adding one to DS, that is, xmod 5 dN/((DS þ
1)/S, we find that the estimate of x is less biased for all
methods (figs. 1c, 2b, and 3b), it also means that x can
be estimated for all genes using the NG method.
The estimates of x and xMod are likely to depend principally upon the absolute numbers of synonymous substitutions (DS) that are estimated to have occurred. To
investigate this, we reran our simulations on genes that
were twice as long; as expected the behavior of all methods
followed that for the shorter genes (supplementary fig. S1,
Supplementary Material online). We also see similar behavior if we rerun the simulations but with x 5 0.5 (supplementary fig. S2, Supplementary Material online). The bias
seems to depend upon the expected value of DS; when
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DS 5, there seems to be relatively little bias in the GY,
NG, or MG methods (figs. 1–3, supplementary figs. S1
and S2, Supplementary Material online).
Application to Empirical Data
The value of x tends to be overestimated by the GY and
MG methods and underestimated by the NG method
when divergences are low. Depending on the divergences
of genes under study, this may cause artifactual positive
and negative correlations. To check whether the positive
correlation between x and dS is due to statistical problems,
we reran the analysis on the different mammalian species
pairs, excluding genes below a certain sequence length x,
such that all genes longer than x had DSODD (if using xEVEN)
5, and, respectively, DSEVEN (if using xODD) 5. Unfortunately, this restriction leaves almost no genes within the
human–chimpanzee data set, so we do not consider this
data set further. For the mouse–rat and human–macaque
data sets, the correlation remains positive for all three
methods, that is, GY, NG, and MG (table 3). Hence, it seems
that the correlation, in these species pairs, is not due to
statistical bias in the estimation of x because when we remove most of this bias, the correlation remains. All subsequent analyses were done excluding genes below a length
such that for all genes DSODD (if using xEVEN) 5, and,
respectively, DSEVEN (if using xODD) 5.
Adjacent Substitutions
The correlation between x and dS could be due to a direct
link between nonsynonymous and synonymous substitutions, for example, by substitutions at adjacent sites. To investigate the effect of adjacent substitutions, we removed
all adjacent substitutions from the human–macaque and
mouse–rat data sets. This turns the positive correlation into a negative correlation, often significant, using all methods (table 4). This suggests that the positive correlation is
due to adjacent substitutions. The negative correlation
probably arises because some adjacent mutations occur
by chance alone and removing these induces a negative
correlation.
A large number of the adjacent substitutions are tandem
substitutions, which may be due to the simultaneous mutation of adjacent sites. Doublet mutations could induce
a positive correlation between x and dS because dS would
become partially dependent upon the constraint at nonsynonymous sites, if the rate of recombination between adjacent sites is low. As such, highly constrained genes have
Positive Correlation between dN/dS and dS in Mammals · doi:10.1093/molbev/msq320
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FIG. 1. The bias in the GY estimate of x. The figure shows the mean and standard error of x plotted against the mean value of DS for simulated
sequences of 900 bp in length. The true x value is 0.2. Each point represents the mean of 1,000 simulated sequences for a particular expected
level of divergence. (a) GY x, (b) GY x for genes with DS . 0.5, (c) GY xmod 5 dN/((DS þ 1)/S).
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FIG. 2. The bias in the NG estimate of x. The figure shows the mean and standard error of x plotted against the mean value of DS for
simulated sequences of 900 bp in length. The true x value is 0.2. Each point represents the mean of 1,000 simulated sequences for a particular
expected level of divergence. (a) NG x, (b) NG xmod 5 dN/((DS þ 1)/S).
low x values and also low values of dS. To investigate the
contribution of potential doublet mutations, we removed
all lineage-specific tandem substitutions; but the positive
correlation remains in both species pairs (table 4).
We also reran the analysis excluding not the adjacent
substitutions from genes but the whole genes that had adjacent substitutions. The positive correlation disappears for
the remaining 338 mouse–rat genes that had sufficient synonymous substitutions (GYd4: 0.1314* and 0.0641 NS).
Adjacent substitutions may be genuine but they may
also be artifacts of errors in sequencing, alignment, or exon
assignment. In order to investigate this further, we took
advantage of two subsets of the data analyzed by Schneider
et al. (2009), which they had subjected to two levels of quality control. In the first set, genes were retained if they were
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longer than 200 bp and all orthologs in the alignment were
less than 5% different in length; in the second set, good
genes had to have additionally high trace coverage, known
annotation status, and 100% alignment HoT scores. We
find that there is a significant positive correlation for both
species pairs in the first subset using all methods of estimating x and dS (table 5). Unfortunately, the second subset of data is sufficiently small that the analysis could only
be performed on mouse–rat. However, in this case, all correlations are positive and most are significant; the exceptions are using the GY and MG methods (table 5).
We note that the positive correlation disappears when
we exclude lineage-specific tandem substitutions from the
second high-quality subset of mouse–rat genes (table 6). In
contrast, when excluding only tandem substitution, in
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Positive Correlation between dN/dS and dS in Mammals · doi:10.1093/molbev/msq320
FIG. 3. The bias in the MG estimate of x. The figure shows the mean
and standard error of x plotted against the mean value of DS for
simulated sequences of 900 bp in length. The true x value is 0.2.
Each point represents the mean of 1,000 simulated sequences for
a particular expected level of divergence. (a) MG x, (b) MG xmod 5
dN/((DS þ 1)/S).
which one substitution occurs in each lineage, the positive
correlation remains (table 6). This difference is not a consequence of numbers because there are similar numbers of
lineage-specific and nonspecific substitutions—5,499 and
4,249, respectively. We further find that the ratio of double
to single substitutions per gene correlates strongly with x
(r 5 þ0.6987***) supporting their contribution to the correlation between x and dS.
Discussion
It has been shown, and we have confirmed, that x is significantly correlated to dS in mouse–rat and human–
macaque comparisons. We have explored two possible explanations for this surprising correlation: first, a statistical
bias in the estimation of x and second, substitutions at
adjacent sites. We show that the correlation between x
and dS remains, not surprisingly, if we control for nonindependence using odd and even codons because the nonindependence should generate a negative correlation. We
also show that the estimation of x is biased when sequence
divergence is low, and this could potentially cause the correlation. However, we find that this statistical bias is not the
primary determinant of the correlation. Instead the relationship between x and dS appears to be a consequence
of substitutions at adjacent sites.
The value of x is a simple and widely used measure of
selection pressure acting on protein-coding genes. Being
a ratio, however, there are potential difficulties with its estimation. We have shown that it is particularly difficult to
estimate x using the GY, NG, or MG methods when the
absolute number of synonymous substitutions is less than
five. There is a bias in the estimation of x when comparing
closely related species or genes; this could affect correlations between x and dS, and it may also have implications
for comparing x values between species that differ in their
level of divergence. Because the methods, which we used,
represent the extremes in terms of their statistical sophistication, it is likely that this behavior will be present in most
methods for estimating x. One may exclude genes below
a certain length such that DS . 5; unfortunately, however,
in closely related species such as humans and chimps, very
few genes have a sufficient number of synonymous substitutions to make a reliable estimation of x per gene. Another problem with estimating a ratio is that the
denominator must not be zero. Under heuristic methods
for estimating rates of synonymous and nonsynonymous
substitution, like NG, x is undefined when the gene does
not experience a single synonymous substitution. To get
around the exclusion of these genes, we suggest adding
one to the observed numbers of synonymous substitutions
for all genes (xMOD modified 5 dN/((DS þ 1)/S)). This simple correction has the added bonus of making the estimate
of x less biased for all methods, although we have not
shown that this is generally true, and there may be no estimate of x that is unbiased when there is little data. To
eliminate this bias when there is too little data, we suggest
summing the numbers of substitutions across genes before
calculating an average x for a group of genes.
Table 3. Table Gives the Correlation between x and dS.
Method Used to Estimate
Substitution Rates for v and dS
GYv–GYdS
GYv–GYd4
NGv–NGdS
NGvmod–NGdS
MGv–MGdS
Species Pairs
Mouse–Rat
10.1019***, 10.1089***
10.2011***, 10.2048***
10.1709***, 10.1865***
10.1746***, 10.1901***
10.0851***, 10.0834***
Human–Macaque
10.1426 ***, 10.1371***
10.1979 ***, 10.1939***
10.3025 ***, 10.3014***
10.3092***, 10.3077***
10.1351***, 10.1506***
NOTE.—To control for statistical bias in the estimate of x, we exclude genes below a length such that for all genes DS 5. For mouse–rat, we analyzed 4,706 genes with
length .1,218 bp, and for human–macaque, we analyzed 821 genes with length .3,000 bp.
*P , 0.05, **P , 0.001, ***P , 0.0005.
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Table 4. Table Gives the Correlation between x and dS.
Method Used to
Estimate Substitution
Rates for v and dS
GYv–GYdS
GYv–GYdS4
NGv–NGdS
NGvmod–NGdS
MGv–MGdS
Exclude Doublet
Mouse–Rat
10.0245 NS, 10.0210 NS
10.1227***, 10.1138***
10.0973***, 10.1016***
10.2217***, 10.2147***
10.0518 ***, 10.0437***
Exclude Any Adjacent
Human–Macaque
10.0635*, 10.0618*
10.1280***, 10.1308***
10.2348***, 10.2155***
10.3888***, 10.3639***
10.0119 NS, 10.0435 NS
Mouse–Rat
20.1329***, 20.1429***
20.0477**, 20.0478***
20.0551***, 20.0478***
20.0518***, 20.0443***
20.0341*, 20.0435**
Human–Macaque
20.1853***, 20.1579***
20.1335***, 20.1079***
20.0711***, 20.0228NS
20.0650*, 20.0172NS
20.0718*, 20.1334***
NOTE.—To investigate the effect of adjacent substitutions, we exclude first two, then all adjacent substitutions. To control for statistical bias in x estimates, we analyzed for
mouse–rat 5,020 genes with length greater than 1,202 bp and 4,805 genes with length greater than 1,251 when excluding doublet and all adjacent substitutions,
respectively. For human–macaque, we analyzed 1,202 genes with length greater than 2,748 and 963 genes with length greater than 3,000 bp when excluding doublet and all
adjacent substitutions, respectively.
*P , 0.05, **P , 0.001, ***P , 0.0005, NS, not significant.
Other statistical issues may be insufficient correction of
multiple hits or an effect of how dS is estimated. Saturation
in dS for some genes can cause an underestimate of dS and
an overestimate of x, thereby leading to a positive correlation between the two statistics. However, because the average synonymous divergence is fairly low in mouse–rat
(0.185) and human–macaque (0.079), this seems an unlikely explanation. Although correlations of dS with other
variables can be sensitive to the method used to estimate
dS, the results are generally independent of the method
used to estimate x and dS. In some cases, however, the
estimates from the GY and MG methods lead to nonsignificant results when the other methods are significant
(table 2 and table 4 mouse–rat subset 2 genes). The GY
method accounts for unequal codon usage when estimating the number of synonymous sites, implicitly assuming
that codon bias is mutational in origin. If codon bias is
due to selection it may provide a less accurate estimate
of the mutation rate (for detailed discussion, see Bierne
and Eyre-Walker 2003 and Yang 2006). It is therefore probably more appropriate to consider a measure of the synonymous substitution rate such as d4 that is an
estimate of the number of substitutions per physical site,
rather than per mutational opportunity.
It seems that although statistical issues of estimating x
might cause a positive correlation between x and dS, this is
not the principle reason for the observed correlation. The
positive correlation between x and dS appears to be due to
adjacent substitutions. Such an effect of adjacent substitutions is not unexpected: compared with single substitutions, adjacent substitutions affect higher proportions of
nonsynonymous sites and with increasing numbers of adjacent substitutions, dN increases more strongly than dS,
which causes x to increase with dS, leading to a positive
correlation between x and dS. It has been shown before
that models that allow multiple adjacent changes fit data
better than models which do not (Whelan and Goldman
2004; Higgs et al. 2007; Kosiol et al. 2007) and that positive
results of the branch-site test of selection for human and
chimpanzee lineages are often caused by codons with multiple nonsynonymous substitutions (Suzuki 2008).
Adjacent substitutions may have various origins. First,
adjacent substitutions may be a consequence of errors
in sequencing, exon assignment, annotation, or alignment.
Such errors may result in clustered substitutions and if the
amount of errors varies sufficiently between genes, it may
cause a positive correlation between x and dS. This is because errors will not differentiate between nonsynonymous
Table 5. Table Shows the Effect of Sequence, Annotation, and Alignment Quality on the Correlation between x and dS.
Method Used to Estimate Substitution
Rates for v and dS
Higher quality genes—first subset
GYv–GYdS
GYv–GYd4
NGv–NGdS
Ngvmod–NGdS
MGv–MGdS
Higher quality genes—second more
stringent subset
GY
GY–d4
NGv–NGdS
Ngvmod–NGdS
MG
Species Pairs
Mouse–Rat
Human–Macaque
10.0639**, 10.0547**
10.1446***, 10.1289***
10.1260***, 10.1233***
10.1299***, 10.1272***
10.0922 ***, 10.0672**
10.1644***,
10.2148***,
10.2783***,
10.2851***,
10.1330***,
10.1765***
10.2376***
10.2921***
10.2991***
10.1217***
10.0203 NS, 10.0126 NS
10.1142***, 10.0894**
10.0900 **, 10.0705 *
10.0943 ***, 10.0746 **
20.0164 NS, 10.0124 NS
Not sufficient data.
NOTE.—To control for statistical bias in x estimates, we analyzed for human–rat 2,315 genes with length greater than 1,000 bp and 1,188 genes with length greater than 909
bp in the first and second subset, respectively; For human–macaque, we analyzed 898 genes with length greater than 2,079 bp in the first subset; for the second subset,
there were not sufficient numbers of human–macaque genes left.
*P , 0.05, **P , 0.001, ***P , 0.0005, NS, not significant.
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Positive Correlation between dN/dS and dS in Mammals · doi:10.1093/molbev/msq320
MBE
Table 6. Table Shows the Effect of Tandem Substitutions on the Correlation between x and dS in the Second More Stringent Subset of HighQuality Mouse–Rat Genes.
Method Used to Estimate
Substitution Rates for v and dS
GYv–GYdS
GYv–GYd4
NGv–NGdS
Ngvmod–NGdS
MG
Exclude Lineage-Specific Tandem Substitutions
20.0642*, 20.0520 NS
10.0164 NS, 10.0259 NS
20.0025 NS, 10.0111 NS
10.0018 NS, 10.0147 NS
10.0456 NS, 10.0274 NS
Exclude Mosaics of Two
10.0218 NS, 10.0215 NS
10.1138***, 10.0966***
10.0889**, 10.0776**
10.0772**, 10.0995***
10.1813***, 10.1266***
NOTE.—Two types of tandem substitutions are considered: lineage-specific tandems and nonlineage-specific tandems, in which one substitution occurs in each lineage. To
control for statistical bias in x estimates, we analyzed for 1,191 genes with length greater than 899 bp and 1,216 genes with length greater than 909 bp.
*P , 0.05, **P , 0.001, ***P , 0.0005, NS, not significant.
and synonymous sites, whereas selection does. Therefore,
dN will increase proportionally more rapidly with error rate
than dS, so a positive correlation between x and dS will be
produced. We show that restricting our data to genes with
high-quality sequences, known annotation, and unambiguous alignments decreases the correlation between x and
dS, indicating a contribution of such errors to the correlation. However, albeit weaker, the correlation between x and
dS in mouse–rat is also present if we restrict our analysis to
those genes that are expected to bear few such errors.
Second, adjacent substitutions may result from mutational nonindependence—the correlation might, for example, be a consequence of simultaneous mutation of
adjacent nucleotides or of sites or regions of the genome
with higher rates of mutation. It is known that two adjacent
nucleotides mutate more together than by chance alone
(Wolfe and Sharp 1993; Averof et al. 2000), their rate, however, appears much smaller than initially estimated
(Kondrashov 2002; Silva and Kondrashov 2002; Smith
et al. 2003; Hodgkinson and Eyre-Walker 2010) and the
observed numbers of doublet substitutions may be partly
due to selection (Smith and Hurst 1999). Processes involving longer runs of simultaneous mutation are not known;
for example, in human polymorphism data two adjacent
single nucleotide polymorphisms (SNPs) are overrepresented but runs of three or four SNPs are not (Hodgkinson
and Eyre-Walker 2010). Also, there is no evidence that sequence- or template-directed mutagenesis, a mutational
mechanism that can simultaneously change several nucleotides, is operating in mammals (Ladoukakis and
Eyre-Walker 2007).
Finally, adjacent substitutions may be due to correlated
selection on adjacent sites. Such correlated selection may
arise if synonymous and nonsynonymous sites are part of
the same structure, for example, if a regulatory element exists within a gene and is under selection, or through the
action of selection on synonymous codons. Wyckoff
et al. (2005) performed simulations involving selection
on synonymous codons and inferred that such selection
could not induce a correlation between x and dS. However,
they assumed that the strengths of selection at synonymous and nonsynonymous sites were uncorrelated, and
it is clear that if this assumption is broken—as for selection
on motifs spanning synonymous and nonsynonymous sites
or on translational accuracy—then x and dS are likely to be
correlated. The precise form of this relationship depends
upon how the strengths of selection on synonymous
and nonsynonymous mutations are related. Negative selection could indirectly cause clusters of adjacent substitutions if only certain regions under less constraint are left
in a gene where mutations accumulate. But probably more
likely, we need to consider selective forces that might induce positive selection across a number of adjacent sites.
First, adaptive evolution of regulatory elements within
a gene could lead to multiple adjacent substitutions. Another obvious idea by Lipman and Wilbur (1985) relates to
optimal codon use. They noted that if the last letter of the
optimal or preferred codon differed between amino acids,
then a nonsynonymous substitution would often change
an optimal codon to a suboptimal codon and this could
then lead to an adaptive synonymous substitution. There
are generally not thought to be optimal codons in mammals; however, a recent study by Drummond and Wilke
(2008) shows higher optimal codon use at conserved—
potentially functionally important—amino acid sites in humans and mice. If such amino acids evolve adaptively, adaptive synonymous changes could follow. However, the
adjacent changes we consider may span multiple codons,
which cannot be explained by correlated evolution of dN
and dS within codon.
We have confirmed that there is a correlation between
x and dS in mouse–rat and human–macaque comparison.
Although errors in sequencing, annotation, and alignments
contribute, we have shown that the positive correlation is
at least in part due to genuine adjacent substitutions. The
remaining positive correlation in high-quality mouse–rat
gene alignments disappears when excluding lineagespecific tandem substitutions. Tandem substitutions and
hence the origin of the positive correlation may be of mutational or selective origin.
Supplementary Material
Supplementary fig. S1 is available at Molecular Biology and
Evolution online (http://www.mbe.oxfordjournals.org/).
Acknowledgments
We thank Paul Higgs and two anonymous referees for
many helpful and insightful comments on the manuscript,
Sergei Pond for help with HyPhy, and Bruce Lahn for helpful
1379
Stoletzki and Eyre-Walker · doi:10.1093/molbev/msq320
discussion. N.S. was supported by the International Union
of Biochemistry and Molecular Biology, the Munich Graduate School for Ecology, Evolution and Systematics, and the
Biotechnology and Biological Sciences Reseach Council
(BBSRC). A.E.W. was supported by the BBSRC.
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