Evolution of base-substitution gradients in primate
Sameer Z. Raina,1Jeremiah J. Faith,1,4Todd R. Disotell,2Hervé Seligmann,1
Caro-Beth Stewart,3and David D. Pollock1,5
1Department of Biological Sciences, Biological Computation and Visualization Center, Louisiana State University, Baton Rouge,
Louisiana 70803, USA;2Department of Anthropology, New York University, New York, New York 10003, USA;3Department of
Biological Sciences, University at Albany, State University of New York, Albany, New York 12222, USA
Inferences of phylogenies and dates of divergence rely on accurate modeling of evolutionary processes; they may be
confounded by variation in substitution rates among sites and changes in evolutionary processes over time. In
vertebrate mitochondrial genomes, substitution rates are affected by a gradient along the genome of the time spent
being single-stranded during replication, and different types of substitutions respond differently to this gradient. The
gradient is controlled by biological factors including the rate of replication and functionality of repair mechanisms;
little is known, however, about the consistency of the gradient over evolutionary time, or about how evolution of
this gradient might affect phylogenetic analysis. Here, we evaluate the evolution of response to this gradient in
complete primate mitochondrial genomes, focusing particularly on A⇒G substitutions, which increase linearly with
the gradient. We developed a methodology to evaluate the posterior probability densities of the response parameter
space, and used likelihood ratio tests and mixture models with different numbers of classes to determine whether
groups of genomes have evolved in a similar fashion. Substitution gradients usually evolve slowly in primates, but
there have been at least two large evolutionary jumps: on the lineage leading to the great apes, and a convergent
change on the lineage leading to baboons (Papio). There have also been possible convergences at deeper taxonomic
levels, and different types of substitutions appear to evolve independently. The placements of the tarsier and the tree
shrew within and in relation to primates may be incorrect because of convergence in these factors.
[Supplemental material is available online at www.genome.org.]
Nucleotide frequencies in mitochondrial DNA vary considerably
across mammalian lineages (Honeycutt et al. 1995; Gissi et al.
2000). This creates considerable difficulties for phylogenetic in-
ference, including biased attraction of branches leading to spe-
cies with similar frequencies (Van Den Bussche et al. 1998; Reyes
et al. 2000; Wiens and Hollingsworth 2000). Rates of evolution
also vary (Honeycutt et al. 1995; Gissi et al. 2000), but it is un-
clear how rates and nucleotide frequencies are related; few stud-
ies have gone into these processes in detail. In reconstruction of
deep primate phylogeny, variation in frequencies and rates is
believed to cause consistent biases (Felsenstein 1978, 2001; Lock-
hart et al. 1992; Graybeal 1993; Meyer 1994; Yoder et al. 1996),
but the reasons are unclear (Philippe and Laurent 1998) and it is
uncertain how it should be taken into account. The underlying
evolutionary mechanism has presumably changed, but how?
One important factor, only recently clarified, is that different
mutation types respond differently to a gradient of single-
strandedness that is generated during mitochondrial replication
(Faith and Pollock 2003). Thus, it is insufficient to assume that
relationships among substitution types are constant across sites
or across evolutionary time, and targeted methods are needed to
evaluate the response to single-strandedness in individual ge-
It is known (Clayton 1991, 2000; Tanaka and Ozawa 1994;
Reyes et al. 1998; Faith and Pollock 2003) that the asymmetric
nature of mitochondrial DNA replication leads to a gradient in
duration of single-strandedness, DssH, and a gradient in suscep-
tibility to mutation (for review, see Faith and Pollock 2003). The
proportional time that a site spends single-stranded can be pre-
dicted (see Methods). Although there is some controversy over
this mechanism of replication (Holt et al. 2000; Yang et al. 2002;
Bowmaker et al. 2003; Holt and Jacobs 2003), a preponderance of
biochemical evidence (Bogenhagen and Clayton 2003a,b) and all
evolutionary analyses (Faith and Pollock 2003) support the “clas-
The single-stranded state is particularly prone to deamina-
tions, especially deaminations of cytosine (C) and adenine (A),
which cause transitions to thymine (T) and guanine (G) on the
heavy strand (Asakawa et al. 1991; Tanaka and Ozawa 1994;
Reyes et al. 1998). Since transition rates are much greater than
transversion rates, these excess transitions lead to higher G/A and
T/C ratios than in their absence. Frederico found that C is very
unstable (Frederico et al. 1990, 1993), and the T/C ratio (or con-
versely, the A/G ratio on the light strand) increases quickly with
increasing DssH, apparently saturating at low values of DssH
(Faith and Pollock 2003). The deamination of A⇒hypoxanthine
(which is replaced by G) is a slower process (Tarr and Comer
1964; Parham et al. 1966; Krasuski et al. 1997), and the gradient
4Present address: Bioinformatics Program, Boston University, Bos-
ton, MA 02215, USA.
E-mail email@example.com; fax (225) 578-2597.
Article and publication are at http://www.genome.org/cgi/doi/10.1101/
15:665–673 ©2005 by Cold Spring Harbor Laboratory Press; ISSN 1088-9051/05; www.genome.org
in DssH causes differences among genes in the rate of
A⇒hypoxanthine deaminations on the heavy strand. This results
in differences in the C/T ratio along the light strand (Limaiem
and Henaut 1984; Delorme and Henaut 1991) and in differences
in compositional bias, particularly at third codon positions and
noncoding sites (Jermiin et al. 1994, 1995; Tanaka and Ozawa
1994; Reyes et al. 1998).
Although skew is a sensitive means of detecting differences
among genes, the two standard skew measures (Perna and Kocher
1995) blend the effects of the two major
single-stranded transitions. Faith and
Pollock (2003), using maximum likeli-
hood (ML) analyses of 45 vertebrates,
found strong evidence that A⇒G substi-
tution rates increase linearly with DssH,
while other substitutions do not. C⇒T
substitutions are more prevalent, but are
uniformly high along the genome and
thus contribute little to differences in
nucleotide content along the genome.
Although it has been traditional (Li-
maiem and Henaut 1984; Tanaka and
Ozawa 1994; Reyes et al. 1998; Faith and
Pollock 2003) to refer to substitutions
and base frequencies with respect to the
light strand, here we will refer to them
based on the complementary heavy
strand as in Krishnan et al. (2004b).
Since the excess mutations occur on the
heavy strand, this reduces the potential
for confusion in the results and discussion, but differentiates our
discussion from that in other papers.
Our current understanding of the evolutionary processes
leading to mutational asymmetry in mitochondria suggests a
means to better understand it. The slope of the G/A gradient is
presumably an inverse function of the rate of replication and
therefore inversely proportional to the efficiency of polymerase-?
(the replicating enzyme in vertebrate mitochondria). The inter-
cept of the gradient is presumably a function of the G/A ratio in
the absence of single-strandedness and the rate at which light-
strand synthesis is initiated (which, in turn, might be affected
by both the shape of the origin of replication and the binding
abilities of the polymerase-? accessory subunit). For other sub-
stitution types, particularly C⇒T, repair mechanisms (Meyer
1994) may alter the slope and intercept, and probably the lin-
earity of response; when functioning efficiently they may
completely eliminate any detectable response to single-
We present here a study of the variation in nucleotide ratio
gradients among primates and two outgroups. The primates,
with 16 complete mitochondrial genomes, are the most densely
sampled vertebrate order, and generally have an increased rate of
evolution relative to other mammals (Gissi et al. 2000). We fo-
cused on the heavy-strand G/A gradient at third codon positions,
since there is a strong expectation that it will increase linearly
with DssH. We also report on the heavy-strand C/T and pyrimi-
dine/purine [Y/R = (C+T)/(A+G)] ratios, and on G/A gradients at
the first and second codon positions. We developed likelihood-
based methods to evaluate the response to single-strandedness. A
joint Bayesian and ML approach was used to evaluate the among-
species differences in response to DssH, and both mixture model
and hierarchical clustering methodologies were used to evaluate
whether different species evolved in similar fashions. With these
tools, we were able to detect and explain divergence and conver-
gence of base frequencies among primates, and thus were able to
provide a causal explanation for possible phylogenetic recon-
struction bias in parts of the tree. To maintain the clarity of the
results narrative, we have placed a great deal of the raw results
from the likelihood analysis in Supplemental data tables, and
reserve the figures and tables presented in the main paper for
critical interpretive information.
in primates and two outgroups
Maximum likelihood values and 95% CI for slopes and intercepts of G/A gradients
SpeciesMax like SlopeIntercept
Pongo pygmaeus abelii
Pongo p. pygmaeus
0.860 (0.228, 1.561)
0.925 (0.363, 1.490)
1.061 (0.491, 1.645)
1.187 (0.578, 1.794)
0.661 (0.110, 1.740)
1.541 (0.502, 2.543)
1.544 (0.735, 2.331)
1.729 (1.216, 2.319)
1.586 (0.962, 2.179)
1.494 (1.039, 2.018)
0.525 (0.195, 0.904)
0.415 (0.190, 0.630)
0.344 (0.091, 0.642)
0.965 (0.609, 1.329)
0.607 (0.359, 0.883)
0.708 (0.420, 0.994)
0.694 (0.303, 1.122)
1.132 (0.582, 1.658)
2.204 (1.768, 2.710)
1.761 (1.403, 2.176)
1.686 (1.326, 2.126)
1.622 (1.266, 2.056)
3.096 (2.443, 3.636)
2.417 (1.853, 3.155)
2.077 (1.643, 2.623)
1.197 (0.906, 1.531)
1.451 (1.134, 1.832)
1.087 (0.830, 1.384)
1.104 (0.893, 1.351)
0.695 (0.567, 0.847)
0.947 (0.743, 1.144)
0.906 (0.709, 1.147)
0.688 (0.536, 0.870)
0.844 (0.673, 1.048)
1.258 (1.006, 1.557)
1.553 (1.224, 1.955)
two near outgroups. Third codon positions containing G/A were grouped
into 20 equal-size bins for each genome, and the ratio of G/A in each bin
is graphed versus the average DssH for that bin.
G/A ratios for complete primate mitochondrial genomes and
Raina et al.
Evolution of G/A gradients
Our expectation, based on a joint analysis of complete vertebrate
genomes (Faith and Pollock 2003), was that synonymous sites in
individual primate genomes would have a linear relationship be-
tween the heavy-strand G/A ratio and the time spent single-
stranded. Markov chain Monte Carlo (MCMC) runs on indi-
vidual genomes showed significantly positive slopes in all cases
(Fig. 1; Table 1). There was considerable variation among ge-
nomes in both slope and intercept, and values for many pairs of
species were apparently different in that they lay outside their
respective 95% credible intervals (Table 1). Comparisons of null
models with one response curve per pair of genomes to models
with independent response curves for each genome in a pair
showed that, based on the ?2
have significantly different responses to time spent single-
stranded (Supplemental Table A). To obtain a better idea of the
meaning of this variation, we clustered species based on their
G/A ratio responses using both a hierarchical clustering approach
and a mixture model analysis with between two and eight mix-
ture models. It is useful to compare and combine the two ap-
proaches, since hierarchical clustering may be order-dependent,
while significance levels for the mixture models have uncertain
validity (McLachlan and Peel 2000).
In the hierarchical clustering (Fig. 2A; Table 2), merging of
the species into one large set of species (Group 10) and five spe-
cies pairs (Groups 5–9) was not rejected at the 0.05% significance
level (for further details, see Supplemental Discussion of Results).
Species in these groups were sometimes but not always closely
related to one another. At moderately large cost (?lnL < 10.0),
these groups could be merged to form four new groups (Groups
11–14). The next two mergers were more incredible
(45 > ?lnL > 60), while all primates and outgroups could only be
merged together as one group at an extremely unbelievable cost
of ?lnL = 497. Other interesting points are that the intercept
tended to matter more in clustering than the slope, and as ex-
2distribution, most pairs of genomes
pected, clusters were more easily joined when a slightly smaller
intercept was balanced with a slightly bigger slope.
In mixture model analyses, all species were evaluated simul-
taneously (the outgroups were excluded), and the best set of
models was determined (Supplemental Table C). In these analy-
ses, the posterior probability that data from each species were
generated by each model can be calculated (equation 5). Accord-
ing to this criterion, species were mostly associated with a par-
ticular model, although there was some variance in the posterior
for the five and six model cases (data not shown). Clustering in
the mixture models is obviously related to the results from the
hierarchical analysis, but owing to the nonhierarchical nature of
the mixture analysis, switches in alliances among groups can
occur for different numbers of clusters (for more details, see
Supplemental Discussion of Results). The mixture analysis shows
that different species often share posterior allegiances between
models, particularly when the ML slope and intercept values of
the species are adjacent to one another (Fig. 3). If the mixture clus-
ters are mapped onto a phylogenetic tree (Fig. 4), it is clear that
the baboons, and to some extent all of the Old World monkeys,
have converged to a similar response curve as the hominoids.
An interpretation of the evolution of the G/A response
curves can now be made (Fig. 5). The three deepest diverging
primates, Lemur, Nycticebus, and Tarsius (strepsirrhines and
tarsier), have similar slopes and intercepts, with some variation.
In the transition to the anthropoid primates (including cebids
and colobines), intercepts remained similar, but the slopes nota-
bly decreased. In apparently convergent events, the Old World
monkeys (baboon, vervet, and macaque) increased their slopes
and intercepts, as did the lesser and great apes. The hominoids
are tightly clustered in intercepts (with the exception of Homo),
and fairly clustered in slopes, but the orangutans and gib-
bon have the highest intercepts among the primates, and their
slopes cover the extremes of the range among greater and les-
ser apes. Interestingly, the outgroup Cynocephalus is very similar
to the gorilla, while the other outgroup, Tupaia, is closest to
Summary of hierarchical clustering results for
Likely clusters (?LnL < 3.0)
5 Orangutans (Ppy, Pab)
6Colubine and loris (Cgu, Nco)
7 Human and gibbon (Hsa, Hla)
8 Langur and lemur (Tob, Lca)
9 Capuchin and tarsier (Cal, Tba)
Flying lemur (Cva; outgroup), chimpanzees and gorilla (Ptr,
Ppa, Ggo; great apes), baboon and macaque (Pha, Msy; Old
Vervet monkey (Cae), tree shrew (Tbe)
More unlikely clusters (3.0 < ?LnL < 10.0)
11Tbe and Group 6
12 Cae and Group 10
13Group 5 and Group 7
14Group 8 and Group 9
Incredible clusters (?LnL > 10.0)
15Group 11 and Group 14
16Group 12 and Group 13
clusters in ratio cluster analyses. We performed mixture (A) and hierar-
chical analyses (B) of G/A ratios, and hierarchical analyses of (C) C/T and
(D) Y/R ratios. Groups are labeled by their order of clustering.
Graph of MLE slopes versus MLE intercepts along with major
Evolution of substitution gradients in primates
Evolution of C/T and Y/R gradients
Although the C/T ratio did not show a clear slope in our earlier
study (Faith and Pollock 2003), we performed individual and
hierarchical analyses on the C/T ratio response to single-
strandedness to determine if there was any variation in the level
of asymmetry or the existence of a slope among the primates
(Supplemental Tables D and E). We also performed these analyses
on the Y/R ratio at 4? redundant third codon positions to see if
there was detectable variation in slopes and intercepts for trans-
versions (Supplemental Tables F and G). As in the G/A analysis,
various clusters were significant at different significance levels,
although in the C/T analysis, there were only three discrete clus-
ters that were not rejected at the 0.05% significance level (Table
3). Results with the C/T ratio are tentative because of the non-
linear response, and indeed, there is considerable complexity in
the evolution of this response curve (Krishnan et al. 2004c).
In the Y/R ratio analysis, Tupaia was the only organism with
a significant slope (Fig. 2D; Table 3; Supplemental Table F).
Tupaia had an even ratio of pyrimidines to purines at zero DssH,
but had a positively increasing bias toward pyrimidines with in-
creasing DssH, and did not group with the likely clusters. The
generally flat slopes in the primates provided little evidence for
excess transversion mutations in response to single-strandedness,
although the significant slope in Tupaia is preliminary evidence
that such a response can exist in some organisms (and is perhaps
usually controlled by efficient repair mechanisms). Interestingly,
Tarsius did not group with the strepsirrhines and outgroups
based on the Y/R ratio, while the deepest-branching New World
monkey, Cebus, did, although the differences between the tarsier
and Lemur were not large (Supplemental Tables F and G).
The bias toward purines in the apes and most monkeys in-
dicates a derived trend. Although such a bias cannot occur in a
perfectly symmetric mutation model (where the mutation pro-
cesses are equivalent on both strands), the strong and consistent
transition bias against C (described above) could conceivably cre-
ate a transversion bias through secondary effects without any
alteration in transversion rates. The pattern of species with this
bias did not match the pattern of species differences in the C/T
bias, however; thus, it seems probable that there may have been
a derived change in the rates of at least one type of transversion.
It is also possible that these differences could be due to derived
changes in the degree of codon bias or some other form of selec-
tion on synonymous sites, although it seems implausible that
such selective alternatives could explain the positive slope in
Correlation of first, second, and third codon positions,
and comparison of phylogenetic trees
Evolutionary changes in the number of deaminations in the
single-stranded state may also affect first and second codon po-
sitions, but because many more changes at first codon positions
and all changes at second codon positions are nonsynonymous,
they are constrained by selection at the amino acid level. At first
codon positions, nine out of 18 slopes are significantly greater
than zero, while for second codon positions no individual slopes
are significant. Nevertheless, linear regressions of the G/A ratio
slope plus intercept of both first and second codon positions on
third codon positions (Fig. 6) are extremely significant (both
probabilities are <0.001). Although the regression slopes are
much less than one, particularly for the slow-evolving second
codon positions, this result indicates, not surprisingly (Thomas
and Wilson 1991; Kondo et al. 1993), that nucleotide biases in
mutation rates also affect amino acid substitution rates, presum-
ably mostly for neutral or nearly neutral substitutions.
model for the five-model mixture. The posterior probabilities are aver-
aged across 10 independent chains. The models in descending order of
magnitude of intercept are black (Group S), gray (Group T), white (Group
U), diagonal lines (Group V), and gray hatch (Group W). Group identifi-
cations are the same as in Figure 2B.
Posterior probabilities for each species to belong to each
of the primate species used in this study. This is the primate phylogeny
most compatible with the mitochondrial sequences, but is probably in-
accurate in some topological details (see Methods). Arrows indicate pos-
sible locations of large changes in the response curve, and are labeled to
match the mixture model clusters in Figure 2B. A double-headed arrow is
used between the flying lemur and the rest of the species to indicate the
slight ambiguity in its outgroup status, as discussed in the text. Clusters
shown are for the model with five clusters, except that clusters V and W
have similar slopes and intercepts, and are grouped into cluster Z as in the
G/A mixture model groups mapped onto a phylogenetic tree
Raina et al.
668 Genome Research
Evolutionary changes in biases in nucleotide and amino
acid composition may affect phylogenetic reconstruction with
mitochondrial data (Felsenstein 1978, 2001; Lockhart et al. 1992;
Graybeal 1993; Meyer 1994; Yoder et al. 1996). The nucleotide
data strongly support a tree (Fig. 7A) that is not consistent with
most current views of primate phylogeny (Fig. 7C), although read
Arnason and colleagues for an alternative viewpoint (Arnason et
al. 2002). The amino acid data support a tree (Fig. 7B) that is only
slightly improved relative to morphological expectations (Fig.
7C), and that is also the second-best tree in terms of DNA-based
likelihood scores. Support for the favored tree is good, both in
terms of relative likelihood scores compared to the expected tree
and alternative intermediates (Fig. 7), and in terms of neighbor-
joining bootstrap and Bayesian posterior probability support for
The results of this study provide details on the evolution of the
response of various substitutions to the gradient of single-
strandedness encountered during mitochondrial replication. For
simplicity, we refer to evolution of this response as “gradient
evolution” and the combined slope and intercept as the “re-
sponse curve.” Gradient evolution was mostly phylogenetically
consistent, but there are clear instances of convergent changes in
the response curve. Since changes in equilibrium base frequen-
cies are the necessary outcome of evolution of the mutation spec-
trum, and because evolution of base frequencies can dramatically
mislead phylogenetic analyses (Felsenstein 1978, 2001; Lockhart
et al. 1992; Graybeal 1993; Meyer 1994; Yoder et al. 1996), this
result may explain some difficulties in primate phylogenies de-
termined by mitochondrial analysis. In particular, the two sup-
posed nonprimate outgroups, the tree shrew (Tupaia) and the
flying lemur (Cynocephalus), do not cluster; this means either that
physiological and nuclear evidence (Disotell 2003), including re-
petitive elements (Schmitz et al. 2002b), is wrong, that mito-
chondria have a dramatically different phylogeny (Arnason et al.
2002) from nuclear genes, or that the inferred mitochondrial tree
is an artifact of mutational convergence in mitochondria. Recent
evidence indicates that repetitive elements in the primates are
extremely good markers with almost no phylogenetic contradic-
tions (Salem et al. 2003; Ray et al. 2004). Furthermore, the con-
troversial placement (Schmitz et al. 2001; Yoder 2003) of the
tarsier as sister group to the strepsirrhines rather than to the
anthropoid primates (if the flying lemur is used as an outgroup,
or as the sister group to all other primates if the tree shrew and
other mammals are used as an outgroup) (Arnason et al. 2002)
may well also be an artifact of mutational convergence.
By placing these mutational convergences in the context of
response to structural aspects of the replication system, we are
able to provide considerable explanatory power to what is oth-
erwise a confusing mixture of outcomes of these processes (i.e.,
the average nucleotide frequencies reached at dynamic equilib-
rium). The response curves for different mutation types that oc-
cur in the single-stranded state are controlled by at least three
biological factors, including the rate of replication (presumably
controlled by the functionality of polymerase-?), the rate of ini-
tiation of light-strand synthesis, and the existence and activity of
specific repair or protection mechanisms. Differences in pro-
tection and repair almost certainly underlie the differences
between C⇒T and A⇒G substitutions, and repair seems ne-
cessitated by the high rate of C⇒T mutations that would
otherwise occur at functional sites. In cases in which the poly-
merase is apparently highly efficient (e.g., the prosimians), repair
may be less critical than in the case of, for example, humans,
where the A⇒G response slope is steep, and polymerase is pre-
sumably less efficient. We do not, however, find any clear asso-
ciations of low A⇒G slopes with details of the C⇒T response
curve. It would be interesting to know whether rates of polymer-
ization in various species are accurately predicted by the A⇒G
The tools we have presented here are useful for comparative
analysis and documenting the extent and range of evolution of
mutational responses. The earlier observation of an average lin-
Summary of hierarchical clustering results for C/T and
Likely clusters (?LnL < 3.0)
8Lemur (Lca) and tarsier (Tba)
12 Pygmy chimpanzee (Ppa) and capuchin (Cal)
13Human (Hsa), orangutans (Ppy, Pab), chimpanzee (Ptr),
gorilla (Ggo), vervet monkey (Cae), macaque (Msy),
colubine(Cgu), langur (Tob)
14Baboon (Pha), flying lemur and tree shrew (Cva, Tbe;
outgroups), gibbon (Hla), loris (Nco)
More unlikely clusters (3.0 < ?LnL < 10.0)
15Group 12 and Group 13
Incredible clusters (?LnL > 10.0)
16 Group 14 and Group 15
Likely clusters (?LnL < 3.0)
6 Human (Hsa), chimpanzees and gorilla (Prt,
Ppa, Ggo; great apes), orangutans (Ppy, Pab)
12Gibbon (Hla), langur (Tob), baboon (Pha),
colubine (Cgu), vervet monkey (Cae),
tarsier (Tba), macaque (Msy)
14Loris and lemur (Nco, Lca; prosimians), capuchin (Cal),
flying lemur (Cva; outgroup)
Tree shrew (Tbe)
Incredible clusters (?LnL > 10.0)
15Group 6 and Group 12
16 Tbe and Group 14
groups showing a summary interpretation of G/A evolution. Arrows in-
dicate possible changes in response curves, and are discussed in the text.
Graph of MLE slopes versus MLE intercepts along with major
Evolution of substitution gradients in primates
ear response of A⇒G substitutions in the vertebrates was based
on a gene-by-gene analysis using phylogeny-based ML tech-
niques (Faith and Pollock 2003), but our ability to assess the
strength of the response in individual genomes with our likeli-
hood approaches is surprisingly good. Based on our current
analysis, incorporation of a gradient evolution model directly
into phylogeny-based likelihood analysis, which could include
allowing for changes in the strength of response along the
phylogeny, will be necessary to obtain accurate estimates and
variances for topology and divergence times. Although this en-
tails considerable challenges, since the mutation process is
different at every site in the genome, the expected power and
accuracy of such a method are much greater than for existing
methods. The consistency of the change in response to the gra-
dient of single-strandedness may potentially allow the develop-
ment of what would be a unique mixture of nonstationary mod-
els with differences in the substitution process at every site in a
The existence of these substitution gradients along the ge-
nome that vary with substitution type and over time helps make
a strong argument for dense taxonomic sampling, that is, “ge-
nomic biodiversity” (Pollock et al. 2000), even stronger. Higher-
density sampling allows for more accurate prediction of site-
specific rates in complex models, and more accurate prediction of
site-specific differences can be extremely beneficial to phyloge-
netic reconstruction using likelihood-based techniques (Pollock
and Bruno 2000). If the taxa sampled are closely related, a more
accurate description of the mutation process should be obtained
(Bielawski and Gold 2002). Furthermore, increased taxonomic
sampling would allow more precise delineation of evolution of
the gradient. We have developed a phylogeny-based Bayesian
analysis to more precisely model the evolution of these gradients
(Krishnan et al. 2004a,c), and greater amounts of taxon sampling
will allow better direct inference of ancestral gradients, as well as
better descriptions of the response curves for other substitutions
besides A⇒G, which are clearly nonlinear (Faith and Pollock
Other potentially important effects of these gradients, and
the evolution of these gradients, that should be considered are
what kind of effect they have had on amino acid substitutions,
whether they can be incorporated into codon-based models, and
whether they substantially affect our ability to detect selection
and adaptation in mitochondria using synonymous versus non-
synonymous substitution ratios. They may also affect how syn-
onymous and nonsynonymous ratios are used in population ge-
netics to understand how selection affects polymorphism levels.
Since mitochondria are so closely tied to metabolism and
energy consumption, it is relevant to consider whether the ob-
served evolutionary changes might be tied to concurrent changes
in physiology. The G/A response intercept has a significant posi-
tive slope when regressed against gestation time (Fig. 8A)
(P < 0.01), and the R/Y response slope versus gestation time is
significantly negative (Fig. 8B) (P < 0.01). In both of these cases,
there are weaker relationships with other physiological factors
that are themselves highly correlated with gestation time, includ-
ing brain weight, longevity, and body mass at birth. The reasons
for these relationships, although interesting, remain highly
speculative. To accurately dissect causal factors and determine
statistical significance will require higher-density sampling
within primates and among other vertebrates and more examples
of large-scale changes in gradient response curves, and more ex-
amples of large changes in brain weight, longevity, body mass at
birth, and/or gestation time.
Analysis of single genomes
All complete primate mitochondrial genomes available at the
time this study was initiated were used (Table 4). As outgroups,
we included the complete genomes of the flying lemur and the
tree shrew. For all genomes, individual protein-coding genes
were extracted and concatenated, and codon positions were de-
termined automatically using C programs or Perl scripts. The
relative duration of time spent single-stranded at any position in
the mitochondrial genome can be predicted based on the stan-
dard model of replication and the relative locations of the heavy-
strand replication (OH) and the origin of light-strand replication
tions. The MLE estimators of slope plus intercept response curves for each
species in the analysis for first codon positions (diamonds) and second
codon positions (circles) versus third codon positions. The regression line
is shown, and the slope, intercept, and R2values are shown adjacent to
Regression of slope plus intercept for different codon posi-
verging primate groups and outgroups. Bootstrap values for the DNA-
based NJ analysis are shown on (A) when <100%. Posterior probabilities
for the nucleotide Bayesian analysis were 100%, and the one branch
<100% in the amino acid analysis is shown in (B). The likelihood is shown
for (A), the most likely topology under the DNA-based analysis, and differ-
ences from the most likely tree are shown underneath topologies (B–E).
Comparison of the most likely trees relating the deeply di-
Raina et al.
(OL) (see above and Faith and Pollock 2003). A normalized mea-
sure of the estimated time spent single-stranded, DssH (Tanaka
and Ozawa 1994), is given in units of the (unknown) time it takes
the polymerase to travel once around the genome.
Likelihoods of slopes and intercepts in the mutational re-
sponse to single-strandedness for individual species were calcu-
lated as follows: based on a model (M) and set of parameters (?),
the likelihood of a particular genome was calculated by multi-
plying across sites, i, in a sequence from species m, (Si
where ?(Ci) is a ? function equal to zero or one depending on
whether the site was in the class of interest (e.g., third codon
positions of 4? redundant codons). For simplicity and clarity,
the M will henceforth be dropped from equations and considered
implicit, as will the ?(Ci). Synonymous third codon positions
were used to obtain sites that were least likely to have been af-
fected by selection, although first and second codon positions
were also analyzed for comparison. Frequency ratios arising from
each pair of reciprocal transitions (G⇔A and T⇔C) were ana-
lyzed separately, as was the ratio arising from transversions be-
tween nucleotide classes (Y⇔R) for 4? redundant third codon
Since G/A ratios are thought to increase linearly with DssH,
it is reasonable, particularly for the G/A ratio, to build a simple
linear model of increase in these ratios, and determine what plau-
sible values are for the slope (?) and intercept (?). Thus, if DssHi
is the calculated DssH value at site i for sequence m, and ? is the
vector of unknown parameters in the model, then
m| ?? = P?Si
For an example using the G/A ratio, f(G/A)i= ?DssHi
P(G)i= f(G/A)i/[1 + f(G/A)i], and P(A)i= 1 ? P(G)i. For each indi-
vidual genome, a Markov chain was run using the Metropolis-
Hastings Monte Carlo algorithm to sample the posterior prob-
ability space (Metropolis et al. 1953; Hastings 1970),
P?? | Sm? =
The prior probabilities, P(?), were assumed to be flat, uninforma-
tive priors, with ? ranging from ?? to ?, and ? ranging from 0 to
?. Proposals for ? and ? where f(G/A) < 0 for some DssHi
excluded. Parameter proposals in the Markov chain were distrib-
uted uniformly (∼U[??, +?]) about the current state, with the
magnitude of ? equal to 0.3 for both ? and ?; values of ? were
chosen so that between 30% and 80% of the proposals were
accepted. The 95% credibility interval was obtained by excluding
the 2.5% most extreme values on either side of the mean, and the
maximum for the run was taken as an estimate of the ML value.
The chain was run for 100,000 generations, where the first 1000
generations were removed as burn-in. The rest of the generations
were sampled at every 100-th spot in the chain. All chains were
run 10 times with different seed values to detect any differences
in ML values or distributions across runs. All likelihood values
were stored and reported as natural logarithms.
Analysis of multiple genomes
To determine the similarity of genomes in their evolutionary
patterns, Markov chains were also run over multiple genomes
simultaneously in hierarchical and mixture model clustering
schemes. In the hierarchical clustering scheme, single sets of ML
estimators (MLEs) of slope and intercept for a group of genomes
were determined jointly. The process began with the testing of all
pairs of genomes, and the difference in log likelihoods (or log of
the likelihood ratio) (?lnL) between the combined and separate
calculations was found. The sequences forming a union with the
smallest ?lnL were then combined into one set. In subsequent
stages, likelihoods and MLEs were calculated for the unions of all
figures, and accession numbers for sequences used
Common names, scientific names, abbreviations used in
Common nameSpecies Abb.Accession
Black & white colobus
Northern tree shrew
Malayan flying lemur
Pongo pygmaeus abelii
Pongo p. pygmaeus
aIngman et al. 2000;bHorai et al. 1995;cXu and Arnason 1996;dArnason
et al. 1996;eArnason et al. 2000;fArnason et al. 1998;gRaumm et al.
2005;hArnason et al. 2002;iSchmitz et al. 2000;jSchmitz et al. 2002a.
gestation time. The slope, intercept, and R2values are shown next to the
Linear regression of (A) G/A intercept and (B) R/Y slope versus
Evolution of substitution gradients in primates
new pairs or sets, and again sequences from the union with the
smallest ?lnL were combined into a single set for the next stage.
Thus, the species or groups of species were made to cluster in a
hierarchical fashion until only one set existed. Since twice the
?lnL for combining sets can be approximated as a ?2distribution
with two degrees of freedom, ?2
likelihood differences as a measure of confidence in the forma-
tion of clusters.
In another clustering scheme, a Markov chain was run on
third codon positions in the complete primate data set using a
series of mixture models (the outgroups were not included in this
scheme). In any one implementation of this method, a predeter-
mined number of models (K) were allowed to exist, with the
constraint that the models were ordered by strength of intercept
to avoid problems of identifiability. The mixture density for a
genome can be written as,
2(Rice 1995), we used the log
P?Sm| ?? =?
where ? is the vector containing all the unknown parameters in
the mixture model, that is, all ?kand ?k, and the different models
were given even and constant mixing proportions, ?k= 1/K. The
? value for updating both the ? and ? parameters was 0.3/√K¯, and
overall likelihoods were calculated by multiplying the likeli-
hoods for each genome. At any time point (i.e., for any set of
parameters, ?) it is possible to calculate the posterior probability
that a particular model applies to a particular species
P?Mk| Sm? =
P?Sm| ?k?P??k| Mk?P?Mk?
P?Sm| ?k?P??k| Mk?P?Mk?
Mixture models were run with two to eight mixed models. The
log likelihoods for these models are presented, but ?lnLs for mix-
ture models are not necessarily distributed as ?2(McLachlan and
Peel 2000), and determining the appropriate number of mixture
models is one of the more difficult problems in statistics. The
improvement in ?lnL going from six to seven models was slight
(only 4.12), and with seven models sequences had mixed affili-
ation among models. Accordingly, we limit results to six mixed
Phylogenetic trees were obtained using the combined sequences
of all 12 proteins coded on the light strand. A neighbor-joining
tree was obtained from DNA sequences using the general time-
reversible (GTR) model in Paup* (Swofford 2000). ML DNA and
amino acids were found using GTR models in MrBayes (Huelsen-
beck and Ronquist 2001). The topologies are similar and largely
uncontroversial except for the deeper nodes (Schmitz et al.
2002b; Yoder 2003). To obtain comparative likelihood values, we
also ran an ML analysis (based on DNA sequences and the GTR
model) using the lscore function in Paup*. We also evaluated
topologies intermediate between these and an alternative esti-
mate of the “true” phylogeny (Schmitz et al. 2002b; Yoder 2003).
We thank Judith Beekman for comments on the manuscript. This
work was supported by grants from the National Institutes of
Health (GM065612-01 and GM065580-01), and the State of Loui-
siana Board of Regents [Research Competitiveness Subprogram
LEQSF (2001-04)-RD-A-08 and the Millennium Research Pro-
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Governor’s Biotechnology Initiative.
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Received August 10, 2004; accepted in revised form February 23, 2005.
Evolution of substitution gradients in primates