brief communications arising
Evolutionary genomics

Codon bias and selection on single genomes
Arising from: J. B. Plotkin, J. Dushoff & H. B. Fraser Nature 428, 942–945 (2004)

a 1.0
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That codon usage bias — measured by either
CAI or volatility — correlates with selective
constraint is well known and unsurprising7,8.
Second, because CAI measures only oneof many known biases in codon usage, toexamine the general effects of differential
codon usage we randomly assigned volatility
scores to each codon and then re-analysed
the Mycobacterium tuberculosis genome
according to the method of Plotkin et al.1.
Figure 1b shows the distribution of volatility
scores for this randomized genome. This distribution has a U-shape similar to that foundin the true volatility distribution forM. tuberculosis,and there is high similarity inthe set of genes that reside in the tails of both
distributions (P1015; Fig. 1b); these outliers show dissimilar codon usage from the
majority of the genes, regardless of the measure used. That a random assignment ofcodon volatilities recovers the same outlier
genes as the true values suggests that volatility itself has little to do with the observed distribution. Our analyses indicate that volatility
may be another measure of codon bias.

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he idea that natural selection on genes
might be detected using only a single
genome has been put forward by
Plotkin and colleagues1, who present a
method that they claim can detect selection
without the need for comparative data andwhich, if correct, would confer greater
power of analysis with less information.
Here we argue that their method depends
on assumptions that confound their conclusions and that, even if these assumptions
were valid, the authors’ inferences about
adaptive natural selection are unjustified.
The volatility analysis of Plotkin et al.1
rests on the observation that synonymouscodons often differ in the number of mutations that take them to different amino acids.
For instance, CGA and AGA both code forarginine, but differ in the number of aminoacids that are one mutation away (4 out of 8
for CGA and 6 out of 8 for AGA; AGA therefore has a higher volatility). Their expectation is that proteins that have undergone
more amino-acid substitutions will havemore highly volatile codons.
To test each gene for selection by looking
at relative codon volatility, Plotkin et al.
construct the null by drawing alternativesynonymous codons from a distribution
parameterized by genome-wide codon frequencies, with a view to identifying genesthat are atypically rich or poor in volatilecodons and which they believe represent
rapidly and slowly evolving genes,respectively.
A premise of this approach is that codon
usage does not vary in a consistent way fromgene to gene.If codon bias is related to volatility in any way — for instance, if CGA is preferentially used over AGA in highly expressed
genes — then the volatility index that theauthors use is simply an alternative measureof within-genome variation in codon-usagebias. In fact, differential codon bias due toboth natural selection and mutation bias
results in a highly heterogeneous distributionof codon usage across multiple genomes2–5.
To investigate the extent to which theauthors’unmet assumption will affect estimation of volatility, we conducted two analyses.
First, we examined the correlation between
volatility P values and the codon adaptationindex (CAI), a common measure of optimal
codon bias, for every gene in the Saccharomyces cerevisiae genome (Fig. 1a). We use
S. cerevisiae because the optimal codons are
known6 and because nucleotide divergencecan be estimated from a closely related outgroup (S.paradoxus).As expected,we found astrong correlation between CAI and volatility,with CAI explaining a much larger proportionof the variance in volatility than the standard
comparative measure of selection, dN/dS.

200

100

0

Figure 1 Codon bias explains volatility. a, Relationship between
the codon adaptation index (CAI) and the volatility P values in the
Saccharomyces cerevisiae genome. An analysis of variance with
CAI and dN/dS (calculated from a comparison with orthologs in
S. paradoxus) as main effects reveals that CAI (F ratio322,
P0.0001) explains more than twice as much of the variation involatility as dN/dS (F ratio153, P0.0001). b, Distribution of
random volatilities in the Mycobacterium tuberculosis genome. We
randomly assigned each codon a volatility score between 0 and 1
and calculated the volatility P values for all the genes in theM. tuberculosis genome using these new values, following themethod of Plotkin et al.1. The proportion of the 78 genes in the 1%
tails of the volatility distribution that are shared between the
random and true volatility distributions is 35% (27 genes in both).
This overlap is highly non-random (P10–15).

NATURE | VOL 433 | 20 JANUARY 2005 | www.nature.com/nature

The authors do not provide formal reasoning to explain why the volatility statistic
should correlate with selective constraint. If
their method is grounded in standard,singlelocus multiple-allele models, their result istrivial: in such models, assigning an allele
lower fitness will deterministically lower its
frequency in a population. And because
volatility only applies to four codon families,
three of which contain synonymous codons
that cannot be reached by a single mutation,
any such population-genetics model involving volatility must violate basic assumptions.
The authors claim both that their method
does not rely on some of the strongest
assumptions of comparative analyses1 andthat their unstated model assumes a population at mutation–selection balance. However,comparative methods for detecting natural
selection (see ref. 9, for example) do not
require populations in mutation–selection
balance. Codon-based comparative methods
do require a mutational process at stationarity9, but so do Plotkin et al.: if they do notassume mutational stationarity, their logic
does not work.
Consider pseudogenes: volatility scoresof these genes will reflect past processes, notcurrent selection, until they reach a stationary state. Volatility is only expected to be
associated with amino-acid turnover as agenome approaches codon-usage stationarity,
but it is not clear how to test the assumptionthat a genome has reached such a state.
The distribution of negative selection
across a genome is unknown and, because ofthis — even if all the assumptions of themodel have been met — one cannot say withcertainty that genes in the tails of the distribution are under increased positive selection or
decreased negative selection. Simply because
there are a handful of genes thought to beunder positive selection present in these tails
does not prove that all or even most of thesegenes are. Although Plotkin et al. provide acaveat to inferences about positive selection in
their penultimate paragraph1, this is undermined by the seven preceding claims of positive selection in the paper. Comparative
analyses such as dN/dS do require data frommultiple taxa, but they provide a clear statistical criterion for detecting positive selection.
Matthew W. Hahn, Jason G. Mezey,
David J. Begun, John H. Gillespie,
Andrew D. Kern, Charles H. Langley,
Leonie C. Moyle
Center for Population Biology and Section of
Evolution and Ecology, University of California,
Davis, California 95616, USAe-mail: mwhahn@ucdavis.edu
doi:10.1038/nature03221
1. Plotkin, J. B., Dushoff, J. & Fraser, H. B. Nature 428, 942–945(2004).
2. Akashi, H. Genetics 136, 927–935 (1994).
3. Chiapello, H. et al. Gene 209, GC1–GC38 (1998).
4. Coghlan, A. & Wolfe, K. H. Yeast 16, 1131–1145 (2000).
5. Marais, G., Mouchiroud, D. & Duret, L. Proc. Natl Acad. Sci. USA
98, 5688–5692 (2001).
6. Ikemura, T. Mol. Biol. Evol. 2, 13–34 (1985).

E5brief communications arising
Expected volatility index

7. Sharp, P. M. J. Mol. Evol. 33, 23–33 (1991).
8. Akashi, H. Curr. Opin. Gen. Dev. 11, 660–666 (2001).
9. Goldman, N. & Yang, Z. Mol. Biol. Evol. 11, 725–736 (1994).
Reply: J. B. Plotkin, J. Dushoff and H. B. Fraser reply to thiscommunication (doi:10.1038/nature03224).

Evolutionary genomics

Detecting selectionneeds comparative data
ositive selection at the molecular levelis usually indicated by an increase in
the ratio of non-synonymous to synonymous substitutions (dN/dS) in comparative data. However, Plotkin et al.1 describe
a new method for detecting positive selection based on a single nucleotide sequence.
We show here that this method is particularly sensitive to assumptions regarding theunderlying mutational processes and does
not provide a reliable way to identify positive selection.
Plotkin et al.1 use a measure for detecting
selection known as the volatility index,
whereby a codon with high volatility is more
likely to have arisen by a non-synonymous
mutation than a codon with low volatility;
so, for high dN/dS, there should be morecodons of high volatility. Positive selection
should be detectable simply by examining
the volatility index in a single sequence.
However,this argument is flawed because
high rates of non-synonymous mutation
will increase the rate of substitution both
into and out of codons with high volatility.Inmodels in which the substitution process isreversible over time, these two factors willcancel each other out, and variations in thestrength of selection at the amino-acid level
do not affect the expected volatility.
Although most models used in studies ofmolecular evolution are time-reversible2, thetrue substitution process probably is not,because of the specifics of the mutational
and population-level processes.
To examine the effect of the substitution
model on the volatility index, we simulated
random-substitution models in which therate of substitution between different
nucleotides was sampled from a uniform
random variable between zero and one. For
these models, we then calculated the equilibrium frequencies of the 61 sense codons in a
Markov chain model that resulted from simulations having varying synonymous andnon-synonymous substitution rates. Basedon the equilibrium frequencies, we could
then calculate the expected value of thevolatility index.
Our results indicate that the volatility
index can be either an increasing or adecreasing function of dN/dS, or have a minimum or maximum at an intermediate valueof this ratio (Fig. 1). We also find that thedN/dS ratio only marginally affects thevolatility index — particularly for values of

P

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Figure 1 Expected value of the volatility index, as defined by
Plotkin et al.1, as a function of the dN/dS ratio for 20 randomsubstitution models.

dN/dS1. Although models can be constructed in which strong stabilizing selection
on particular amino acids has a marked
effect on the volatility index, there is no evidence that the volatility index captures muchinformation regarding positive selection.
Realistic models of positive selection will
predict an increased rate of substitution bothin and out of codons with high volatility.
What then explains the results of Plotkin
et al.1, in which the volatility index correlateswith the rate of amino-acid substitution incomparative data and with the amount ofexpression? Non-random codon usage iscommon in most organisms, particularly inbacteria and yeast3–7, and may be caused by
selection for optimal codon usage and affectedby variation in the nucleotide compositionand other factors. In bacteria, the strength ofcodon-usage bias is correlated with theamount of expression3–5 and with the extent
of amino-acid substitution6,7; this may be
because highly expressed genes tend to be
more conserved at the amino-acid level andhave more codon-usage bias than genes withlow expression. The degree of amino-acidsubstitution might also correlate with local
nucleotide frequencies because regions thatdiffer in this respect could have different
rates and patterns of mutation.
To investigate the extent to which thevolatility index is sensitive to local nucleotide
content, we took advantage of the fact that
only codons with sixfold degeneracy or withstop codons as neighbours can contribute to
the volatility index. Using all other codons
we obtained independent estimates of thenucleotide frequencies. We also calculated a
P value for a one-tailed test of increase in thefrequency of a particular nucleotide by using
the methodology of Plotkin et al.1, but calculated only for codons that do not contributeto the volatility index.
Applying this approach to the Plasmodium
falciparum data analysed by Plotkin et al.1,
the correlation coefficient between the log P
value of the volatility index and the log P
value associated with the percentage ofthymine is 0.29. Variation in third-position
nucleotide content is one of the factors
explaining the distribution of volatility-

NATURE | VOL 433 | 20 JANUARY 2005 | www.nature.com/natureindex-related P values in P. falciparum.
Correlation of the volatility index with theamount of amino-acid substitution could becaused by the presence of covariates such as
nucleotide frequencies, selection for optimal
codon usage bias and/or expression levels.
The results of Plotkin et al.1 might also be
explained by variation in the amino-acidfrequencies among genes. If the true evolutionary model is not time-reversible, thesefrequencies should influence codon usage
and the volatility P value. Indeed, many of
the amino-acid frequencies show correlation with the volatility P values calculated by
Plotkin et al.1. For example, the correlation
coefficient between the frequency of glutamine and the log volatility P values is 0.32.
All codons for glutamine have the samevolatility, but this amino acid is one mutational step away from arginine and leucine,which both affect the volatility index. The
volatility index in models that are not timereversible can therefore be affected by stabilizing selection on particular amino acids,
because such selection affects the aminoacid frequency. But whether the volatility
index correlates positively or negatively withsuch selection depends on which amino acidis the target of selection. Positive selectionthat increases the rate of amino-acid substitution does not have the same impact on thevolatility index.
We argue that the volatility index cannot
be applied to detect positive selection as it isunder greater influence from other factors,
such as amino-acid and nucleotide frequencies. However, the results of Plotkin et al.1
should spur efforts to identify the causes of
non-random codon usage in bacteria andother organisms.
Rasmus Nielsen*†, Melissa J. Hubisz†*Centre for Bioinformatics, University of Copenhagen,
Universitetsparken 15, 2100 Copenhagen, Denmark
e-mail: rasmus@binf.ku.dk†Department of Biological Statistics andComputational Biology, Cornell University, Ithaca,
New York 14853, USA
doi:10.1038/nature03222
1. Plotkin, J. B., Dushoff, J. & Fraser, H. B. Nature 428, 942–945(2004).
2. Lio, P. & Goldman, N. Genome Res. 8, 1233–1244 (1998).
3. Ikemura, T. J. Mol. Biol. 151, 389–409 (1981).
4. Grantham, R., Gautier, C., Gouy, M., Jacobzone., M &Mercier, R. Nucl. Acids Res. 9, 43–74 (1981).
5. Grosjean, H. & Fiers, W. Gene 18, 199–209 (1982).
6. Sharp, P. M. J. Mol. Evol. 33, 23–33 (1991).
7. Akashi, H. & Gojobori, T. Proc. Natl Acad. Sci. USA 99,
3695–3670 (2002).
Reply: J. B. Plotkin, J. Dushoff and H. B. Fraser reply to thiscommunication (doi:10.1038/nature03224).

Evolutionary genomics

Codon volatility does
not detect selection

Plotkin et al.1 introduce a method todetect selection that is based on anindex called codon volatility and thatE6

brief communications arisinguses only the sequence of a single genome,
claiming that this method is applicable to alarge range of sequenced organisms1.
Volatility for a given codon is the ratio of
non-synonymous codons to all sensecodons accessible by one point mutation.
The significance of each gene’s volatility isassessed by comparison with a simulated
distribution of 106 synonymous versions ofeach gene, with synonymous codons drawn
randomly from average genome frequencies. Here we re-examine their method anddata and find that codon volatility does notdetect selection, and that, even if it did, thegenomes of Mycobacterium tuberculosis andPlasmodium falciparum, as well as those of
most sequenced organisms, do not meet theassumptions necessary for application of
their method.
Because of codon table regularity, 16 of 20
codon families have the same volatility foreach synonymous codon. The authors’ assertion that there are 22 codons that have at least
one synonym with a different volatility1
obscures the fact that these 22 codons
represent only four amino acids: the fourfold-degenerate glycine codons and the sixfold-degenerate arginine, leucine and serine
codons. Therefore, even if the method werevalid, volatility neglects any selection acting
on the remaining codons. Figure 1 shows thatthe volatility P values of Plotkin et al.1, which
are purported to detect selection, are largely ameasure of the codon usage of serine, withsmaller contributions from glycine, arginine
and leucine.A codon-usage index dominatedby a single family is not generally useful forstudying codon bias, much less selection —unless the genic signature of natural selection
is merely serine-codon usage.
The theoretical basis of the method of
Plotkin et al.1 is unclear: either it depends
critically on the only theoretical justification
offered by the authors, a model by van
Nimwegen et al.2, or it is unfounded. Assuming the null model is that of Nimwegen et al.,it
requires that all synonymous codons are ofequal fitness, that all members of a family aremutually accessible by a path of neutral mutation,and that the product of the effective population size and mutation rate, Ne, is muchgreater than one. But these requirements arerespectively violated in that selection forcodon usage in highly expressed genes is common3; the twofold-degenerate serine codons
cannot access the fourfold-degenerate codons
without passing through a non-synonymousintermediate; and most sequenced genomes

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Figure 1 Volatility P value plotted against volatility deviation. For each gene in the Plasmodium falciparum genome, the relationshipbetween the volatility P values of Plotkin et al.1, which reportedly consider all codon contributions, and the difference between theobserved volatility contributions for given codons and the volatility contributions expected by their genome average frequency is shown.
Serine is the only amino acid for which the tails of the statistic are significantly associated with extremes in the P value. This analysis was
repeated for each gene in the Mycobacterium tuberculosis genome (data not shown). a, Arginine; b, leucine; c, glycine; d, serine; e, allother families, excluding arginine, leucine, glycine and serine; and f, all 20 families.
NATURE | VOL 433 | 20 JANUARY 2005 | www.nature.com/nature

have an estimated Ne
1 (ref. 4). Specifically, Ne for pathogens is constrained byrepeated bottlenecks caused by transmission.
In fact, the highest estimated Ne values forboth P. falciparum and M. tuberculosis are of
the order of 103 or less5,6.
In Table 1 of Plotkin et al.1, the authors
present ten genes (including five of putative
function, not identified as such, and one
hypothetical protein) that they say show themost significant volatility P values and that
therefore “show the strongest signs of positive selection”, although they ignore 27 othergenes (see their supplementary information) with P values indistinguishable fromthose in their table. These include a putativecell-cycle control protein, histone deacetylase, and DNA-directed RNA polymerase —highly conserved genes not expected to show
signs of recent positive selection. Furthermore, genes encoding transfer RNA andribosomal RNA are included in their analysis
and assigned volatility P values, althoughthese genes do not have codons.
The reality at present is that the community must continue to rely on other methods
to detect natural selection.
Ying Chen*, J. J. Emerson*, Todd M. Martin†*Department of Ecology and Evolution, and†Committee on Genetics, University of Chicago,
Chicago, Illinois 60637, USA
doi:10.1038/nature03223
1. Plotkin, J. B., Dushoff, J. & Fraser, H. B. Nature 428, 942–945(2004).
2. van Nimwegen, E., Crutchfield, J. P. & Huynen, M. Proc. Natl
Acad. Sci. USA 96, 9716–9720 (1999).
3. Akashi, H. Curr. Opin. Genet. Dev. 11, 660–666 (2001).
4. Lynch, M. & Conery, J. S. Science 302, 1401–1404 (2003).
5. Hughes, A. L. & Verra, F. Proc. R. Soc. Lond. 268, 1855–1860 (2001).
6. Sreevatsan, S. et al. Proc. Natl Acad. Sci. USA 94, 9869–9874(1997).
Reply: J. B. Plotkin, J. Dushoff and H. B. Fraser reply to thiscommunication (doi:10.1038/nature03224).

Plotkin et al. reply — The criticisms of ourresults1 by Hahn et al.2, Nielsen andHubisz3, and Chen, Emerson and Martin4
fall into three categories: the formal justification for our method, the potential for
confounding factors, and the interpretationof our empirical results.
In response to assertions2,4 that we do notformally discuss why codon volatility shouldreflect selection pressures on proteins, ourmethod is grounded in the standard multiallele model of population genetics5,6. Hahn
et al. note that assigning an allele lower
fitness will deterministically lower its frequency in a population2, but this fundamentally misunderstands why volatility reflects
selection: even if all synonymous codons for
an amino acid are assigned equal fitness,selection at the amino-acid level will bias therelative frequencies of synonymous codons.
Consider, for example, a site under negative selection for arginine. Assigning equal
fitness to arginine codons and lower fitness
to all other codons, the multi-allele model5
indicates that a less volatile arginine
E7brief communications arisingcodon will occur with higher equilibrium
frequency6. The expected volatility at such asite depends monotonically on the strengthof selection for arginine6.In a finite population
at steady state, the standard Fisher–Wrightmodel7 yields the same result, although thestrength of the volatility signal depends
upon the population size6. We agree with
Hahn et al. (and never claimed otherwise)that this logic implicitly assumes stationarity,
as is likewise assumed by all comparative
methods for estimating selection2,8.
Nielsen and Hubisz3 question whether
volatility can detect selection because, theyclaim,“variations in the strength of selection
at the amino-acid level do not affect the
expected volatility”. This claim is true only
under simplified models of sequence evolution that ignore population variability8.Suchmodels (used to produce their Fig. 1) are reasonable approximations when comparing
divergent lineages8, but they fail to detect theeffect of amino-acid selection on synonymous codon usage.
There is an intuitive explanation for this.
Such models consider a single sequence thatis assumed to represent the dominant genotype in a population at any time. Mutationand selection are modelled simultaneously
by adjusting the transition rates between
codon states8. Under the standard assumption of time reversibility3,8, the equilibrium
rate of transitions into a codon state must
equal the rate out of that state: therefore,synonymous codons occur with the sameprobability regardless of the strength of negative selection3.
By contrast, in a more realistic Fisher–
Wright model of a replicating population, theequilibrium rate of mutations away from acodon is not compensated by an equal rate of
mutations back into that codon: many lineages that acquire a non-synonymous mutation are removed from the population by
selection, before back-mutation. As a result,codons with a greater chance per unit time ofnon-synonymous mutation (that is, morevolatile codons) occur with lower equilibrium
frequency6.Thus, models that ignore population variability3,9 do not adequately describe
the patterns of synonymous codon usage.
Chen et al.4 note that our treatment ofserine violates van Nimwegen’s model10. But
our method is grounded more generally inthe standard multi-allele model5, whose
assumptions are not violated by the arrangement of serine codons. In fact, serine is particularly informative for positive selection6,
which may explain why more signal isderived from serine4.
These authors argue4 that Ne is too small
to support a volatility signal of negative selection for Plasmodium falciparum or Mycobacterium tuberculosis. But the effective population sizes of microorganisms are debatable.
Estimates of Ne can vary by four orders ofmagnitude and depend strongly on assump-

tions about population structure11 andhomogeneity of mutation rates12. More
important, the population size estimatedfrom neutral polymorphism data4 is generally
not the same as the population size relevant tovolatility: common phenomena such as transient hypermutators in microbes can vastly
improve the power of volatility to detect negative selection, even when the typical neutral
site heterozygosity is much less than one6.
Moreover, even if the relevant effective population size is small, there is a signal (of theorder of Ne per site) that distinguishes negative selection from neutrality6. Last, concerns
about population size do not apply in thecontext of positive selection: a more volatilecodon is much more likely to occur at a sitethat has undergone a positively selected
sweep,regardless of the population size6.
The authors2–4 are concerned that thevolatility signal may be compromised byother sources of differential selection on synonymous codons across a genome — a pointthat we also highlighted1 and which likewiseapplies to dN/dS. The observation2 thatvolatility P values correlate with the codon
adaptation index (CAI) in yeast does notinvalidate our method of estimating selection,
especially given that dN/dS also correlateswith CAI, to the same extent6. Moreover,volatility P values are significantly correlatedwith dN/dS even after controlling for CAI(partial correlation P1033) — indicatingthat the two measures yield fairly consistentestimates of selection, even aside from any
signal inherent in CAI.The observation3 thatvolatility correlates with amino-acid or
nucleotide content does not discredit its
ability to detect selection; analogous correlations are found for dN/dS.
Hahn et al.2 note that several M. tuberculosis genes exhibit extraordinary codon usage
and will typically appear in one or the othertail of the distribution when assigning “random volatility”2.Although these outliers may
influence the overall shape of the distribution,
it is critical to recognize that “random volatility”2 does not assign the same genes to the sametails as volatility1 does. When applied toM. tuberculosis,random volatility is not correlated with the rate of protein evolution(P0.23), nor does it show increased values
among the antigenic PE/PPE proteins(P0.8), nor depressed values among thosegenes required for bacterial growth (P0.4)
or among those genes conserved between
species (P0.5). By contrast, our volatility
measure shows highly significant correlations(P106) in all four of these cases1 — indicating that volatility is not simply an alternative metric of codon bias,but rather a measurethat co-varies with selection pressures on
M. tuberculosis proteins,as expected6.
Chen et al.4 note that volatility detects asignal from four amino acids, comprising
about 25% of sites in a typical gene, and that
more signal arises from serine in P.falciparum.

NATURE | VOL 433 | 20 JANUARY 2005 | www.nature.com/nature

They suggest that a signal obtained from so
few sites would be insufficient to detect selection, but provide no evidence to support thisclaim. By contrast, we present strong empirical evidence that volatility P values reflect
known selection pressures on proteins1.
Moreover, comparative analyses of selection
often rely on signals obtained from fewer than
5% of sites13,14.
Chen et al.4 contend that volatility fails to
detect selection because they find three highly
volatile P. falciparum genes that they do not
expect to experience positive selection, basedon their putative biological functions. Even
assuming that the putative functional annotations are correct, Chen et al. present no evidence that these three genes experience strong
negative selection.It is possible (owing to gene
duplication, for example) that members of ahighly conserved gene family experience
relaxed negative or even positive selection15;in
fact, these three genes each have at least one
paralogue in P. falciparum.In any case, even if
these three genes do actually experience negative selection, a handful of false positives
among a screen of over 5,000 genes would
hardly invalidate our method of estimating
relative selection pressures across a genome.
Hahn et al. point out that it cannot be said
with certainty that genes in the tails of the
distribution are under increased positive or
decreased negative selection2. We agree, andcontinue to emphasize that volatility P values
are intrinsically relative: we still cannot conclude that any gene is under positive selection
in an absolute sense and can only conclude
that some genes are under more positive, orless negative,selection than others1.
J. B. Plotkin*, J. Dushoff†‡, H. B. Fraser§*Harvard Society of Fellows, 7 Divinity Avenue,
Cambridge, Massachusetts 02138, USAe-mail: jplotkin@fas.harvard.edu†Department of Ecology and Evolutionary Biology,
Princeton University, Princeton, New Jersey 08540,
USA‡Fogarty International Center, National Institutesof Health, Bethesda, Maryland 20892, USA§Department of Molecular and Cell Biology,
University of California, Berkeley, California 94720,
USA
doi:10.1038/nature03224
1. Plotkin, J. B., Dushoff, J. & Fraser, H. B. Nature 428, 942–945(2004).
2. Hahn, M. W. et al. Nature doi:10.1038/nature03221 (2004).
3. Nielsen, R. & Hubisz, M. J. Nature doi:10.1038/nature03222 (2004).
4. Chen, Y., Emerson, J. J. & Martin, T. M. Nature
doi:10.1038/nature03223 (2004).
5. Haldane, J. B. S. Proc. Camb. Phil. Soc. 23, 838–844 (1927).
6. Plotkin, J. B. et al. Preprint at http://arxiv.org/abs/
q-bio/0410013 (2004).
7. Wright, S. Genetics 16, 97–159 (1931).
8. Goldman, N. & Yang, Z. Mol. Biol. Evol. 11, 725–736 (1994).
9. Dagan, T. & Graur, D. Mol. Biol. Evol.
doi:10.1093/molbev/msi033 (2004).
10. van Nimwegen, E., Crutchfield, J. P. & Huynen, M. Proc. Natl
Acad. Sci. USA 96, 9716–9720 (1999).
11. Berg, O. Genetics 142, 1379–1382 (1996).
12. Tajima, F. Genetics 143, 1457–1465 (1996).
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