Debate
The neutral theory is dead. Long
live the neutral theory
ory is not generally correct. What follows is a personal
account of the theory as it has been put to the test.
Martin Kreitman
Defining neutrality
Before proceeding, I must comment on precisely what is
meant by ‘the neutral theory of molecular evolution’. The
issue is whether the neutral theory applies only to those
models in which there is absolutely no selection (completely
neutral mutations only), or to models in which genetic drift
dominates the fate of a mutation (effectively neutral mutations). The distinction is not trivial, as this slight semantic
change in the theory has been shown to have severe consequences on the predicted patterns of genetic variation and
on the substitution rate. Therefore, specifying the theory is
important for evaluating data.
The neutral theory is generally equated with genetic drift,
where gene frequency flux results from stochastic sampling
processes operating in finite populations. Genetic drift is the
sole evolutionary force acting on gene frequencies under the
completely neutral theory, but it is also the driving force for
mutations subject to sufficiently weak selection. This has led
some to equate the neutral theory with the theory of ‘nearly’
neutral mutation. The two, however, should not be confused.
The best developed among the weak selection models is the
slightly deleterious
which postulates that weakly
deleterious mutations, driven by genetic drift, are the major
source of polymorphism and evolutionary change. Under this
theory, the interactionof genetic drift with weak selection leads
to qualitativelydifferent predictionsabout the tempo and mode
of molecular evolution from those of the completely neutral
theory. In particular,the rate of molecular evolution under the
completely neutral theory is only dependent on the mutation
rate to neutral alleles, whereas it is also dependent on the population size when there is weak selection (the ‘nearly neutral’
theory). From a practical perspective, postulating a particular
sequence of change in population size allows the slightly deleterious model to account for a surprisinglywide array of molecular evolutionary data. Unlike the completely neutral theory,
the slightly deleterious model is rather difficult to reject on
empirical grounds (see accompanying article by Ohta). For
this reason alone, the completely neutral model is more attractive as a null model of genetic drift.
Gillespie has investigated a class of models involving
strong balancing selection in which a type of drift, which he
calls genealogical drift, is imposed by the mutational flux of
new selectively favored alleles, causing a positive correlation
between the level of polymorphism and the rate of substitution.
The result is indistinguishablefrom that under a purely neutral
model of molecular evolution(3).Thus, one of the strongest
evolutionary signatures of genetic drift - the positive correlation between polymorphism and divergence - is, in fact, not
unique to the theory. Therefore for the purpose of testing for
the presence of genetic drift in empirical data, it is essential not
only to specify the null model but the alternativeas well.
Summary
The neutral theory of molecular evolution has been
instrumental in organizing our thinking about the
nature of evolutionary forces shaping variation at the
DNA level. More importantly, it has provided empiricists with a strong set of testable predictions and
hence, a useful null hypothesis against which to test for
the presence of selection. Evidence indicates that the
neutral theory cannot explain key features of protein
evolution nor patterns of biased codon usage in certain
species. Whereas we now have a reasonable model of
selection acting o n synonymous changes in
Drosophila, protein evolution remains poorly understood. Despite limitations in the applicability of the neutral theory, it is likely to remain an integral part of the
quest t o understand molecular evolution.
Introduction
I gave a talk with the same title two years ago at a meeting
on molecular evolution at Oxford, England in which I tried to
explain my drug-like dependence on a theory that I believed
was not, in general, correct (as opposed to good for me). By
‘correct’ I must immediately offer a qualification, since the
theory in its purely analytical form is certainly correct as a
description of the fate of mutations with no fitness effect.
Rather, my claim was that the neutral theory would eventually be shown not to be adequate as an explanation of many
features of molecular variation and evolution, while, at the
same time, would provide the very framework for proving
this thesis. This point of view explains my dependence on
this easily falsifiable theory and my desire for its longevity.
Dr Motoo Kimura, who is rightly credited both with developing the theory and with husbanding it to a position of prominence in molecular evolutionary biology, upon seeing the title
of my talk, fired off an angry fax requesting a printed copy.
Fortunately, I hadn’t one, and so was saved from the critical
scrutiny it would certainly have received. Sadly, Dr Kimura is
no longer with us to muse over this, the revised version of that
talk. But I hope that the schizophrenia I have towards the theory would not have severely offended him: like many molecular evolutionary biologists, I have an abiding admiration for
this conceptually simple but powerful theory, and it remains a
stable platform for rationalizing many observations about
molecular evolution. But, in addition to its analytical tractability, the theory also makes a number of testable predictions.
And, as an empiricist, it is this testability of the theory that has
captured my attention. It has also led to the belief that the the-
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Kimura’s own descriptions of the neutral theory were not
always consistent with respect to the inclusion of weakly
selected mutants. The very first sentence of his 1983 landmark treatise, The Neutral Theory of Molecular Evolution(4),
provides a capsule summary of the theory and reveals the
problem at hand. ‘The neutral theory asserts that the great
majority of evolutionary changes at the molecular level, as
revealed by comparative studies of protein and DNA
sequences, are caused not by Darwinian selection but by
random drift of selectively neutral or near/-vneutral mutants’
(emphasis added). The question is, what is a nearly neutral
mutant? It is not until 48 pages later, in chapter 3, that he
provides an answer, ‘...if a mutant has selection coefficient
much smaller in absolute value than 1/(2N& it behaves like
a neutral mutant so that this equation (the rate of evolution
of a strictly neutral mutation) holds approximately’ (emphasis added). Ne is the evolutionary effective population size.
But under the heading Some Misunderstandings in a later
article on the neutral theory@),his description of neutrality
has been relaxed: ‘If the (neutral) variants represent amino
acid changes in a protein, this means that such changes are
equally acceptable for the working of the protein in the body.
Furthermore, this equaliiy need not be exact; all that is
required is that the resulting difference in fitness be small,
say, for example. less than 1/(2Ne)’(emphasis added). Note
the change from ‘much smaller’ to ‘less than’.
Estimating the limits of selection in Drosophila
Experimental population geneticists have generally
restricted their attention to testing predictions of the strictly
neutral model. In practice, this means testing for the presence of mutations with absolute fitness effect, where selection coefficient (s)<<l/(2Ne). Considering the importance of
effective population size in delineating the theory, it should
be of some interest to have an estimate of this critical population parameter. Unfortunately, the closest we can come to
obtaining such an estimate from sequence data is the product of Neand the mutation rate p. Under strict neutrality, polymorphism is governed by a single pseudoparameter,
8=4Nep, and the number of segregating sites in a population
sample of DNA sequences can be used to obtain an unbiased estimate of the neutral parameter. For Drosophila
melanogaster, an estimate of €I(per nucleotide site) for polymorphic noncoding regions of the genome is 6=0.01 The
neutral mutation rate per generationfor Drosophila has been
estimated to be approximately 4x10-9 per generati~n(~J).
By
substituting this estimate of the mutation rate into the equation for 8 [O.O1=4x(4xl O-’)xNe] we can obtain a rough estimate of the evolutionary population size, Ne=106. Other
species of Drosophila yield similar or, if anything, higher estimates of effective population size. For a multitude of
reasons, these estimates must be conservative.
The first lesson we have learned from the observation of
high polymorphism levels in Drosophila molecular population genetics data is that a mutation must have a fitness
effect exceedingly close to zero in order for the neutral theory
to apply. Note the irony in this conclusion, however: the very
evidence for neutrality in Drosophila - a high level of polymorphism restricted to silent sites in the genome - is the very
same evidence that population sizes are large and genetic
drift weak. Unless selection is very strong - many orders of
magnitude above the threshold between drift and selection cage experiments, or even bacterial chemostat experiments,
are orders of magnitude too insensitive to reveal selective
differences among naturally occurring variants.
Weak selection can account for codon bias in
Drosophila
The efficacy of exceedingly weak selection in species with
large population size can be illustrated by considering codon
bias. There is abundant evidence that synonymous mutations - changes at third (and some first) positions of codons
that do not cause any change in the amino acid sequence are subject to weak selection in Drosophila, Saccharomyces
cerevisiae and fscherichia coli. I will briefly summarize the
evidence here (see ref. 9 for more detail). The three species
exhibit nonrandom usage of alternative codons, with a subset of codons being ‘preferred’. In S. cerevisiae-and E. coli
(and possibly Drosophila), preferred codons correspond to
the most abundant tRNA(s) for each amino acid. The degree
of codon bias varies among genes and is positively correlated with expression levels. Synonymous divergence rates
between closely related species vary inversely with the
degree of biased codon usage, suggesting stronger selective constraints on silent sites in more highly biased genes. In
Drosophila (but not E. coli), codon usage within a gene is
positively related to functional constraint acting at the protein
level, indicating that selection on synonymous mutations
may be related to translational accuracy(lO).
Despite these obvious indications of selection acting on
synonymous mutations, silent sites in coding regions of
Drosophila show relatively high levels of polymorphism and
correspondingly high rates of divergence. The data suggest a
model of mutation, selection and genetic drift, in which a mutation from a preferred codon to an unpreferred one is slightly
deleterious,and conversely,a mutationfrom an unpreferredto
a preferred codon is slightly beneficial. For genes with high
codon bias, most synonymous mutations will be preferred +
unpreferred, reflecting the high proportion of preferred
codons. Silent polymorphism, therefore, should exhibit an relative excess of preferred -+ unpreferred mutations compared
to the opposite type, unpreferred+I preferred.The fixed silent
changes between species will be expected to have equal
numbers of the two type of mutationalchanges, for if this were
not the case the system would not be at equilibrium. This
equality is achieved by weak selection eliminating unpreferred
mutationswhile fixing preferred mutations.
In an innovative analysis of synonymous changes within
and between closely related Drosophila speciedg), Akashi
was able to confirm this prediction: unpreferred and pre-
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ferred mutations are unequally distributed within and
between species for the five genes constituting the study. In
addition, using the magnitude of the difference between the
ratios of po1ymorphism:divergence for unpreferred mutations within and between species and using a sampling theory developed by Sawyer and Hartl(’l), he was able to estimate the average strength of selection acting on these
mutations. For D. simulans, his estimate was Nes=2.3,with
a bootstrap maximum likelihood confidence interval (95%),
-3.6<Nes<-1.3. Akashi’s estimate of the average strength
of selection is close to s=1/2Ne, but he could nevertheless
reject a completely neutral model (s=O).
In addition, the data revealed a curious difference in the
rate and type of fixed synonymous substitution between the
D. simulans and D. melanogaster species’ lineages. As
expected under an equilibrium model, D. simulans had
nearly equal numbers of preferred and unpreferred substitutions, 7 versus 5, respectively. However, in the D.
melanogaster lineage there were 32 unpreferred substitutions, a vast excess compared to six preferred substitutions.
The analysis of additional gene sequences between the
species revealed the same pattern: almost ail D.
melanogaster genes have lower codon bias than their D.
simulans homologs. This suggests that tinpreferred mutations, which are prevented from reaching fixation by being
weakly selected against in D. simulans, are either drifting to
fixation in D. melanogaster or are now favorably selected.
Akashi (like myself) favors the former explanation, suggesting that population size must have been smaller in the lineage leading to D. melanogasterthan it was in the ancestral
species or in the lineage leading to D.simulans. Under such
a scenario, unpreferred mutations would drift to fixation at a
relatively higher rate, despite being selected against. If
Akashi’s estimate of Nes is accurate, population size need
only have been two- or threefold smaller in the D.
melanogasterlineageto have produced the observed loss of
codon bias. The relatively large evolutionary effect of a small
change in population size reinforces an important point
about nearly neutral mutations: it is not so r r w h a question of
whether strictly neutral mutations exist - probably no mutation is absolutely neutral - but whether the strength of selection for or against that mutation is much smailer or greater
than the strength of genetic drift. The answer to this question
will always be contingent on the current population size.
In summary, the patterns of polymorphism and divergence at silent sites in the coding regions of Drosophila
genes are inconsistent with the strictly neutral model. Weak
selection, only slightly greater than the reciprocal of the
effective populationsize, is sufficient to have driven the evolution of highly biased codon usage(’”). Akashi’s work
reveals the importance of weak selection in shaping the
evolution of this large class of sites in the genome and
underscores the importance of distinguishing between
weak selection and strict neutrality when analyzing molecular data. The presence of genetic drift, which in this case is
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thought to be the major force acting to establish unpreferred
mutations as polymorphisms and as fixed differences, is an
insufficient criterion for claiming neutrality.
Natural selection and protein evolution
I have attempted to establish two ‘facts’ about Drosophila
molecular population genetics and evolution thus far. (1) Evolutionary population sizes are relatively large, so that genetic
drift is only importantfor mutationswith fitness much less than
the order 10-6, and (2) synonymous mutations are not completely neutral, but instead are under weak selection. Assuming both to be true, it ought to be a small leap of faith to believe
that protein evolution must also be governed by natural selection. Amino acid replacement changes, after all, should be
expected to have greater consequences on function (and fitness) than synonymous changes. Unfortunately,the problem
is not so simple, and such a leap is supported neither by logic
nor by empirical evidence. First, it must be true that amino
acid replacement mutations are, on average, subject to
stronger selection than synonymous mutations. This is indicated by the evolutionary conservation of protein sequences
compared to silent sites, and proves the importance of constraining selection. But, constraining selection cannot explain
protein evolution because the observed polymorphisms and
fixed differences in proteins must, by definition, be ones that
have escaped strong constraining selection. The question is,
have they escaped by virtue of their selective neutrality (or
near-neutrality) or by virtue of their selective advantage. To
this question, we still have no satisfactory answer. After
almost 30 years of evolutionary study, proteins remains molecular evolutionary biology’s black hole.
There are, in fact, many lines of evidence against strictly
neutral evolution of p r o t e i n ~ ( ~ n ’ ~I will
, ~ ~only
) . briefly mention a few of them here. An unexpectedly high variance in
the rate of protein evolution, sometimes referred to as
overdispersion of the molecular clock, is the longest-standing evidence against strict neutrality. Based almost exclusively on protein data from mammalian orders, the variance
in rate of substitution along these mammalian lineages
exceeds the mean rate by a factor of seven, on average,
violating an expected ratio of one under strict neutrality(’3).
However, recent theoretical work by Gille~pie(~)
on origination and substitution processes in molecular evolution indicates that neutral as well as several competing selection
models all predict regular bursts of substitution, but with the
bursts occurring on a much shorter timescale than that over
which the high variance in substitution rates is observed.
Thus, according to him, we are left without a viable model of
protein evolution, and with considerable uncertainty as to
the meaning of the large variance in the rate.
It is, of course, possible that unforeseen factors contribute
to the unexpectedly large variance in protein evolution. In
Drosophila, for example, where gene order within chromosome arms (but not between arms) changes quickly in
species evolution, chromosomal location (with respect to
recombination,for example) may be an important factor influencing rates of substitution of weakly selected mutations. But
without appealing ad hoc or context-specific explanations,
overdispersionof the molecular clock remains a mystery.
Silent sites show a generation-time effect in mammals,
with evolutionary rate being inversely related to generation
length(15).This observation is consistent with neutrality so
long as mutation rate is positively correlated with generation
time, as it is generally thought to be. Proteins, however,
appear to show a much weaker dependency on generation
length, suggesting slightly deleterious selection as well as
population size differencedi6). Additional protein evidence
in support of a slightly deleterious model is reported by
Ohta(2)and reviewed by Kreitman and Akashi(14).
Accelerated protein divergence following gene duplication offers some of the most convincing evidence in support
of adaptive e v ~ l u t i o n ( ~ In
~ ~practice,
~ * ) . however, rate acceleration caused by the relaxation of selective constraints following duplication can be difficult to distinguish from positive
selection(’g). Perhaps the most unambiguous case for
adaptive evolution following gene duplication involves a
retroposed copy of alcohol dehydrogenase in Drosophila
yakuba and D. teissieri, two close relatives of D.
melanogastehz0).Acceleration can be seen both between
paralogswithin lineages (Adh and jingwei, the new gene) as
well as between homologs between lineages. In addition,
the adaptive interpretation is independently supported by
population genetic data.
Unambiguous evidence for positive natural selection driving protein evolution has been found by comparing the rate
of amino acid replacement substitution with the rate of synonymous substitution (examples are given in ref. 21). Positive
selection is indicated if the replacementrate exceeds the synonymous rate of substitution, an exceedingly stringent
requirement for demonstrating positive selection. A more
relaxed test for positive selection was developed by McDonald and Kreitrnadz2),based on a comparison of synonymous
and replacement variation within and between species. This
test, however, has yielded only a few examples of accelerated protein evolution (see ref. 23 for a dramatic example)
from among a growing number of applications of the test. The
test has also yielded evidence for ‘decelerated’ protein evolution, indicative of the occurrence of slightly deleterious mutations(24). In all cases, the interpretation of a significant test
result is dependent on an assumption of selective neutrality
for synonymous changes, an assumption we now know is not
correct for genes with codon bias. Therefore, caution is
required in the interpretation of the Kreitman-McDonaldtest.
Kimura’s neutral theory has been construed not only as a
theory championing genetic drift, but also as a theory assailing balancing selection as a pervasive mechanism for maintaining protein polymorphi~m(4.~~).
In this regard, the evidence favors Kimura’s view. A theoretical prediction of
balancing selection is that alleles maintained for a sufficiently long period of time by selection will have accumu-
lated neutral mutations linked to the site(s) under selection(26~z7).
A statistical test of this predictiodZ8), mostly
applied to Drosophila data sets, has failed to find much support for balancing selection(6).In Drosophila, either balancing selection is not pervasive, or the persistence times of
balanced polymorphismsare relatively short.
Is weak selection important in protein evolution?
At present, I do not think any particular model of protein evolution - neutral, slightly deleterious, house of cards (allowing for adaptive as well as deleterious mutations), underdominance or overdominance - enjoys particularly strong
support. If anything, the slightly deleterious model is the
simplest model to account for many empirical observations.
As pointed out by Gillespie, however, the slightly deleterious
model (and the house of cards) is applicable only within a
very narrow range of small selection coefficients, and rates
of evolution should be sensitive to population size. There is,
in fact, evidence for population size affecting the rate of protein evolution in the direction predicted by the slightly deleterious model (see accompanying article by Ohta). But the
data are from relatively distantly related species whose populational histories cannot possibly be reconstructed, and I
do not consider the evidence compelling.
Ohta and Gillespie both argue that most selection on mutations in proteins leading to polymorphism and substitution is
weak. Where they disagree is what is meant by weak. According to Gillespie, selection is likely to be much stronger than the
reciprocal of population size, whereas accordingto Ohta it will
be close to the reciprocal of population size. The most compelling evidence for weak selection on protein variants comes
from the study of null allozyme allele frequencies in D.
r n e i a n ~ g a s t e h ~These
~ ~ ~ ~studies
).
find a substantial occurrence of null alleles in natural populations, leading to an estimate of 1 . 5 ~0-3
1 for the average selection against heterozygotes. As pointed out by Gillespie(I3),selection acting on
naturally occurring enzyme variation cannot possibly be
stronger than selection against null alleles. Additional support
for weak selectioncomes from a statistical analysis by Sawyer
eta/. of replacement polymorphism site frequencies in 6-phosphogluconate dehydrogenase (gnd locus) in E. co/i3l) in
which they estimate an average selection coefficient of
-1.6~10-~.
However, work on PGI allozyme polymorphism in
Colias butterflies by Watt et a/.(32)suggests fitness differences
between PGI genotypes of the order of several percent!
Part of the difficulty in attempting to make general statements about forces governing protein evolution is the nonhomogeneity of selection with respect to sites in the protein.
Constraining selection, for example, will vary according to
the functional importance of a site. Positively selected mutations can also be restricted to particular sites in a protein. As
an example, a single point mutation in the y-aminobutyric
acid receptor gene, found repeatedly in many species, is
solely responsible for target site insensitivity to the pesticide
cyclodiene(33).Individual sites within a protein are highly
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nonequivalent, and have distinctly different potential for
evolutionary change. Unlike synonymous sites, where the
selective consequence of mutations between unpreferred
and preferred states may be largely independent of position,
selection on proteins cannot be reduced to a single summary statistic.
quasi-neutral), provides a barometer for detecting selection
acting at linked sites. From an empirical population geneticist's perspective, the benchmark of neutrality remains critical to the success of the molecular evolutionary research
program. But the goal of this program is not only to explain
major features of molecular variation and evolution, but to
understandthe molecular and genetic basis of adaptation. It
is my thesis that the neutral theory (and noncoding variation) will continue to play a leading role in this quest to detect
selection, even as it is being rejected. For this reason, I say,
long live the neutral theory.
Conclusion
The struggle to distinguish stochastic from deterministic
forces in evolution is almost as old as population genetics
itself. In each generation, this struggle has taken the form of
a new empirical observation about genetical evolution, be it
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Marty Kreitman replies:
Ohta and I agree that certain features of molecular polymorphism and evolution are not compatible with strict neturality.
That battle may be over, but new battle lines appear to have
been drawn. As the originator of the slightly deleterious model
of molecular evolution, Ohta argues for the importance of
nearly neutral mutations. In my view the only solid statistical
support for the nearly neutral model involves synonymous
changes and the evolution of codon bias, as discussed in
both of our articles. I do not consider the higher ratio of
replacement changes to synonymous changes in the primate
lineage compared to rodent lineage to be strong evidence for
slightly deleterious evolution, as the time separating these
species is too great to safely conclude that population sizes
have been the cause of the slightly different rates in the two
lineages. Other observations about molecular variation and
evolution discussed by Ohta either do not speak directly to
the issue of strength of selection, or they incorrectly shoehorn
data into the slightly deleterious model. For example, Ohta
argues that a relative excess amino acid replacement change
Martin Kreitman is at the Department of Ecology and Evolution,
University of Chicago, 1101 E 57th St, Chicago, IL 60637, USA.
E-mail: mkre @ midway.uchicago.edu
the McDonald-Kreitman test, fits the slightly deleterious
model if one assumes a bottleneck at speciation. However,
Tomoko Ohta replies:
Kreitman correctly points out that some confusion arises
from the ambiguous definition of the neutral theory. It apparently means the strictly neutral theory to many evolutionary
biologists, whereas I sometimes used the term in its
extended form, which includes the nearly neutral theory.
Perhaps, ‘the neutral theory’ should be used in the narrow
sense to avoid confusion. One could use ‘the neutral theory
in the broad sense’ to include the nearly neutral process, or
‘the nearly neutral theory’ should be used explicitly.
A notable difference between my view and Kreitman’s
may be found in the interpretation of the McDonald-Kreitman test. To me, the excess of nonsynonymous substitutions between closely related species may reflect slightly
deleterious amino acid substitutions at bottlenecks,
whereas to Kreitman, it is caused by positive selection. The
opposite situation may again be explained by the slightly
deleterious mutation model, if linkage, migration and other
factors are considered.
I agree with Kreitman that the nearly neutral theory is less
useful as a null hypothesis than the strictly neutral theory. I
also admit that the nearly neutral theory in its present form is
neither complete nor correct everywhere. We need more
studies, both theoretical and experimental, for our full
that instant in time. The number of amino acid polymorphisrns
segregating between alleles, if present day Drosophila populations are any indication,are far too few in number to account
forthe excess of fixed substitutionsobserved at several loci in
Drosophila. Therefore, the speciation/bottleneck hypothesis
(which itself is without support) cannot explain these data.
The battle line may have shifted slightly from complete
neutrality to near neutrality. But this slight shift is a quantum
leap in terms of the difficulty in distinguishing between the
nearly neutral model and stronger selection models. As
revealed in the example given above, one can almost
always propose a particular history of changes in population
size in that will account for almost any pattern of molecular
variation or change. Thus, unlike the strictly neutral theory,
the slightly deleterious model cannot be easily falsified. Yet
the question of the relative magnitude of the mutational flux
falling into the very small region of fitness space we call the
nearly neutral region (Isl<l/N) in relation to the mutational
flux of positively selected mutations (s>>l/N) remains central to our understanding of molecular evolution. Like Ohta, I
believe the statistical analysis of molecular divergence data
will allow us to resolve this issue. What is required, however,
is better molecular data from closely related species, which
should allow more informed interpretations of evolutionary
rate differences.
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