Evidence that Adaptation in Drosophila Is Not Limited by
Mutation at Single Sites
Talia Karasov., Philipp W. Messer., Dmitri A. Petrov*
Department of Biology, Stanford University, Stanford, California, United States of America
Adaptation in eukaryotes is generally assumed to be mutation-limited because of small effective population sizes. This view
is difficult to reconcile, however, with the observation that adaptation to anthropogenic changes, such as the introduction
of pesticides, can occur very rapidly. Here we investigate adaptation at a key insecticide resistance locus (Ace) in Drosophila
melanogaster and show that multiple simple and complex resistance alleles evolved quickly and repeatedly within individual
populations. Our results imply that the current effective population size of modern D. melanogaster populations is likely to
be substantially larger ($100-fold) than commonly believed. This discrepancy arises because estimates of the effective
population size are generally derived from levels of standing variation and thus reveal long-term population dynamics
dominated by sharp—even if infrequent—bottlenecks. The short-term effective population sizes relevant for strong
adaptation, on the other hand, might be much closer to census population sizes. Adaptation in Drosophila may therefore
not be limited by waiting for mutations at single sites, and complex adaptive alleles can be generated quickly without
fixation of intermediate states. Adaptive events should also commonly involve the simultaneous rise in frequency of
independently generated adaptive mutations. These so-called soft sweeps have very distinct effects on the linked neutral
polymorphisms compared to the standard hard sweeps in mutation-limited scenarios. Methods for the mapping of adaptive
mutations or association mapping of evolutionarily relevant mutations may thus need to be reconsidered.
Citation: Karasov T, Messer PW, Petrov DA (2010) Evidence that Adaptation in Drosophila Is Not Limited by Mutation at Single Sites. PLoS Genet 6(6): e1000924.
Editor: Harmit S. Malik, Fred Hutchinson Cancer Research Center, United States of America
Received December 4, 2009; Accepted March 24, 2010; Published June 17, 2010
Copyright: ? 2010 Karasov et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This work was funded by the NIH and NSF grants to DAP, funds from CEEG and Conservation Biology Centers at Stanford University, and a HFSP
fellowship to PWM. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: email@example.com
. These authors contributed equally to this work.
The speed of adaptation in eukaryotes is commonly assumed to
be limited by the waiting-time for an appropriate adaptive
mutation. This notion is based on estimates of the population
parameter H=4Nem (the product of effective population size Ne
and per-site mutation rate m) derived from levels of standing
neutral variation. H can be interpreted as the rate at which new
mutations arise in the population . In contrast to many
prokaryotes or viruses, where H can easily be on the order of one
or larger - and consequently most single nucleotide mutations exist
in the population at every given time – estimated values of H in
eukaryotes are typically much smaller than one . Adaptation
should thus be substantially retarded, especially when adaptive
alleles need to carry several independent mutations.
However, adaptation to anthropogenic changes such as the
evolution of insecticide resistance has been observed to occur very
rapidly and often involves complex alleles [2–7]. One possible
explanation for such cases of rapid adaptation is that complex
resistant alleles predate environmental changes [8,9]. The other
possibility is that adaptive mutations emerge more quickly in
eukaryotic populations than commonly believed. The latter would
imply that estimates of H have to be reconsidered in the context of
In order to understand the population parameters that allow for
rapid adaptation in eukaryotes, we study here a well-documented
example: the evolution of pesticide resistance in D. melanogaster.
Acetylcholinesterase (AChE), a key neuronal signalling enzyme,
is the major target of the most commonly used insecticides,
organophosphates (OPs) and carbamates (CMs) . Introduced
in the 1950–1960’s, these insecticides have been used pervasively
around the world since then. Within a few years of their
introduction cases of insecticide-resistant AChE alleles emerged
 and today insecticide-resistant AChE has been observed and
characterized in numerous arthropod species [2–7].
In D. melanogaster, four particular point mutations at highly
conserved sites (I161V, G265A, F330Y, G368A) of Ace (the gene
coding for AChE) lead to resistance to OPs and CMs [5,12]
(Figure S1). Alleles carrying these mutations singly and in
combination have been found in natural populations worldwide
. In the presence of OPs, these mutations confer semi-additive
resistance: single mutations provide moderate levels of resistance
to ,75% of OPs, any two mutations in combination provide
higher levels of resistance to ,80% of OPs, while alleles with three
or four mutations lead to strong resistance to practically all OPs
. One 3-mutation allele (I161V, G265A, F330Y) was found
worldwide at particularly high frequencies and is a key
determinant of resistance to OPs . In the absence of pesticides
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all resistant alleles are strongly deleterious with the selective
coefficient on the order of negative 5–20% [13,14].
Here we collect data and provide quantitative arguments (both
analytical and simulation-based) that the observed signatures of
adaptation at Ace imply a much larger (,100-fold or more)
effective population size than is commonly assumed for D.
melanogaster. We discuss the implications of our results for the
study of adaptation in Drosophila and other species with large
Fast and repeated evolution of simple and complex
resistance alleles within individual subpopulations of D.
D. melanogaster evolved in sub-Saharan Africa (AF) and spread
worldwide over the past 10–16 thousand years . The
worldwide spread was associated with a severe bottleneck that
resulted in sub-sampling of AF diversity by the out-of-Africa
strains . Resistant alleles found outside of AF may either have
arisen in situ in the derived out-of-Africa populations or were
present in the AF population prior to the bottleneck (similar to
[8,9]). These two hypotheses can be distinguished by studying
haplotype backgrounds of the resistant alleles. Resistant mutations
that evolved in derived populations in situ, unlike ancient AF
resistant alleles, should reside on the background of sensitive
haplotypes common in the exposed out-of-Africa populations that
passed through the bottleneck.
We collected D. melanogaster sequence data (,1.5 kb covering the
known four sites of resistant mutations in Ace) from 93 resistant and
sensitive strains. We sequenced 9 alleles from the ancestral AF
populations, 10 alleles from the derived Eurasian and American
populations collected prior to the 1950s (M strains) , and 74
alleles from the recently collected (1990–2009) derived populations in
North America (NA) and Australia (AUS) (Table S1 and Table S2).
We detected resistant mutations at the first three sites (I161V,
G265A, F330Y) but did not find the resistant mutation at the
fourth site (G368A). We estimated that ,40% of the strains
contain resistant mutations in the modern NA and AUS
populations of D. melanogaster. Figure 1 shows the most parsimo-
Figure 1. Haplotype network at Ace. Alleles containing mutations
I161V, G265A and F330Y are numbered 1, 2 and 3 respectively. Sizes of
the circles correspond to the number of identical sequences
representing each haplotype; tick marks along a branch indicate the
number of mutations between two neighbouring haplotypes. Sensitive
haplotypes are labelled with capital letters and resistant haplotypes
with lowercase letters. Note that our sample is enriched for resistant
haplotypes. Resistant NA alleles containing a single mutation (all at the
first site) appear to have arisen on the common out-of-Africa haplotype
L, with one specific L-related allele (labelled p) present at the highest
frequency. The resistant AUS alleles also cluster together. AUS resistant
alleles containing a single resistant mutation in the first or second site
appear to have arisen either on the background of the common out-of-
Africa sensitive haplotype L, or on the background of the specifically
AUS haplotype N. The alleles containing two mutations in NA (first plus
second or first plus third sites) are all related to the sensitive L
haplotype and the common resistant allele (labelled p) containing the
mutation in the first site. The 3-mutation alleles are present both in NA
and AUS populations (v and w) and are the most closely related to the
sensitive L haplotype. There are two resistant alleles containing single
mutations in the first and the second site that we detected in AF. One of
these is very similar to the AUS alleles containing the second mutation
and is likely a migrant from out-of-Africa back to AF. The other appears
to have arisen in situ in AF (u).
Adaptation in eukaryotes is often assumed to be limited by
the waiting time for adaptive mutations. This is because
effective population sizes are relatively small, typically on
the order of only a few million reproducing individuals or
less. It should therefore take hundreds or even thousands
of generations until a particular new mutation emerges.
However, several striking examples of rapid adaptation
appear inconsistent with this view. Here we investigate a
showpiece case for rapid adaptation, the evolution of
pesticide resistance in the classical genetic organism
Drosophila melanogaster. Our analysis reveals distinct
population genetic signatures of this adaptation that can
only be explained if the number of reproducing flies is, in
fact, more than 100-fold larger than commonly believed.
We argue that the old estimates, based on standing levels
of neutral genetic variation, are misleading in the case of
rapid adaptation because levels of standing variation are
strongly affected by infrequent population crashes or
adaptations taking place in the vicinity of neutral sites. Our
results suggest that many standard assumptions about the
adaptive process in eukaryotes need to be reconsidered.
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nious haplotype network of the sequenced alleles. Figure 2 shows
the segregating sites for sensitive haplotypes, as well as the I161V
1-mutation and the 3-mutation haplotypes (Table S2 shows
segregating sites for all sequenced alleles).
In all cases the NA and AUS resistant alleles show no signs of
having predated the spread of D. melanogaster out-of-Africa. Instead,
the resistant alleles appear to have arisen in situ in different
populations, as indicated by the observation that locally common
resistant alleles are present on the locally common sensitive
haplotypes. For instance, AUS alleles with the resistant mutation
in the first site (marked t) have the haplotype background that is
identical to the sensitive haplotype N that is common in AUS but
has not been detected by us in NA. In contrast, the NA first site
mutation alleles (marked p through s) have the haplotype
backgrounds that are nearly identical to the sensitive haplotype
L that is common in NA. Additionally, the haplotype background
of one of the AF alleles (marked u) with the resistant mutation
I161V is substantially diverged from the NA and AUS resistant
strains and is more similar to the sensitive alleles common in AF.
This suggests a third independent origin of the mutation I161V in
Figure 2. Soft sweeps at Ace. The table shows segregating sites within the 1.5-kb region of Ace. Each strain is named according to the
corresponding letter in Figure 1. When multiple strains shared the same haplotype, they were named with the same letter but with different numbers
(i.e. w-1, w-2, w-3). For the names and origins of the strains refer to Table S1 and Table S2. The nucleotide position and the consensus sequence at the
top of the table correspond to the y1; cn1bw1sp1strain. The positions of the three resistant mutations are shaded. The table shows all sensitive
haplotypes observed more than once as well as all haplotypes containing the resistant mutation at the first site (I161V) and the ones that contain all
three resistant mutations.
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AF. Note that the complex 2- and 3-mutation haplotypes also
appear to have arisen in situ in the derived populations as their
haplotype backgrounds are most closely related to the common
out-of-Africa sensitive haplotype L.
In summary, the sequence analysis of the resistant and sensitive
alleles reveals two signatures of the adaptive evolution of pesticide
resistance at the Ace gene. First, adaptation has been rapid enough
such that in the past 50 years (1000 to at most 1500 generations
) multiple resistant alleles including a complex allele
containing three independent mutations at three different sites
evolved and spread to high frequencies worldwide. Second, many
resulting resistant alleles are present on distinct haplotypes that
differ in the immediate vicinity of the adaptive sites, such as the
adaptive change from A to G at the first site (I161V) in NA and
AUS that is located on the haplotypes p, q, r, s, and t (Figure 2).
Patterns of evolution at Ace are inconsistent with small
values of H: analytical considerations under simple
Below we consider a simple scenario of a single locus in a
panmictic population of effective size Ne. We assume that the
resistant alleles were in mutation-selection balance prior to
pesticide application with a strongly deleterious selection coeffi-
cient of 25% [13,14] and that they became advantageous after the
application of pesticides.
In Box 1 we show that if H,0.01 the probability of successful
adaptation from standing genetic variation is less than 1% even if
positive selection is extremely strong (s,100%). Thus, if H,0.01,
as previously estimated based on analyses of neutral loci in
Drosophila [18,19], we only need to consider the case of
adaptation from de novo mutations.
The probability of successful adaptation from de novo mutations
depends on the expected waiting time for an adaptive mutation to
emerge and to reach substantial frequencies in the population.
This waiting time is the sum of the expected times to complete two
distinct phases: (1) the establishment phase in which an adaptive
mutation arises and reaches the frequency at which its escape from
stochastic loss is assured and (2) the sweep phase in which the
adaptive allele reaches an intermediate population frequency such
that it can be readily observed. In Box 1 we show that the overall
waiting time can be estimated as
This equation implies that selection must already be very strong
for a single 1-mutation allele to arise and to become prevalent in
less than 1500 generations (s.20% for H=0.01). Selection
coefficients associated with the 2-mutation and 3-mutation alleles
need to be even stronger given that they have to outcompete the 1-
mutation and 2-mutation alleles respectively.
We have established that under this simple model if H is 0.01,
the adaptation at Ace likely involved very strong positive selection
acting on de novo mutations. Can we then explain the second
empirical observation, namely that the same adaptive mutation by
state is observed on several haplotypes that differ in the immediate
vicinity of the adaptive site?
We can imagine two scenarios that would generate this
observation. In the first, the so called hard sweep scenario, a
single adaptive mutation arises in frequency in the population and
eventually ends up on different haplotypes due to recombination
or mutation events that take place in its vicinity during the sweep.
Box 1. Probability of adaptation from standing
genetic variation and waiting time for de novo
mutation. Consider a single locus in a panmictic diploid
population of constant effective size Ne. New resistant
alleles arise at rate Hu=H/3 (only one out of three
mutations give rise to an adaptive allele). Evolution is
modelled in a Wright-Fisher infinite alleles framework with
selection. Heterozygotes have fitness 1+s, fitness is
multiplicative, and the locus evolves independently of
other loci. Prior to pesticide application resistant alleles are
deleterious with selection coefficient sd,0. The density
function g(x) for the frequency distribution of resistant
alleles in mutation-selection balance is then given by 
We thus do not expect resistant alleles to be present in the
population most of the time for H=0.01 (Ne,106) and
become advantageous (s.0). The probability of successful
adaptation from standing genetic variation is approxi-
After the onset of pesticide application, resistant alleles
Under the above scenario, Psgvis very low even in the case
of extremely strong positive selection (Psgv,1% for
Let us now consider de novo resistant mutations that arise
after the onset of pesticide application. The average time it
takes for an adaptive mutation to emerge and to reach
sufficiently high frequency, x,1/(4Nes), assuring its escape
from initial stochastic loss, the so-called establishment
time Te, is on the order of [34,48]
Once established, the frequency trajectory x(t) of the
adaptive mutation becomes essentially deterministic and
can be modelled by 
From establishment it takes on the order of
generations for the mutation to rise to intermediate
population frequency (,50%). The overall expected
waiting time Twfor a de novo adaptive mutation to reach
intermediate frequencies is then
which is Equation (1) in the main text.
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In the other, an example of the so-called soft sweep scenario,
several independent adaptive mutations take place on different
haplotypes and increase in frequency simultaneously.
Theoretical investigations under simple scenarios by Pennings
and Hermisson [20–22] showed that such soft sweeps are
extremely uncommon if H per site is on the order of 0.01
independently of the strength of positive selection. The probability
of the hard sweep scenario resulting in the observation of the
haplotypic diversity in the vicinity of the adaptive allele is
calculated in Box 2. Specifically, we demonstrate that the
probability Pdthat at least two haplotypes are observed at the
end, where the minor haplotype is present in at least a fraction d of
the population, is approximately
Here R is the total rate of mutation or recombination in the locus
per individual per generation and s is the strength of positive
selection. For our locus of length ,1500 bp we have R,6*1026
when assuming a recent estimate for the single-site mutation rate in
D.melanogaster of m,2.5*1029 and a measured recombination
rate of r,0.15 cM/Mbp . The probability to observe different
haplotypes is therefore still very small (Pd,1%) even for a low
population frequency of d=2% and assuming s to be 5%. Note that
this calculation is very conservative given that in our data multiple
haplotypes are present at much higher frequency than 2%, multiple
haplotypes vary at sites extremely close to the adaptive allele (within
38 bp), and positive selection was likely much stronger.
In conclusion, under this simple scenario, our empirical
observations at Ace are unexpected if H is indeed on the order
of 0.01. Specifically, considering how strong selection must be, we
should not be seeing more than one distinct haplotype containing
the same adaptive mutation.
Note that if H were much higher, for example on the order of
one or larger, then all of our observations are expected. Soft
sweeps would be commonplace because many more mutations
enter the population in every generation and can increase in
frequency simultaneously thereby generating multiple haplotypes
containing the same adaptive mutations , as observed in the
data. The establishment time would become smaller making it
easier to observe complex, 3-mutation alleles at Ace in less than
1500 generations. However, selection would still need to be strong
because the time it takes for an adaptive allele to reach
intermediate frequencies is only weakly (logarithmically) depen-
dent on the effective population size and inversely proportional to
the selection coefficient.
Patterns of evolution at Ace require large values of H:
numerical investigations for a large range of evolutionary
We have shown above that under very simple population
scenarios the pattern of adaptive evolution at Ace requires large
Box 2. Probability of distinct haplotypes in a hard
sweep. Consider a single adaptive mutation that reaches
establishment frequency in generation t=0. Its subsequent
frequency trajectory is x1(t). Mutated or recombined variants
of its original haplotype become established in the
population at rate
Here R is the rate of either mutation or recombination taking
place on the sweeping initial haplotype per individual per
generation, and the factor 2s is the probability of an adaptive
overestimate of the establishment probability of the second
with a probability that is closer to 2s(12x1).
What is the probability that a mutated or recombined
haplotype also reaches at least frequency d in the population?
Such a second haplotype has to emerge within a limited
number Td of generations after the first. Otherwise the
population will already be dominated by the first haplotype,
neutralizing any selective advantage of the second.
Let us assume that the second haplotype becomes
established at time Td. We denote its frequency trajectory
by x2(t). The crucial observation allowing us to calculate Tdis
that the ratio x1(t)/x2(t) remains constant for all t$Td, as both
haplotypes have the same fitness. In particular, because we
require that the second haplotype is eventually present in a
fraction d of the population, we have
The latter approximation applies for small d%1. At t=Td, the
trajectory x1(t) can still be modelled by Equation (B4); no
interference between different adaptive haplotypes has
occurred until then because the second allele has been
extremely rare or absent for t,Td. Recalling that the second
haplotype becomes established when it reaches a frequency
x2,1/(4Nes), we thus have:
Solving Equations (B8) and (B9) for Tdand assuming Nesd&1
The condition Nesd&1 is justified when positive selection is
strong and d is large enough that there is a chance of
sampling the second allele.
Mutations establishing after Tdcan only reach a population
frequency smaller than d. The probability of observing two
different haplotypes with the minor haplotype being present
in at least a small fraction d of the population can therefore
be estimated from the probability that a new variant of the
initial adaptive haplotype emerges within the first Td
generations. We obtain
where we again assumed Nesd&1. Note that Pddoes not
depend on H.
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values of H. However, it is unclear whether such large values of H
are required under more complex and realistic scenarios.
Variation in strength of selection, recombination rate, and
population structure might affect the probability of evolving
complex 3-mutation alleles from the simpler 1- or 2-mutation
alleles  and the probability of observing multiple haplotypes
containing the same adaptive mutations.
To investigate quantitatively the potential impact of such effects
we conducted extensive simulations of adaptation at Ace under a
large number of selective (s=2.5% to 500%) and demographic
scenarios (1 to 100 subpopulations, migration rates M=0.01 to 10
individuals per generation between any two subpopulations), and
with varying recombination rate (r=0 to 10 cM/Mbp) (Table
In Figure 3A and 3B we show the frequency trajectories of
adaptive haplotypes for two representative simulation runs in a
simple single population scenario together with summary statistics
across a large number of runs for the two key H regimes (H=0.01
and H=1). We use four statistics: P1m and P3m are the
probabilities that a single adaptive mutation (1m) allele or the 3-
mutation allele (3m) were ever present in at least 10% of the
population during the simulation; Pssis the probability that a single
adaptive mutation is present on distinct haplotypes in a sample of
reasonable size (the observation that we will call the soft sweep
signature from now on); and Pcis the combined probability of
observing both the complex 3-mutation allele and a single-
mutation soft sweep signature during the same simulation.
Figure 3A and 3B show results consistent with our analytical
considerations. When H,0.01 and selection is of moderate
strength, neither the evolution of complex 3-mutation alleles nor
soft sweeps signatures are likely. Only when H approaches one do
both observations become commonplace.
Figure 3C shows the summary of the results for the more
complex scenarios (complete results are shown in Table S3). In
these more complex scenarios we assessed H by using coalescent
simulations to estimate the average heterozygosity per site (Hp) at
neutral sites and by summing H across all subpopulations (HS)
. Our simulations confirm that only when both Hpand HS
become on the order of one or larger is it likely to observe fast
evolution of complex 3-mutation alleles and at the same time soft
sweep signatures. Strong selection does indeed improve the
probability of seeing complex adaptive alleles but also, as expected,
does not generate signatures of soft sweeps when H is small.
Interestingly our simulations show that if H,1, then most of the
observed signatures of soft sweeps are generated by multiple de novo
mutations and are not due to the recombination of the same
adaptive mutation onto different haplotypes. This is because
signatures of soft sweeps are still commonly observed in
simulations even when the recombination level is set at zero. It
is also consistent with analytical considerations under simple
scenarios (Text S1).
Our data and analysis strongly suggest that the patterns of
adaptation observed at Ace in the last 1000–1500 generations are
highly unlikely in a population in which H per site is on the order
of 0.01 as it is commonly assumed. Instead, it appears that H per
site must have been at least 0.1 and more likely on the order of one
or larger. It is possible to elevate H by increasing the mutation rate
or by increasing the effective population size. We assessed whether
Ace had an unusually high mutation rate by estimating divergence
of Ace in D. melanogaster from its D. simulans ortholog at synonymous
sites. We found the divergence to be 7.9%, which is similar to the
genome average of ,10% [27,28]. In addition, Hp per site
estimated from polymorphisms at synonymous sites in sensitive
alleles is 0.008, which is also consistent with the genome average
. Thus we conclude that the effective population size in D.
melanogaster over the past 1000–1500 generations is likely to be very
Such a large value of Nemight appear puzzling given that levels
of standing neutral polymorphism suggest that Neis much smaller
[18,19]. To resolve this discrepancy it is necessary to take a closer
look at the concept of an effective population size. Effective
population size is commonly defined by the inverse magnitude of
the frequency-fluctuations of a neutral allele in two consecutive
generations . Over a number of generations, effective
Figure 3. Population dynamics of resistance adaptation for
different H regimes. (A) Frequency trajectories of resistant haplo-
types from a typical simulation of a single population with H=0.01
during the first 1500 generations after pesticides are applied. The
selection scenario is s1m=0.05, s2m=0.1, s3m=0.2. Trajectories are
shown for all resistant haplotypes that reached a population frequency
above 2%. On the right, summary statistics for P1m, P3m, Pss, and Pc
estimated from 105runs are shown. (B) Frequency trajectories of a
typical simulation run and summary statistics for a single population
with H=1. This simulation shows a soft sweep for the 3-mutation allele
(two different haplotypes at high frequencies; their frequencies
together add to 100%). Also, note that 2-mutation alleles do not rise
to high frequencies before being taken over by the fitter 3-mutation
alleles. (C) Pcfor a variety of different selection, recombination, and
population substructure scenarios as specified in Table S3. Probabilities
Pcof each scenario are plotted against the average heterozygosity Hp
of the entire population estimated from coalescent simulations.
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population size is the harmonic mean of the effective population
sizes over individual generations and thus is dominated by the
smallest values of Ne. (Equivalently, frequency fluctuations over
many generations are dominated by the largest fluctuations over
single generations). Estimates of the effective population size using
frequent neutral polymorphisms reflect Neharmonically averaged
over long periods of time and are therefore very sensitive to any
periods of low population size even far back into the past .
In sharp contrast, adaptation at Ace occurred within less than
1500 generations. The Ne relevant to adaptation at Ace is the
harmonic mean of Nevalues over the past 1500 generations or
even fewer. Unlike Nemeasured from ancient standing variation, it
is not reduced by the bottlenecks and nearby selective sweeps that
occurred more than 1500 generations ago. Consider a simple
bottleneck scenario outlined in Figure 4 that is similar to the out-
of-Africa scenario of Thornton and Andolfatto . It is apparent
that even if the current Ne is 100-fold larger than commonly
assumed, population behaviour of a frequent neutral allele does
not change substantially and the estimates of H from standing
variation are not altered. To give another example, if D.
melanogaster populations were to spend 90% of their time with Ne
of 1010and 10% at Neof 105with the shifts occurring about every
1000 generations, the harmonic mean Nederived from common
neutral polymorphisms would be ,106and yet the adaptive
process would take place primarily in populations of 1010with
H.1 per site. In this case, strong adaptation in Drosophila would
not be limited by mutation most of the time.
The short-term Neis bounded by the census population size (N)
and thus if N is much smaller than the reciprocal of the mutation
rate per site we can be certain that adaptation would be mutation-
limited. In many species N can be much larger than the reciprocal
of mutation rate and thus in these species it is possible that
adaptation is not limited by mutation at single sites. However, it is
Nemeasured over time scales relevant for adaptation and not N
that needs to be assessed to answer this question. Even short-term
Nemight be much smaller than N if populations crash regularly on
very fast temporal scales (such as those induced by winters in
temperate climates) or if the numbers of successfully reproducing
adults in each generation is sharply limited by extrinsic factors, for
example by available substrates for laying eggs. Thus the studies of
strong adaptation, such as the one presented here, are essential to
determining whether adaptation in general is mutation-limited in a
It is reasonable that Drosophila and many other organisms
undergo recurrent boom-bust cycles thereby reducing the long-
term Nestrongly but allowing adaptation during the boom years to
occur in populations of large short-term Ne. In addition, Drosophila
appears to undergo pervasive adaptation [30,31] with most
common neutral polymorphisms estimated to have been affected
by several selective sweeps in their genomic vicinity . Such
pervasive adaptation generates dynamics similar to recurrent
bottlenecks and will also reduce the long-term Nevalues even if the
short-term Nemight be consistently large. This situation is similar
to that found in HIV, where the effective population size estimated
from observed diversity underestimates the census size by many
orders of magnitude and is likely to underestimate the short-term
Nerelevant for adaptation as well .
The possibility that adaptation at single sites in D. melanogaster is
not limited by mutation has profound implications. The distinction
between standing variation and de novo mutations at single sites is
blurred since virtually all single-site mutations then exist in the D.
melanogaster population at any given time. Strong adaptation should
be much more rapid and generally result in soft sweeps. Complex
adaptations that require multiple changes can be generated
without fixation of interim states and with an enhanced chance
of crossing fitness valleys . This raises the question of whether
the widespread use of the weak mutation, strong selection
(‘‘WMSS’’) model for the study of adaptation should be broadened
to include cases of strong mutation [34,35].
The number of sweeps (hard or soft) might also in general be
lower than the number of adaptive substitutions if complex
adaptations requiring multiple substitutions are common. Indeed,
in our simulations of evolution at Ace in the strong mutation regime
(H per site on the order of 1), the complex 3-mutation alleles
generally evolve without fixation of intermediate 1- and 2-
mutation alleles (Figure 3). The number of adaptive substitutions
estimated using McDonald-Kreitman approaches should then be
larger than the number of independent adaptive fixations and the
prediction of the number of selective sweeps derived from the
number of adaptive substitutions should be upwardly biased .
Note that all of these expectations hold especially well for strong
selection because it operates over shorter time scales and is
therefore less sensitive to recurrent but infrequent bottlenecks 
and neighbouring selective sweeps.
Most of the current statistical approaches for the study of
adaptation rely on the expected signatures of hard sweeps .
Such methods should regularly miss or misidentify strong
Figure 4. Population dynamics of neutral and adaptive alleles
in a population with a bottleneck. (A) The population history
similar to that inferred by Thornton and Andolfatto for D. melanogaster
. Values of Hpand Watterson’s Hwwere obtained from coalescent
simulations with 100 sampled genomes. (B) Same scenario as (A) except
for the current population size is changed to 108.
Adaptation in Drosophila Not Limited by Mutation
PLoS Genetics | www.plosgenetics.org7June 2010 | Volume 6 | Issue 6 | e1000924
adaptation if it in fact commonly involves soft sweeps as in the case
of Ace . For example, if one searches exclusively for hard
sweeps, then complete soft sweeps might appear as ongoing hard
sweeps and the polymorphisms associated with the most frequent
haplotype would appear as the likeliest candidates for the adaptive
mutation whereas the true adaptive mutation would be fixed in the
population. Methods exist that have high power to detect soft
sweeps , but they are used less often because soft sweeps have
been considered unlikely a priori. However, a number of cases of
adaptation in Drosophila and mosquitoes show clear signatures of
soft sweeps [38–40]. Soft sweeps might also be common in
humans, with the soft sweep associated with lactase persistence
providing the strongest signature of adaptation in humans [41,42].
Our results suggest that the possibility of pervasive soft sweeps
needs to be taken seriously.
Recurrent boom-bust cycles are a general feature in population
dynamics of most studied organisms. Adaptation and recurrent
selective sweeps reducing the long-term but not the short-term Ne
might also be common. It follows then that short-term and long-
term Nevalues are likely to be different as a rule. The shortest term
Neis only bounded by the census population size, which is often
very large and can easily be in the billions, particularly for insects
or marine organisms. It is thus possible that strong adaptation at
single sites may not be limited by mutation in many eukaryotes,
similar to the situation found in bacteria and viruses .
Materials and Methods
Ace locus genotyping
We sequenced 1450 bp encompassing exons 2 through 4 of Ace.
Resistant mutations I161V and G265A lie in the 3rd exon while
F330Y and G368A lie in the 4th exon (Figure S1). Initially we
sequenced this locus in 68 strains from 20 populations chosen to
represent the Ace locus in a variety of geographical locations. The
list of the populations and the number of lines investigated are
given in Table S1 and Table S2. For some of the strains that
appeared heterozygous after sequencing of the PCR product, the
DNA was first amplified using a proofreading DNA polymerase
(Platinum Pfx; INVITROGEN) and cloned using Zero Blunt
TOPO PCR cloning kit (INVITROGEN) before sequencing.
Note that not all heterozygous strains were cloned, only those that
contained a resistant mutation and the AF strains. The primers
used for PCR amplification of the Ace locus were:
PCR products were then sequenced. Of the 68 sequenced
strains, 26/68 (,40%) have a single or multiple resistant
mutations. Mutations at I161V, G265A and F330Y were
identified in isolation and in combination in multiple populations,
while G368A was never observed. We then used PASA  to
identify strains that contained one or more of the three observed
mutations and sequenced the identified strains. The primers used
for PASA were:
The 161 primer pair amplifies more effectively in the presence
of the mutation I161V. The 265 primer pair is specific to G265A
and the 330 primer pair is specific to G330Y. The annealing
temperatures required for allele specific priming used for 161, 265
and 330 were 61.5uC, 59.5uC and 60.6uC respectively. As positive
and negative controls we performed PASA on strains in which the
resistant sites had been previously characterized. We sequenced 37
strains from 8 populations that had amplified with one or more of
the allele-specific primers. 31/37 (84%) of these strains contained
resistant mutations. The incorrect classification of the 6 strains is
likely due to the addition of excess template to these PCR reactions
resulting in non-specific priming. In total, we sequenced the Ace
locus in 105 strains from 27 populations from five different
continents (Table S1). Twelve of these strains were excluded from
the analysis due to poor sequence quality.
Construction of haplotype network
The most parsimonious haplotype network was constructed
using TCS 1.21 . All resistant alleles, except those for which
we had poor sequence data, and all sensitive alleles observed more
than once were used for the construction of the network. All AF
strains and M strains were also included in the network to provide
information on ancestral and modern variation respectively at the
Estimation of Hpand divergence
Measures of Hpand divergence with Drosophila simulans at the
Ace locus were obtained using DnaSP . All sensitive strains
analyzed in this study were used for the estimation.
Forward simulations of Ace adaptation
Our simulation models the population frequency dynamics of
haplotypes at the 1.5 kb-long sequenced Ace locus and incorpo-
rates mutation, recombination, selection, and population sub-
Haplotypes are classified by their particular adaptive allele
configuration at the three adaptive sites. We describe this
configuration in terms of a vector a1a2a3, indicating whether at
site i the resistance-conferring mutation is present (ai=1) or not
(ai=0). A configuration 101, for example, specifies resistant
mutations at sites one and three, but no resistant mutation at
We use an infinite alleles model for new haplotypes, i.e. every
mutation or recombination event at the locus is assumed to give
rise to a new haplotype, which can be distinguished from all other
haplotypes in the population. This is implemented in our
simulations by assigning a unique ID to every new haplotype.
The specific nucleotide sequence of the new haplotype is not
relevant for our purposes; only changes in the adaptive-allele
configuration are modelled explicitly. We also do not distinguish
different sensitive haplotypes as we focus on the population
dynamics of adaptive haplotypes. These simplifications substan-
tially increase the performance of our simulations, allowing us to
investigate scenarios with population sizes up to 109in reasonable
Mutations at adaptive sites and recombination events where the
recombination breakpoint lies between two adaptive sites can
generate new haplotypes with different adaptive-allele configura-
tion (Table S4). Note that at each site only one specific nucleotide
Adaptation in Drosophila Not Limited by Mutation
PLoS Genetics | www.plosgenetics.org8June 2010 | Volume 6 | Issue 6 | e1000924
is the resistant allele and thus only one out of three mutations of a
sensitive allele will give rise to it.
The evolution of haplotype frequencies is simulated in terms of
a Wright-Fisher model with directional selection, i.e. we assume
panmictic subpopulations of constant size and non-overlapping
generations . Every haplotype h has a specific selection
coefficient s(h). The mean fitness of a subpopulation at time t is
generation t+1 are obtained by sampling from a multinomial
We group resistant haplotypes into three classes according to
the number of resistance-conferring mutations they bear: 1m
haplotypes have one resistant allele (100,010,001), 2m haplotypes
have two (011,101,110), and 3m haplotypes have all three
resistant alleles (111). For simplicity, we assume that all
haplotypes in the same class have equal selection coefficients
s1m, s2m, and s3m, respectively. Prior to pesticide application all
resistant haplotypes are modelled to be deleterious with selection
The key simulation parameters are the selection scenario
defined by the selection coefficients s1m, s2m, and s3m, the
recombination rate r, the number n of subpopulations, the
migration rate M between subpopulations, and the value of H
within subpopulations. We use a constant mutation rate of m=2.5
* 1029per site per generation . Different H-values thus
correspond to different subpopulation sizes. In particular,
H=0.01 corresponds to N=106, and H=1.0 corresponds to
N=108. We estimated a recombination rate of r=0.15 cM/Mbp
for our locus , but investigate also other recombination rates in
Simulation runs start with one single sensitive haplotype present
in all subpopulations at 100% frequency. Before pesticide
application commences, mutation-selection equilibrium of resis-
tant haplotypes is established within a burn-in period of 1000
generations. This fully suffices to establish equilibrium due to the
strong purifying selection against all resistant haplotypes prior to
pesticide application (Box 1). We also verified that longer burn-in
times do not change our results. After the burn-in period, pesticide
application starts by switching to the corresponding selection
scheme. The simulation is then followed for another 1500
generations representing approximately 50 years of pesticide
usage. During every generation individual subpopulations evolve
according to the following steps:
h½s(h)xh(t)?, where xh(t) is the frequency of haplotype
h in the subpopulation at time t. Haplotype frequencies in
1)A random number of mutation events is drawn from a
Poisson distribution with mean m * 1.5 kb * 2N. For each
mutation a random haplotype is drawn from the subpop-
ulation and mutated at a randomly chosen position.
2) A random number of recombination events is drawn from a
Poisson distribution with mean r * 1028* 1.5 kb * 2N. For
each recombination event two random haplotypes are
drawn from the subpopulation and recombined at a
randomly chosen breakpoint.
3) The numbers of migrating individuals to each other
subpopulation are drawn from a Poisson distribution with
mean M. For each migrating individual two random
haplotypes are drawn from the source population and
added to the destination subpopulation.
4)All haplotype frequencies are evolved one generation
according to the above-described binomial sampling proce-
During a simulation run we analyze whether resistant
haplotypes emerged and whether soft sweep signatures among
1m haplotypes were observed. We define 1m resistance by at least
one of the three 1m adaptive-allele configurations (001, 010, or
100) ever being present in more than 10% of the population
during the run. Accordingly, 3m resistance is defined by the
complex 3-mutation allele (111) ever present in at least 10% of the
population. A soft sweep signature (ss) is ascertained if at any time
during the run two independently drawn alleles have greater than
10% probability to bear the same 1m configuration on different
haplotypes. The statistics P1m, P3m, and Pss are the respective
probabilities averaged over many runs. Pcdenotes the combined
probability that 3m resistance emerged and a soft sweep signature
was observed during the same run.
A crucial assumption of our simulation is the applicability of an
infinite alleles model, i.e. all mutation or recombination events are
assumed to be detectable. This can lead to an overestimation of
the probabilities to observe soft sweep signatures in our simulations
if independent mutation events frequently occur on the same
haplotype, or if newly recombined haplotypes often resemble
haplotypes already present in the population. We can estimate the
resulting error from the probability that an individual is
homozygous for the 1.5 kb-long locus. From coalescent simula-
tions using ms  we infer it to be on the order of ,10% when
assuming a per site heterozygosity of out-of-Africa D. melanogaster
subpopulations of Hp,0.5% [18,19] and the above specified
recombination and mutation rates for our locus. Note, however,
that in any case the infinite alleles model can only lead to an
overestimation of the probability to observe soft sweep signatures.
It is therefore always conservative in terms of our analysis. The
probabilities P1mand P3mare not affected by the choice of an
infinite alleles model.
The simulation was implemented in C++. Runs were performed
on the Bio-X2 cluster at Stanford University. All source code is
available from the authors upon request.
Found at: doi:10.1371/journal.pgen.1000924.s001 (0.04 MB PDF)
Structure of the Ace gene.
Found at: doi:10.1371/journal.pgen.1000924.s002 (0.05 MB PDF)
Description of D. melanogaster strains.
Found at: doi:10.1371/journal.pgen.1000924.s003 (0.07 MB PDF)
Segregating sites at the Ace locus in all strains
Found at: doi:10.1371/journal.pgen.1000924.s004 (0.06 MB PDF)
Dynamics of resistance adaptation for different
Found at: doi:10.1371/journal.pgen.1000924.s005 (0.04 MB PDF)
Change of mutation configuration due to mutation or
Found at: doi:10.1371/journal.pgen.1000924.s006 (0.11 MB PDF)
Origin of soft sweep signatures.
We thank members of the Petrov lab, Hunter Fraser, Ward Watt, Marcus
Feldman, Joanna Kelley, Graham Coop, Molly Przeworski, Joachim
Hermisson, Richard Lewontin, Daniel Fisher, John Novembre, Georgii
Bazykin, two anonymous reviewers, and the participants of the Aspen 2010
Biophysics Conference ‘‘Populations, Evolution and Physics’’ for helpful
comments and discussion.
Adaptation in Drosophila Not Limited by Mutation
PLoS Genetics | www.plosgenetics.org 9June 2010 | Volume 6 | Issue 6 | e1000924
Conceived and designed the experiments: TK PWM DAP. Performed the
experiments: TK PWM. Analyzed the data: TK PWM DAP. Contributed
reagents/materials/analysis tools: TK PWM DAP. Wrote the paper: TK
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Adaptation in Drosophila Not Limited by Mutation
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