Download ADAPTATION AND MALADAPTATION IN SELFING AND

O R I G I NA L A RT I C L E
doi:10.1111/j.1558-5646.2012.01778.x
ADAPTATION AND MALADAPTATION IN
SELFING AND OUTCROSSING SPECIES: NEW
MUTATIONS VERSUS STANDING VARIATION
Sylvain Glémin1,2 and Joëlle Ronfort3
1
Institut des Sciences de l’Evolution de Montpellier, UMR 5554 CNRS, Place Eugéne Bataillon, 34095 Montpellier cedex 5,
France
2
3
E-mail: [email protected]
INRA, UMR AGAP, 2 place Pierre Viala F-34060 Montpellier cedex 1, France
Received March 28, 2012
Accepted July 12, 2012
Evolution of selfing from outcrossing recurrently occurred in many lineages, especially in flowering plants. Evolution of selfing
induces dramatic changes in the population genetics functioning but its consequences on the dynamics of adaptation have been
overlooked. We studied a simple one-locus model of adaptation where a population experiences an environmental change at a
given time. We first determined the effect of the mating system on the genetic bases and the speed of adaptation, focusing on the
dominance of beneficial mutations and the respective part of standing variation and new mutations. Then, we assumed that the
environmental change is associated with population decline to determine the effect of the mating system on the probability of
population extinction. Extending previous results, we found that adaptation is more efficient and extinction less likely in outcrossers
when beneficial mutations are dominant and codominant and when standing variation plays a significant role in adaptation.
However, given adaptation does occur, it is usually more rapid in selfers than in outcrossers. Our results bear implications for
the evolution of the selfing syndrome, the dynamics of the domestication process, and the dead-end hypothesis that posits that
selfing lineages are doomed to extinction on the long run.
KEY WORDS:
Adaptation, dominance, extinction, mating systems, selfing, variation.
Although the majority of eukaryotes reproduce sexually via outcrossing, selfing (at least partial) is common in many groups,
especially in angiosperms (Igic and Kohn 2006) but also in animals (Jarne and Auld 2006). In plants, the transition from outcrossing to selfing has been recognized as a major evolutionary
trend that recurrently occurred (e.g., Darwin 1876, 1878; Stebbins
1974). Selfing can evolve from outcrossing thanks to two main
advantages: reproductive assurance under pollen limitation, such
as in pioneering plants colonizing new habitats (Baker 1955),
and the twofold transmission of genes (Fisher 1941). Inbreeding
depression opposes these advantages and explains the maintenance of outcrossing (reviewed in Charlesworth 2006). However,
the increase in homozygosity in selfing populations will lead to
the expression and the elimination of many recessive deleteri-
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No claim to original U.S. government works.
Evolution 67-1: 225–240
ous mutations by selection (Lande and Schemske 1985), which
should purge their inbreeding depression. This is the reason why,
once self-fertilization has evolved, reversion to outcrossing is,
in theory, very unlikely: after purging, inbreeding depression is
expected to be too low to overcome the advantages of selfing.
Moreover, outcrossing is commonly ensured by complex mechanisms such as self-incompatibility (SI) systems involving pollen–
pistil recognition at the molecular level. Breakdown of such systems, allowing evolution of self-fertilization, are thus much more
frequent than the evolution of new complex SI systems. Accordingly, unilateral transitions have been documented in several studies (e.g.,Takebayashi and Morrell 2001; Igic et al. 2006; Escobar
et al. 2010). Although transitions toward selfing seem to be mainly
unidirectional, the vast majority of species are outcrossing. This
S . G L É M I N A N D J. RO N F O RT
requires lower diversification (i.e., speciation – extinction) rates
in selfing clades (for self-compatibility see Igic et al. 2008),
which should be evolutionary dead-ends, as initially suggested by
Stebbins (1957). Supporting this view, most selfing lineages are of
recent origin (Takebayashi and Morrell 2001) and it has been recently showed in Solanaceae that self-compatible species have
higher extinction rates than self-incompatible ones (Goldberg
et al. 2010).
Nevertheless, the underlying causes of such an evolutionary
dead-end are still unclear. On one hand, selfing reduces effective
population size, Ne , by two because of nonindependent gamete
sampling during reproduction (Pollak 1987; Nordborg 1997),
which reduces the efficacy of selection. On the other hand, selfing
also exposes alleles in homozygotes, facilitating selection. Both
effects exactly compensate for intermediate dominance, whereas
selection is more (resp. less) efficient in selfing than in outcrossing
for recessive (resp. dominant) alleles (Caballero and Hill 1992;
Charlesworth 1992; Pollak and Sabran 1992). However, Ne is expected to be reduced beyond the twofold automatic effects (1)
by genetic hitchhiking effects (Maynard-Smith and Haigh 1974;
Charlesworth et al. 1993a), because effective recombination is low
in selfers (Nordborg 2000) and (ii) by recurrent bottlenecks that
are expected to be more frequent in selfers because a single seed
can found a new population (Schoen and Brown 1991; Ingvarsson
2002). If Ne is significantly reduced beyond the twofold threshold,
selfing lineages should be prone to the accumulation of deleterious mutations (Glémin 2007). This hypothesis has been tested
in several species through molecular phylogenetic approaches,
and no signature of relaxed selection in selfers has been found
so far (Wright et al. 2002; Cutter et al. 2008; Haudry et al. 2008;
Escobar et al. 2010). This suggests that selfing could be of too
recent origin and that the accumulation of deleterious mutation
would not be the main cause of their extinction, contrary to what is
observed in clonal species (reviewed in Glémin and Galtier 2012).
Reduced adaptive potential in selfers is the other major—and the
first initially proposed—cause underlying the dead-end theory
(Stebbins 1957). However, it is still not clear how selfing affects
the dynamics of adaptation. Despite ongoing developments, most
models of the adaptation process are based on panmictic populations and selfing has only been taken into account in the simplest
ones, mainly the adaptation from new mutations at one locus (e.g.,
Caballero and Hill 1992; Charlesworth 1992; Roze and Rousset
2003; Glémin 2007). However, it is increasingly recognized that
standing variation could play a significant role in adaptation (Orr
and Betancourt 2001; Hermisson and Pennings 2005; Barrett and
Schluter 2008; Pritchard et al. 2010). Interestingly, Stebbins arguments relied on the idea that selfing species have reduced polymorphism, and thus lower adaptive opportunities from standing
variation (Stebbins 1957, 1974).
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EVOLUTION JANUARY 2013
A better understanding of the dynamics of adaptation in selfing species would also be useful in other contexts for which
theoretical clarification is needed. For instance, the effect of selfing versus outcrossing on the dynamics of adaptation during the
domestication process has been questioned in this particular case:
contrary to the arguments of the dead-end hypothesis, selfing
could have facilitated adaptation during domestication by favoring
the fixation of recessive traits (Zohary and Hopf 2000; Diamond
2002; Glémin and Bataillon 2009). A shift toward selfing is also
commonly associated with the evolution of specific traits (the socalled selfing syndrome), such as flower size reduction and lower
investment in the male function (reviewed in Sicard and Lenhard
2011), sometimes over a short time scale, as in Capsella rubella
(Foxe et al. 2009; Guo et al. 2009), or Leavenworthia alabamica
(Busch et al. 2011), although it is not clear if this is simply due to
the relaxation of constraints on reproduction or to the adaptation
toward a new optimum of resource allocation. Moreover, the genetic bases of selfing syndrome evolution are not well understood,
partly because the selfing rate evolves with the evolution of these
traits (for instance see discussion in Fishman et al. 2002). Investigating the dynamics of adaptation following the shift in mating
systems would help in resolving these issues.
The aim of this article is to predict whether the genetic bases
of adaptation vary with mating systems and how selfing may
affect the adaptive potential of the species. Especially, can a lack
of adaptation doom selfing species to extinction, as assumed by
the dead-end hypothesis? Here, we focus on the simplest case of
adaptation: the fixation of a beneficial allele at a single locus. We
extend previous models (Hermisson and Pennings 2005; Orr and
Unckless 2008) by including partial selfing and scenarios specific
to selfing species.
General Formulation
We consider a single population of size N, with a selfing rate σ, and
nonoverlapping generations. Except when explicitly mentioned,
the population size and the selfing rate are assumed to be constant.
Following Hermisson and Pennings (2005), we consider that this
population experiences an environmental change at some time
that changes the selection regime at a given biallelic locus. At this
locus, the “wild” allele A mutates with rate u to a new allele, a,
which is beneficial after the environmental change. Allele a could
be initially present, but not fixed, before the environmental change
and was either neutral or deleterious. The three genotypes, AA, Aa,
and aa have the relative fitness 1, 1 – hd sd , and 1 – sd before, and 1,
1 + hb sb , and 1 + sb after the environmental change, where sd and
sb stand for the deleterious and beneficial selection coefficients
and hd and hb for the dominance coefficients. Back mutations are
neglected. As we consider a single locus, we assume that, during
M AT I N G S Y S T E M S A N D A DA P TAT I O N
the adaptation process, there is no interference between mutations
because of linkage or epistasis.
With partial selfing, the effective population size is given by:
Ne =
αN
1+ F
1.0
0.8
0.6
(1)
σ
2−σ
where F =
is Wright’s fixation index (Pollak 1987; Caballero
and Hill 1992) and α summarizes the hitchhiking and demographic effects of selfing that reduce the effective population size
beyond the automatic twofold effect (Glémin 2007). α = 1 for
σ = 0 and 0 < α ≤ 1 otherwise. For instance, Ne can be reduced
because of the recurrent elimination of strongly deleterious mutations, the so-called background selection process (Charlesworth
et al. 1993a): considering a focal locus, the effective number of
gametes contributing to future generations is reduced because
those carrying deleterious alleles cannot remain on the long run.
Background selection can thus be strong in selfing species where
recombination is ineffective to breakdown the associations with
deleterious alleles. Under the background selection model, α can
be written as
1
1
α = Exp −U
−
(H + F − H F)S + C(1 − F)
HS + C
(2)
where U is the genomic mutation rate toward strongly deleterious
mutations, C is the genomic recombination rate, S the mean selection coefficient against strongly deleterious mutations, and H
is their dominance coefficients (e.g., Glémin 2007). When there
is no background selection (U = 0), α tends toward 1. Here, we
assume that the proportion of strongly deleterious mutations is independent of the selfing rate, which is an approximation because
some mutations strongly selected when Ne is large can become
nearly neutral when Ne is smaller. U should thus weakly decrease
with F, however, in highly selfing species, nearly neutral mutations can also reduced Ne through Muller’s ratchet (Charlesworth
et al. 1993b), which is not taken into account here. Several examples of the evolution of the Ne /N ratio as a function of the selfing
rate under background selection are given in Figure 1, showing
that Ne is strongly reduced mainly for high selfing rates and/or
low recombination rates. Note, however, that the results presented
below only rely on single locus theory and that the use of a modified effective size is an approximation of multilocus dynamics.
Explicit models of the effect of selfing on adaptation at multiple
loci are not treated here and are still to be developed.
First, we study the genetic bases and the time for adaptation
and we assume that the population size remains constant. In the
last part, we study the probability of extinction due to a lack of
adaptation following the method proposed by Orr and Unckless
(2008). We assume that the population exponentially declines after the environmental change and that it either goes extinct or
Ne N
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Selfing rate σ
Ne /N ratio as a function of selfing rate under background selection as given by equation (2). Bold line: no back-
Figure 1.
ground selection. Thin line: U = 0.2, C = 5. Dashed line: U = 0.5,
C = 5. Dotted line: U = 0.5, C = 1, H = 0.2, and S = 0.1.
is rescued by the fixation of the appropriate beneficial mutation (see below). We derive analytical approximations, especially
by extending previous results obtained for panmictic populations
(Hermisson and Pennings 2005; Orr and Unckless 2008) to the
case of partially self-fertilizing ones. We thus directly give the results in the main text and the details are dispatched in Supporting
information Material. To make the article self-contained, we also
summarize useful previous results obtained by other authors. All
notations are summarized in Table 1.
Simulations
The analytical predictions were checked against stochastic simulations of a Wright–Fisher model. When population size remains
constant, the frequency of each of the three genotypes is followed.
Every generation, reproduction occurs with a proportion σ of the
population reproducing through selfing, and then selection. The
expected frequencies after reproduction and selection are computed. The genotype frequencies of the new generation are drawn
from a multinomial distribution with probabilities corresponding
to the expected frequencies. When recurrent mutations are taken
into account, the number of mutant alleles is drawn from a Poisson distribution with mean 2Npu, where p is the frequency of the
A allele, and attributes randomly to AA and Aa genotypes according to their frequency weighted by the number of A alleles they
carry (two or one). To compute the probability of fixation from
standing genetic variation, simulations are started 6N generations
before the environmental change as in (Hermisson and Pennings
2005) to let the population reach mutation–drift or mutation–
selection–drift balance (for initially neutral or deleterious mutations, respectively). After 6N generations, new mutational input
is stopped and the selection coefficient of the allele a changes
EVOLUTION JANUARY 2013
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S . G L É M I N A N D J. RO N F O RT
Table 1.
Notations.
N
Ne
α
U, H, S, C
N0
r
σ
F
u
sd , sb
hd , hb
he (h)
π(h,s,x)
ρ(h,s,x)
Pnew
neutral
delet
Psv , Psv
, Psv
Psv
h lim
sv
T fnew
ix , T f ix
Twait
Tadapt
Trelax
neutral
ext , new
, delet
ext , ext
ext
h ext
lim
Demographic population size.
Effective population size.
Coefficient summarizing the hitchhiking and demographic effects of selfing that reduce the effective
population size beyond the automatic twofold effect.
Genomic parameters of deleterious mutations for the background selection model: mutation rate,
mean dominance coefficient, mean selection coefficient, mean recombination rate.
Demographic population size before the environmental change in the extinction model.
Rate of population decline in the extinction model.
Selfing rate.
Wright’s fixation index (FIS ).
Mutation rate from A to a.
Selection coefficients of the a allele before (deleterious effect) and after (beneficial effect) the
environmental change.
Dominance coefficients of the a allele before and after the environmental change.
Effective dominance coefficient.
Probability of fixation of an allele starting at frequency x.
Stationary density function of the frequency of the a allele before the environmental change,
conditioned on a being the derived allele.
Probability of fixation from new mutation.
Probabilities of fixation from standing variation, from initially neutral, and initially deleterious
variation, respectively.
Threshold dominance coefficient above which Psv is higher in outcrossers than in selfers.
Average times to fixation, given fixation has occurred, from new mutation and standing variation,
respectively.
Average waiting time of appearance of the mutation destined to be fixed.
Average time until complete adaptation, that is, until fixation of the beneficial allele either from
standing variation or recurrent mutations.
Average time until fixation of a neutral allele either from initially deleterious standing variation or
recurrent mutations.
Probabilities of extinction, general expression, without standing variation, including initially neutral
standing variation, and including initially deleterious standing variation, respectively.
Threshold dominance coefficient above which new
ext is higher in outcrossers than in selfers.
from neutral or deleterious (sd ) to beneficial (sb ). The simulations
stop when the a allele is either fixed or lost and the probability
of fixation is computed as the proportion of simulations leading
to fixation. To compute the total time until adaptation, recurrent
mutations are added after the environmental change and the simulations stop when the frequency of the aa genotype reaches one.
The time to adaptation was computed as the average time over the
simulations.
To simulate extinction and rescue, we used the procedure of
Orr and Unckless (2008). In the first environment, the population
remains constant with size N 0 . After the environmental change,
the number of individuals of each genotype is followed, not only
their frequencies. To simulate drift, we did not use a multinomial sampling but the number of individuals produced by each
genotype is drawn from a Poisson distribution according to their
absolute fitness, which now depends on the rate r of population
decline (Absolute fitness of AA, Aa, and aa: wAA = 1 – r , wAa =
1 + hb sb – r , waa = 1 + sb – r). Note that the demography is thus
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EVOLUTION JANUARY 2013
stochastic, although we used a deterministic approximation for
analytical expression (see below). The simulations stop (1) when
population size equal to zero, (2) when the a allele is fixed, or (3)
when the population size reaches the value of 10N 0 . We used this
last condition to avoid infinite growth because we did not include
density dependence. We chose 10N 0 instead of N 0 because the
population size can be a bit higher than N 0 through stochastic
variations just after the environmental change, especially when
N 0 is low. Choosing 10N 0 ensures that the beneficial mutation
has reached high frequency and will not be lost. The proportion
of simulations leading to extinction was recorded.
Probability of Fixation of a Beneficial
Mutation
In this section, the population size is assumed to remain constant
over time.
M AT I N G S Y S T E M S A N D A DA P TAT I O N
NEW MUTATIONS
According to Kimura (1962), the probability of fixation of a mutant allele starting at frequency x is given by
x
G(h, s, z)dz
π(h, s, x) = 01
.
(3)
0 G(h, s, z)dz
In the case of partial selfing (Caballero and Hill 1992)
with Ne given by equation (1). The probability of fixation of a
newly arisen mutation has already been obtained (Caballero and
Hill 1992; Charlesworth 1992) and is simply
1
Pnew = π h b , sb ,
.
(5)
2N
(6)
Here, we have introduced the α coefficient. This is thus equivalent to the selection of heterozygoted in a panmictic population
with an “effective” dominance coefficient
h e (h) = h + F − h F
Pnew 0.010
0.000
0.0
0.2
0.4
0.6
0.8
1.0
B
0.020
0.015
Pnew 0.010
When Ne (h b + F − h b F)s >>1,
2α(h b + F − h b F)sb
.
1+ F
0.015
0.005
G(h, s, z) = exp[−2Ne sz(2(h + F − h F) + (1 − F)(1 − 2h)z 2 )]
(4)
Pnew ≈
A
0.020
(7)
(Caballero and Hill 1992 but see below and Glémin 2012 for
the problem with the use of he ). As emphasized by Charlesworth
(1992), equation (6) shows that Pnew is independent of hb in complete selfers whereas in outcrossers, dominant mutations are more
easily fixed than recessive ones, the so-called “Haldane’s sieve”
(Haldane 1927). For hb = 12 , Pnew reduces to 2αsb . If there is no
additional reduction in Ne beyond its twofold effect (i.e., α = 1),
selfing has no effect on the probability of fixation (Fig. 2). These
classical results also hold true in subdivided populations, although
the sieve is weaker (Roze and Rousset 2003).
STANDING VARIATION
The probability of fixation of an allele from standing variation is
given by:
1
Psv =
π(h b , sb , x)ρ(h d , sd , x)d x
(8)
0
where ρ(hd , sd , x) is the stationary density function for the frequency of the a allele at mutation–selection–drift balance before
the environmental change, conditioned on a being the derived
alleles. Following Hermisson and Pennings (2005), we give the
complete expression in Supporting information Material 1. These
authors also found approximations for ρ(hd , sd , x) and Psv when
selection on heterozygotes is strong enough. In Supporting information Material 1, we show that we can directly use their results
0.005
0.000
0.0
0.2
0.4
0.6
0.8
1.0
C
0.020
0.015
Pnew 0.010
0.005
0.000
0.0
0.2
0.4
0.6
0.8
1.0
Selfing rate (σ)
Probability of fixation of a single new mutation (in frequency 1/2N) as a function of selfing rate for different dominance
coefficient, given by equation (6). Dots correspond to numerical
Figure 2.
integration of equation (3). N = 20,000, sb = 0.01, no mutational
input. From bottom to top: hb = 0.1, 0.3,0.5,0.7,0.9. (A) Without
background selection. (B and C) With background selection: U =
0.5, H = 0.2, S = 0.1, and C = 5 (B) or C = 1 (C).
by replacing h by he (h) given by equation (7). For 4Ne he (hb ) sb >
(1 – 2he (hb ))/2he (hb ), we thus obtained
delet
Psv
≈ 1 − exp (−4Ne u ln(1 + R))
(9)
4Ne (h b +F−h b F)sb
with R = 1+4N
and Ne is given by (1). R is defined
e (h d +F−h d F)sd
by Hermisson and Pennings (2005) as “the relative selective
advantage [that] measures the selective advantage of [a] in the
new environment relative to the forces that cause allele frequency
changes in the ancestral environment, deleterious selection and
EVOLUTION JANUARY 2013
229
S . G L É M I N A N D J. RO N F O RT
drift”. For initially neutral alleles, equation (9) is not very accurate so we preferred the less approximated expression given by
Hermisson and Pennings (2005) in their appendix (their equation
A9)
neutral
Psv
≈1−
(1 + 4Ne u)
(1 + 4Ne (h b + F − h b F)sb )−4Ne u
(10)
where (z) is the Gamma function (Abramowitz and Stegun
1970).
As for new mutations, Psv is independent of dominance in
complete selfers (Fig. 3). In outcrossers, for initially neutral or
weakly deleterious alleles (either recessive or dominant), Psv is
higher for dominant alleles, although the relative effect of dominance is weaker than for Pnew . For initially strongly deleterious
a alleles and assuming that hb = hd , Psv is mostly independent
of dominance in outcrossers, the R ratio in equation (9) tends
toward sb /sd (see also Orr and Betancourt 2001): selection is initially lower for recessive alleles but they segregate at a higher
frequency before the environmental change. However, equation
(9) does not hold for very recessive alleles and Orr and Betancourt (2001) showed that Psv is highest for very recessive alleles,
the opposite of Haldane’s sieve, because their initial frequency
more than compensate the lower selection they experience after
the environmental change.
The probability of fixation from standing variation increases
with Ne . As Ne is lower in selfing than in outcrossing species,
Psv decreases with selfing rate under most conditions, contrary to
what is expected for Pnew (compare Figs. 2, 3). Using equation
(9), we can determine the threshold dominance coefficient above
which Psv is higher in outcrossers than in selfers by solving in hb :
Psv |σ=0 = Psv |σ=1 . General expressions are given in Supporting
information Material 1. For α = 1, strong selection (Ne hs >> 1),
and an initially deleterious allele we obtained
Psv
h lim
≈
h d sd
sb
1+
sb
−1 .
sd
(11a)
When considering an initially neutral allele we obtained:
e−γ/2
Psv
≈ √
h lim
2 2N sb
(11b)
where γ ≈ 0.577 is the Euler’s constant. Even when α = 1,
Psv
h lim
is low under most conditions and tends toward 0 for strong
selection. This suggests that, except for specific conditions (very
recessive and weakly advantageous mutations), the probability of
fixation from standing variation should be less likely in selfers
than in outcrossers. This is due to two effects of selfing: (1) lower
levels of polymorphism are maintained in selfers because Ne is
reduced and (2) initially deleterious alleles are maintained at lower
frequencies because of the purging process.
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EVOLUTION JANUARY 2013
Time to Fixation and Rate
of Adaptation
We now turn on to the effect of the mating system on times
to fixation and rates of adaptation. Do outcrossing populations
adapt more quickly than selfing ones, and, if yes, under which
conditions? We are therefore interested in the time until fixation
of the a allele. Kimura (1980) obtained the average time until
fixation of a mutant allele under recurrent mutations starting from
frequency x, T(h, s, x). Here, we still assume that population size
is constant. Under the environmental change scenario, the average
time until complete adaptation is thus
1
T (h b , sb , x)ρ(h d , sd , x)d x.
(12)
Tadapt =
0
The general expression of Tadapt is given in Supporting information Material 2. To get an approximation of Tadapt , we can
decompose it into the waiting time until the appearance of the first
mutation destined to be fixed—which is null if adaptation is due
to standing variation—and the time to fixation of this mutation
sv
Tadapt = (1 − Psv ) Twait + T fnew
i x + Psv T f i x
(13)
Psv is given by equation (9). Assuming that the occurrence
of mutations destined to be fixed follows a Poisson process with
mean 2NuPnew , the time until the first occurrence of such a mutation is exponentially distributed with mean
Twait =
1
2N u Pnew
(14)
with Pnew given by equation (6). Hermisson and Pennings (2005)
gave an approximation for T fnew
i x . However, their expression is
not very accurate as far as h is far from 12 —either close to 0 or
1–and it cannot be simply extended to partial selfing by substituting he to h: the reparameterization of the dominance coefficient
is only valid at low allele frequency—low z in equation (3)—
which is insufficiently accurate to approximate the fixation time
that depends on the whole allele trajectory between 0 and 1.
We thus used the more accurate expression obtained by Glémin
(2012)
T fnew
ix ≈
1
sb (h b + F − h b F)(1 − (1 − F)h b )
× ((3h b − 1 + F(2 − 3h b )) ln(1 − (1 − F)h b )
+ (2 − 3h b + F(3h b − 1)) ln(h b + F − h b F)
+ (1 + F)(ln(4Ne sb ) + γ))
(15)
Finally, noting Tfix (h, s, x), the time to fixation starting from
frequency x is given by
1
T f i x (h b , sb , x)ρ(h d , sd , x)d x.
(16)
T fsvi x =
0
M AT I N G S Y S T E M S A N D A DA P TAT I O N
0.5
0.20
A
B
0.4
0.15
0.3
PSV
PSV
0.10
0.2
0.05
0.1
0.0
0.0
0.2
0.4
0.6
0.8
0.00
0.0
1.0
0.5
0.2
0.4
0.6
0.8
1.0
0.20
C
D
0.4
0.15
0.3
PSV
PSV
0.10
0.2
0.05
0.1
0.0
0.0
0.2
0.4
0.6
0.8
0.00
0.0
1.0
0.5
0.2
0.4
0.6
0.8
1.0
0.20
E
F
0.4
0.15
0.3
PSV
PSV
0.10
0.2
0.05
0.1
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.00
0.0
0.2
Selfing rate (σ)
Figure 3.
0.4
0.6
0.8
1.0
Selfing rate (σ)
Probability of fixation from standing variation as a function of selfing rate for different dominance coefficients, given by
equations (9) and (10). Dots correspond to observed data from 10,000 simulations. Results from numerical integration of equation (8) are
indiscernible from the simulation results. N = 20,000, u = 10−6 , sb = 0.01. From bottom to top: hb = 0.1, 0.3, 0.5, 0.7, 0.9. (A, C, and E)
Initially neutral allele. (B, D, and F) Initially deleterious allele: sd = 0.01, hd = hb . (A and B) Without background selection. (B, D, E, and F)
With background selection: U = 0.5, H = 0.2, S = 0.1, and C = 5 (C and D) or C = 1 (E and F).
Using results obtained by (Glémin 2012), equation (16) can be
approximated by (see Supporting information Material 2)
T fsvi x ≈ T fnew
ix −
×
1
sb (h b + F − h b F)
γ + ln(4Ne (h b + F − h b s)sb )
1
−
γ
−4N
u
e
1 − (4Ne (h b + F − h b s)sb e )
4Ne u
deleterious alleles using the deterministic frequency at mutation–
selection balance
T fsvi x ≈ T f i x h b , sb ,
(17)
for initially neutral mutations. Similarly, we also obtained an approximation for mildly deleterious mutations but it is formidable
and not useful. A simpler expression can be obtained for strongly
u
sd (h d + F − h d F)
γ + ln 4Ne sb (h b + F − h b F)
u
sd (h d + F − h d F)
=
sb (h b + F − h b F)
u
1
ln 1 −
−
sb (1 − (1 − F)h b )
sd (h d + F − h d F)
EVOLUTION JANUARY 2013
231
S . G L É M I N A N D J. RO N F O RT
(1 − F)(1 − 2h b )
sb (h b + F − h b F)(1 − (1 − F)h b )
u
(1 − F)(1 − 2h b )
× ln 1 +
.
h b + F − h b F sd (h d + F − h d F)
−
(18)
Note that T fsvi x , T fnew
i x , and Twait scale in 1/sb and so does
Tadapt . The total waiting time, (1 – Psv )Twait , is always lower
in outcrossers for dominant beneficial mutations. When Psv is
substantial, higher than 0.5, the total waiting time is also lower in
outcrossers for mildly recessive allele, especially if Ne is strongly
reduced in selfers, α < 1: when Ne is small in selfers, adaptation
from standing variation is less likely and the waiting time is
longer. On the contrary, T fnew
i x is always shorter in selfers than in
outcrossers because Ne is lower and he (h) is higher (for details see
Glémin 2012). T fsvi x is also shorter in selfers than in outcrossers,
except for highly dominant beneficial mutations and if adaptation
from standing variation is substantial. As a result, if α = 1, the
total time for adaptation will be shorter in selfers under most
conditions. In general, the total time for adaptation will be higher
in selfers only if α < 1 (Fig. 4).
Shift in Mating System Associated
with the Environmental Change
Shift toward selfing is commonly associated with the evolution
of specific traits (the so-called selfing syndrome). Our model allows exploring this scenario by considering the case for which the
environmental change is associated with a shift from outcrossing
toward selfing. Under this scenario, the probability of fixation
from new mutations remains as given by equations (5) and (6).
The probability of fixation from standing variation is also given by
equation (8), however, ρ(h, s, x) is computed for a panmictic population whereas π(h, s, x) is computed for a selfing one—or more
generally two different selfing rates can be used (see Supporting
information Material 3 for detailed equations). Similarly, the average time until complete adaptation can be obtained by slight
modifications of the terms in equation (13). Twait and T fnew
i x are
computed for a selfing population, Psv is modified as explained
above and T fsvi x is slightly modified: Ne u is replaced by Nu for
initially neutral mutations and u/(hd + F – hd )sd is replaced by
u/hd sd for initially deleterious mutations (see Supporting information Material 3).
Adaptation from standing variation is expected to be higher
just after the shift from outcrossing than for population selffertilizing for a long time. Some numerical examples are given in
Table 2. The analysis of this scenario yields to another prediction
about the dominance of selected mutations. In contrast to ancient
selfers, the dominance of mutations affects the probability of
fixation if they are initially deleterious: recessive mutations segregates in higher frequency in the initial outcrossing popula-
232
EVOLUTION JANUARY 2013
tion and are thus more prone to be fixed after the shift toward
selfing.
Finally, it is also interesting to focus on the case of relaxed selection following the environmental and mating system change to
analyze whether the selfing syndrome could evolve by relaxation
of selection pressures, not by positive selection. We need to compute the probability and time to fixation of an initially deleterious
allele becoming selectively neutral after the shift. The probability
of fixation is simply equal to the initial frequency of the allele
before the environmental change and the time until fixation of the
allele, Trelax , is given by (see Supporting information Material 3)
Tr elax ≈
1
+ 4Ne .
u
(19)
Simple numerical explorations (Table 2) show that the evolution of the selfing syndrome under this scenario takes a very
long time compared to the adaptation scenario.
Lack of Adaptation and Extinction
In previous sections, we assumed that the adaptation lag following the environmental change did not challenge the survival of
the population. The population size remained constant and given
sufficient time, adaptation eventually occurred. However, environmental change may affect demography and challenge population
survival, eventually leading to extinction. We focused on a simple
model where adaptation or extinction depends on a single biallelic
locus, in the line of the rest of the article. Here, the key variable
is the waiting time because nonextinction is conditioned by the
appearance of the rescuing mutation. Hence, the time to complete
fixation does not matter. To quantify the effect of selfing versus
outcrossing on the risk of extinction under this framework, we
naturally extended the model of Orr and Unckless (2008) by including diploidy and partial selfing. Advantages and limitations
of this model have been discussed by these authors. As in Orr
and Unckless (2008), we assumed that (1) population deterministically declines with an exponential rate of population decline r
(r > 0) from an initial size N 0 , (2) selection is strong enough and
initially acts mainly on heterozygotes in outcrossing populations
(Ne he (hb )sb >> 1), and (3) beneficial mutations are sufficiently
rare to enjoy independent fate without interacting.
After the environmental change, the population goes extinct
if all preexisting mutations and all mutations occurring after the
environmental change are lost. The probability of extinction is
thus
∗
)
ext = (1 − Psv
∞
∗
(1 − Pnew
)2N0 u(1−r ) .
t
(20)
t=0
Here, the probability of fixation from standing variation and
from new mutations is computed for a population declining exponentially. We added a star in superscript to distinguish this case
M AT I N G S Y S T E M S A N D A DA P TAT I O N
15 000
A
15 000
10 000
10 000
Tadapt
Tadapt
5000
5000
0
0.0
30 000
Tadapt
0.2
0.4
0.6
0.8
1.0
0
0.0
30 000
C
25 000
25 000
20 000
20 000
15 000
15 000
10 000
10 000
5000
5000
0
0.0
20 000
Tadapt
B
0.2
0.4
0.6
0.8
1.0
15 000
15 000
10 000
10 000
5000
5000
0
0.0
0.2
0.4
0.6
0.8
1.0
0.4
0.6
0.8
1.0
0.2
0.4
0.6
0.8
1.0
0.4
0.6
0.8
1.0
D
0
0.0
20 000
E
0.2
F
0
0.0
0.2
Selfing rate (σ)
Figure 4.
Selfing rate (σ)
Total time for adaptation as a function of selfing rate for different dominance coefficients, given by equation (13). Dots
correspond to observed data from 10,000 simulations. Results from numerical integration of equation (12) are indiscernible from the
simulation results. N = 20,000, u = 10−6 , sb = 0.01. Dotted line: hb = 0.1, small dashed line: hb = 0.3, thick line: hb = 0.5, large dashed
line: hb = 0.7, thin line: hb = 0.9. (A, C, and E) Initially neutral allele. (B, D, F) Initially deleterious allele: sd = 0.01, hd = hb . (A and B)
Without background selection. (B, D, E, and F) With background selection: U = 0.5, H = 0.2, S = 0.1, and C = 5 (C and D) or C = 1 (E and F).
from previous results obtained for stable population size. In equation (20), 2N0 u(1 − r )t is the number of beneficial mutations that
appear at generation t. To calculate the probability of extinction,
we followed Orr and Unckless (2008) and we showed in Supporting information Material 4 that when the mutation is initially
strongly deleterious, we have
delet
ext
(h b + F − h b F)sb − r
−4Ne u
r
≈e
(h b + F − h b F)sb + (h d + F − h d F)sd − r −4Ne u
×
(21) .
(h d + F − h d F)sd
When the mutation is initially neutral, we have
neutral
≈e
ext
−4Ne u
(h b + F − h b F)sb − r
r
(1 + 4Ne u)
×
(1 + 4Ne ((h b + F − h b F)sb − r ))4Ne u
(22)
where (z) is the Gamma function (Abramowitz and Stegun
1970). When there is no standing variation, equations (21) and
(22) vanish to
new
ext ≈ e
−4Ne
(h b + F − h b F)sb − r
.
r
EVOLUTION JANUARY 2013
233
(23)
S . G L É M I N A N D J. RO N F O RT
Table 2. Evolution of a selfing syndrome under three scenarios: probability of evolution from standing variation (SV) and time to
fixation of the trait.
Time to fixation of the selfing syndrome1
Probability of adaptation from SV
u=10−6
h3 =0.1
h=0.5
h=0.9
h=0.1
h=0.5
h=0.9
u=10−7
Initially
neutral2
Initially
deleterious2
Relaxed
selection2
Initially
neutral2
Initially
deleterious2
Relaxed
selection2
0.406
0.406
0.406
0.051
0.051
0.051
0.133
0.054
0.035
0.014
0.006
0.004
0.001
<0.001
<0.001
<0.001
<0.001
<0.001
2654
2654
2654
25,018
25,018
25,018
3303
3598
3673
25,938
26,166
26,219
1,039,000
1,039,800
1,039,890
10,039,000
10,039,800
10,039,900
1
In generations.
2
Details of the equations used are given in Supporting information Material.
3
h = hb = hd .
N = 20,000, sd = sa = 0.01. σ = 0 in environment 1 and σ = 1 in environment 2.
These approximations are relatively good when compared to
simulations for relatively weak population decline and selection
(r = 0.001 and sb = 0.05; Fig. 5), which leads to extinction
in few thousand generations (if rescue does not occur). Similar
patterns and accurate approximations can also be observed for
stronger population decline and selection (e.g., r = 0.004 and
sb = 0.2) and more rapid extinction of the order of few hundreds
generations. From equation (23), we can easily show that the
threshold dominance coefficient above which new
ext is higher in
selfers than in outcrossers is given by
h ext
lim ≈
α r (2 − α)
.
+
2
2sb
(24)
For α = 1, h ext
lim is thus higher than 1/2 and the range of mutation parameters for which the probability of extinction is higher
in selfers than in outcrossers is quite restricted. When standing
variation is taken into account, these conditions are less restrictive
1
and h ext
lim is lower than 2 when α = 1 (Fig. 6). To explain higher
extinction rates in selfers compared to outcrossers as assumed by
the dead-end hypothesis, Ne must be (greatly) reduced beyond the
twofold level and/or the role of standing variation in adaptation
must be significant and/or beneficial mutations must be dominant
on average (Figs. 5, 6).
Using equations (21)–(23) we can also compute the role of
standing variation in preventing extinction, which is simply given
P∗
by 1−svext . Figure 7 shows that standing variation plays a crucial
role in preventing extinction when population size rapidly declines (relatively to the effect of the rescuing mutation): under
rapid decline, the population can be rescued only if the rescuing
mutation is initially available or appears shortly after the population starts to decline. As expected, the role of standing variation is
also higher in large populations. Note, however, that this simple
result should be considered with caution because rapid popula-
234
EVOLUTION JANUARY 2013
tion decline should correspond to abrupt environmental change
for which adaptation from standing variation is less likely.
Discussion
Through a population genetics model, we explored how the selfing rate may affect the dynamics of adaptation. Although very
simplistic, this model allows the definition of general trends on
the effect of the mating system on the genetic bases and the rate
of adaptation. This helps in understanding how selfing species
may adapt or fail to adapt to a new environment, in relation to the
evolution of adaptive traits in selfers (such those involved in the
selfing syndrome) and the hypothesis that selfing is an evolutionary dead-end.
THE GENETIC BASES OF ADAPTATION IN SELFERS
AND OUTCROSSERS
It was already well known that the genetic bases of adaptation
should differ between selfers and outcrossers regarding dominance of new beneficial mutations. In outcrossers, dominant
mutations are more easily fixed than recessive ones (Haldane
1927), whereas in selfers, the dominance is of little importance.
As a consequence, the dominance spectrum of fixed mutations
reflects the spectrum of newly arising mutations (Charlesworth
1992). Here, we showed that this is less true when adaptation proceed from standing variation (Fig. 3), especially for initially deleterious mutations (see also Orr and Betancourt 2001). Outcrossers
and selfers also differ regarding the fraction of adaptation that can
be due to new mutations versus standing variation. Under most
conditions, independent of dominance, adaptation from standing variation is less likely in selfers than in outcrossers (Fig. 3),
which can easily be explained as selfing is expected to reduce
M AT I N G S Y S T E M S A N D A DA P TAT I O N
1.0
1.0
A
0.8
B
0.8
0.6
0.6
Pext
Pext
0.4
0.4
0.2
0.2
0.0
0.0
1.0
0.2
0.4
0.6
0.8
0.0
0.0
1.0
1.0
C
0.8
0.2
0.4
0.6
0.8
1.0
0.2
0.4
0.6
0.8
1.0
0.4
0.6
0.8
D
0.8
0.6
0.6
Pext
Pext
0.4
0.4
0.2
0.2
0.0
0.0
1.0
0.2
0.4
0.6
0.8
0.0
0.0
1.0
1.0
E
0.8
F
0.8
0.6
0.6
Pext
Pext
0.4
0.4
0.2
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Selfing rate (σ)
0.0
0.0
0.2
1.0
Selfing rate (σ)
Probability of extinction as a function of selfing rate for different dominance coefficients, given by equations (20) and (21).
Dots correspond to observed data from 10,000 simulations. N = 10,000, u = 10−6 , sb = 0.05, r = 0.001. Dotted line: hb = 0.1, small dashed
Figure 5.
line: hb = 0.3, thick line: hb = 0.5, large dashed line: hb = 0.7, thin line: hb = 0.9. (A, C, and E) Initially neutral allele. (B, D, and F) Initially
deleterious allele: sd = 0.01, hd = hb . (A and B) Without background selection. (B, D, E, and F) With background selection: U = 0.5,
H = 0.2, S = 0.1, and C = 5 (C and D) or C = 1 (E and F).
polymorphism maintained both at mutation–drift and mutation–
selection balance (Charlesworth and Charlesworth 1995).
The analysis of the genetic bases of adaptation in natural populations is still too scarce to test these predictions. However, in domesticated plants, we recently showed that QTL fixed during the
domestication process (considered as an adaptation process) tends
to be more dominant in outcrossers than in selfers (J. Ronfort and
S. Glémin, unpubl. ms.), in agreement with Haldane’s sieve occurring on new mutations in outcrossers. Nevertheless, some do-
mestication QTLs are recessive in outcrossers, suggesting that the
corresponding alleles likely preexist in wild populations. In maize
(an outcrossing species) for instance, several major genes involved
in the domestication syndrome, including Tb1, contribute to standing variation in its wild progenitor, Teosinte (Weber et al. 2007).
“Maize-like” alleles were already present in wild populations and
increases in frequency during domestication (Jaenicke-Despres
et al. 2003; Weber et al. 2007). Selection from standing variation during domestication also likely occurred in pearl millet
EVOLUTION JANUARY 2013
235
S . G L É M I N A N D J. RO N F O RT
1.0
1.5
Log10 s
2.0
2.5
3.0
3.5
4.0
0.0
0.2
0.4
0.6
0.8
1.0
h
Range of mutation parameters (hb and sb ) under which
the probability of extinction is higher in a complete selfer than in
Figure 6.
a complete outcrosser (shaded areas). N = 20,000, u = 10−6 , r =
0.0001. Dark gray: α = 1, Light gray: α = 12 .
of rescue due to SV
1.0
0.8
0.6
0.4
0.2
0.0
0.000
0.002
0.004
0.006
0.008
0.010
r
Figure 7.
Proportion of population rescue due to standing varia-
tion as a function of the population decline rate for different population sizes, in a panmictic population. The y-axis corresponds to
the number of cases where population rescue is due to the fixation of preexisting mutations over the total number of rescue.
u = 10−6 , sb = 0.02, hb = 0.5. From bottom to top, N = 5000,
10,000, 25,000, 50,000.
(another outcrossing species) on the Tb1 orthologue (Remigereau
et al. 2011) and in artificial selection for flowering time in maize
(Durand et al. 2010).
THE RATE OF ADAPTATION IN SELFERS
AND OUTCROSSERS
The genetic bases of the adaptation process condition how the
mating system affects the rate of adaptation (Fig. 4). The total
time required for adaptation until the fixation of the beneficial
allele can be decomposed into two parts: the waiting time until
236
EVOLUTION JANUARY 2013
the appearance of the beneficial mutation destined to be fixed
(which can be null if the mutation is already segregating before
the environmental change) and the fixation time of this mutation.
The fixation time is always shorter in selfing species (Glémin
2012) but the waiting time strongly depends on the amount of
standing variation available and on the dominance of mutations:
waiting time is lower in outcrossers than in selfers when the probability of adaptation from standing variation is high and when
beneficial mutations are not too recessive. On the contrary, the
waiting time can be much shorter in selfers when beneficial mutations are partly recessive, except if Ne is strongly reduced under
selfing (α << 1). However, the higher standing variation found
in outcrossers does not seem to play a crucial role on the total
adaptation time. When the product Ne u is high, standing variation
contributes significantly to adaptation in outcrossers and reduces
the waiting time of the beneficial mutation destined to be fixed,
but, when the waiting time is short, the fixation time constitutes
an important part of the total adaptation time, which is an advantage for selfers. Overall, selfing slows down adaptation only if
Ne is strongly reduced, α << 1 (compare cases with and without
background selection on Fig. 4).
The distribution of dominance coefficients of new beneficial
mutations is thus crucial to understanding whether selfing should
speed up or slow down the rate of adaptation. Unfortunately, such
a distribution is very poorly known and no firm conclusions can
be drawn from empirical data (reviewed in Orr 2010). Recently,
Manna et al. (2011) used Fisher’s geometric model and suggested
that beneficial mutations should be codominant or dominant on
average, as long as adaptation can be well described by stabilizing
selection on a set of phenotypic traits and populations are not
too far from their optimum. The last assumption corresponds to
rather small environmental changes, such that the new optimum
does not differ much from the old one. Under these conditions,
we thus also expect that a significant part of standing variation
initially available in the first environment could be beneficial in
the second one. Under rather slow and regular environmental
changes, outcrossers should adapt more rapidly than selfers.
When considering strong environmental changes, adaptation
from standing variation is less likely: mutations that are beneficial
in the new environment are far from the optimum of the first environment, hence strongly deleterious, and are maintained at very
low frequencies. The dominance coefficients of such mutations
were not considered by Manna et al. (2011) and would require
additional theoretical developments. The selection of some domesticated traits could fit this scenario of a strong environmental
change. For instance, nondispersing forms were selected in many
crops whereas they are strongly deleterious in wild populations.
Empirical data on the genetic bases of some of these traits, such as
nondispersing alleles, suggest that the domesticated alleles (beneficial in the new environment) tend to be recessive (J. Ronfort and
M AT I N G S Y S T E M S A N D A DA P TAT I O N
S. Glémin, unpubl. ms.). Under these conditions, selfers should
adapt more rapidly than outcrossers. Selfing could have facilitated
adaptation during domestication by favoring the fixation of recessive, initially strongly deleterious traits, which could contribute
to explaining the bias toward selfing among domesticated species
(Zohary and Hopf 2000; Diamond 2002; Glémin and Bataillon
2009).
ADAPTATION TO SELFING AND EVOLUTION
OF THE SELFING SYNDROME
The evolution of specific traits is often associated with shift toward selfing (the so-called selfing syndrome, reviewed in Sicard
and Lenhard 2011), sometimes over a short time scale. In C.
rubella, extensive phenotypic evolution may have occurred over
25,000 years (Foxe et al. 2009; Guo et al. 2009). Such rapid phenotypic changes suggest that they have been triggered by positive selection toward a new optimum of floral resource allocation (Sicard
et al. 2011; Slotte et al. 2012) but in other species they could simply result from relaxed selective constraints on reproductive traits.
We extended our model to compare these two scenarios. Numerical explorations (Table 2) show that the evolution of the selfing
syndrome under the “relaxed constraint” scenario takes a very
long time and is thus very unlikely, whereas the timing of selective scenarios are compatible with rapid evolution such as in C.
rubella or L. alabamica (Busch et al. 2011). Selfing syndrome
traits, even those not directly linked to the increase in selfing rate,
are thus expected to evolve under positive selection pressures,
as already suggested by empirical studies (Fishman et al. 2002;
Goodwillie et al. 2006; Sicard et al. 2011; Slotte et al. 2012).
Our model also gives predictions on the genetic bases of the
evolution of the selfing syndrome. Adaptation from standing variation is expected to be higher just after a shift from outcrossing
than for a population that has been self-fertilizing for a long time,
suggesting that the evolution of the selfing syndrome from standing variation could be rather frequent, except when the transition
to selfing is associated with a strong bottleneck. In agreement
with this prediction, floral traits associated with the evolution of
selfing in Mimulus nasutus (Fishman et al. 2002) and Leptosiphon
bicolor (Goodwillie et al. 2006) could have evolved from standing
variation available in their outcrossing ancestor. On the contrary,
the role of standing variation in the evolution of selfing syndrome
traits is likely negligible in C. rubella (Slotte et al. 2012). This
can be related to the strong loss of polymorphism associated with
the bottleneck experienced by this species (Foxe et al. 2009; Guo
et al. 2009).
This model also predicts that the genetic bases of adaptation should evolve during the mating system transition. Initial
alleles increasing the selfing rates are more likely to be dominant because they can pass through the Haldane’s sieve. Once
the selfing rate has increased, alleles selected from standing vari-
ation are more likely to be recessive, because they segregate at
higher frequencies in the initially outcrossing populations where
they are masked. Finally, after the complete shift to selfing, the
dominance of new fixed alleles should directly mirror the dominance of arising mutations as initially showed by Charlesworth
(1992). Few studies are still available to test these predictions in
details, but at least, they do not contradict them. In C. rubella, the
self-compatible allele initially allowing the evolution of selfing is
dominant as expected, and the C. rubella (selfing) alleles at QTLs
determining other floral traits changes that should have evolved
later are codominant or slightly recessive (Slotte et al. 2012).
In M. nasutus and L. bicolor, both dominant and recessive alleles
have been fixed, which could correspond to the different phases of
the process although the order of fixation is not known (Fishman
et al. 2002; Goodwillie et al. 2006).
MALADAPTATION IN SELFERS AND THE DEAD-END
HYPOTHESIS
On the long run, selfing has been proposed to be an evolutionary
dead-end (Stebbins 1957). Stebbins initially suggested that selfing species are doomed to extinction because of their low levels
of variation resulting in low adaptive potential. However, in the
last few decades, population genetics theory mostly focused on
the consequences of deleterious mutations on the fate of selfing species (e.g., Charlesworth et al. 1993b; Lynch et al. 1995).
Selfing lineages should be prone to the accumulation of deleterious mutations and mutational meltdown could contribute to their
extinction. However, this hypothesis received little empirical support so far. Although current relaxed selection has been found in
selfing species through the analysis of polymorphism data (e.g.,
Slotte et al. 2010; Qiu et al. 2011), no signature of long-term
accumulation of deleterious mutations has been found in selfing
lineages (Wright et al. 2002; Cutter et al. 2008; Haudry et al.
2008; Escobar et al. 2010). To explain this lack of results, it has
been proposed that either selfing lineages are of too recent origin
to show signature of genomic degradation or that Ne reduction
in selfers is not sufficiently strong (α close to one) (Glémin and
Galtier 2012).
Alternatively, we analyzed whether a lack of adaptation
could contribute to higher extinction rates in selfing lineages. Especially, we were interested in the possibility that selfers could be
less adapted than outcrossers even when Ne is not strongly reduced
(α close to one). When focusing on the time required for complete
adaptation (Fig. 4), selfers appear to be as efficient as and in
some cases more efficient than outcrossers, unless Ne is strongly
reduced in selfers (α << 1), and standing variation only plays
a minor role. This is mainly due to the fact that the fixation time
is always shorter in selfers (as discussed above and see Glémin
2012). However, when the extinction dynamics is explicitly taken
into account, only the presence or the appearance of the rescuing
EVOLUTION JANUARY 2013
237
S . G L É M I N A N D J. RO N F O RT
mutation before extinction does matter. Standing variation thus
plays a more important role because initially available mutations
and those arising in first generations after the environmental
changes contribute the most to rescue (Orr and Unckless 2008).
This is especially true when population size decreases rapidly
(Fig. 7).
If beneficial mutations are codominant or dominant, on average, as suggested by Manna et al. (2011), and the contribution of
standing variation to adaptation is substantial, extinction rates can
be higher in selfers than in outcrossers, even if α is close to one.
This could occur under frequent, but rather slight, environmental
changes for which outcrossers would easily adapt using standing
variation whereas selfers would eventually fail to respond to
environmental changes. By erasing standing variation, bottleneck episodes would increase extinction rates in selfers without
strongly affecting Ne on the long run. This could explain why no or
weak signatures of relaxed selection against deleterious mutations
have been found through phylogenetic approaches. Alternatively,
Ne could be strongly reduced in selfers (α << 1) but selfers could
go extinct before having accumulated enough deleterious mutations that are detectable through phylogenetic approaches. The
time to extinction due to maladaptation depend on the frequency
and intensity of environmental changes. It could be much shorter
than the time for extinction due to mutational meltdown, which
is short only under obligate selfing and for very small population
size (Lynch et al. 1995). Moreover, low rates of outcrossing are
sufficient to slow down mutation accumulation (Charlesworth
et al. 1993b). Overall, this suggests that extinction of selfing
species is more likely due to the lack of adaptive potential than
to the accumulation of deleterious mutations. This contrasts
with clonal species for which accumulation of deleterious
mutations is more easily detectable and more likely to contribute
to their extinction (see discussion in Glémin and Galtier 2012).
More explicit models including both deleterious and beneficial
mutations in changing environments are necessary in the future
to address this issue.
ACKNOWLEDGMENTS
This publication is the contribution ISEM 2012-096 of the Institut des
Sciences de l’Evolution de Montpellier (UMR 5554–CNRS). This work
was supported by the French Centre National de la Recherche Scientifique
and Agence Nationale de la Recherche (ANR-11-BSV7-013-03).
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Associate Editor: M. Johnston
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Supporting Information
The following supporting information is available for this article:
1. Probability of fixation from standing variation
2. Time to adaptation
3. Environmental change associated with a shift in mating system
4. Probability of extinction
5. Derivation of equation (S.20)
Supporting Information may be found in the online version of this article.
Please note: Wiley-Blackwell is not responsible for the content or functionality of any supporting information supplied by the
authors. Any queries (other than missing material) should be directed to the corresponding author for the article.
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