ADAPTATION AND MALADAPTATION IN SELFING AND OUTCROSSING SPECIES: NEW MUTATIONS VERSUS STANDING 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 deleterious 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 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, N_e, 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, N_e 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 N_e 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).

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 so-called 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 –h_ds_d, and 1 –s_d before, and 1, 1 +h_bs_b, and 1 +s_b after the environmental change, where s_d and s_b stand for the deleterious and beneficial selection coefficients and h_d and h_b for the dominance coefficients. Back mutations are neglected. As we consider a single locus, we assume that, during the adaptation process, there is no interference between mutations because of linkage or epistasis.

With partial selfing, the effective population size is given by:

(1)

where 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, N_e 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

(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 N_e is large can become nearly neutral when N_e is smaller. U should thus weakly decrease with F, however, in highly selfing species, nearly neutral mutations can also reduced N_e through Muller's ratchet (Charlesworth et al. 1993b), which is not taken into account here. Several examples of the evolution of the N_e/N ratio as a function of the selfing rate under background selection are given in Figure 1, showing that N_e 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 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.

Table 1. Notations.

N	Demographic population size.
Ne	Effective population size.
α	Coefficient summarizing the hitchhiking and demographic effects of selfing that reduce the effective population size beyond the automatic twofold effect.
U, H, S, C	Genomic parameters of deleterious mutations for the background selection model: mutation rate, mean dominance coefficient, mean selection coefficient, mean recombination rate.
N 0	Demographic population size before the environmental change in the extinction model.
r	Rate of population decline in the extinction model.
σ	Selfing rate.
F	Wright's fixation index (FIS).
u	Mutation rate from A to a.
sd, sb	Selection coefficients of the a allele before (deleterious effect) and after (beneficial effect) the environmental change.
hd, hb	Dominance coefficients of the a allele before and after the environmental change.
he(h)	Effective dominance coefficient.
π(h,s,x)	Probability of fixation of an allele starting at frequency x.
ρ(h,s,x)	Stationary density function of the frequency of the a allele before the environmental change, conditioned on a being the derived allele.
Pnew	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.
Twait	Average waiting time of appearance of the mutation destined to be fixed.
Tadapt	Average time until complete adaptation, that is, until fixation of the beneficial allele either from standing variation or recurrent mutations.
Trelax	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 is higher in outcrossers than in selfers.

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 from neutral or deleterious (s_d) to beneficial (s_b). 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 N₀. 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: w_AA= 1 –r , w_Aa= 1 +h_bs_b–r , w_aa= 1 +s_b–r). Note that the demography is thus 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 10N₀. We used this last condition to avoid infinite growth because we did not include density dependence. We chose 10N₀ instead of N₀ because the population size can be a bit higher than N₀ through stochastic variations just after the environmental change, especially when N₀ is low. Choosing 10N₀ 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.

NEW MUTATIONS

According to Kimura (1962), the probability of fixation of a mutant allele starting at frequency x is given by

(3)

In the case of partial selfing (Caballero and Hill 1992)

(4)

with N_e 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

(5)

When N_e(h_b+F−h_bF)s >>1,

(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

(7)

(Caballero and Hill 1992 but see below and Glémin 2012 for the problem with the use of h_e). As emphasized by Charlesworth (1992), equation (6) shows that P_new is independent of h_b in complete selfers whereas in outcrossers, dominant mutations are more easily fixed than recessive ones, the so-called “Haldane's sieve” (Haldane 1927). For h_b=½, P_new reduces to 2αs_b. If there is no additional reduction in N_e 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:

(8)

where ρ(h_d, s_d, 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(h_d, s_d, x) and P_sv when selection on heterozygotes is strong enough. In Supporting information Material 1, we show that we can directly use their results by replacing h by h_e(h) given by equation (7). For 4N_eh_e(h_b) s_b > (1 – 2h_e(h_b))/2h_e(h_b), we thus obtained

(9)

with and N_e is given by (1). R is defined 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 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)

(10)

where Γ(z) is the Gamma function (Abramowitz and Stegun 1970).

As for new mutations, P_sv is independent of dominance in complete selfers (Fig. 3). In outcrossers, for initially neutral or weakly deleterious alleles (either recessive or dominant), P_sv is higher for dominant alleles, although the relative effect of dominance is weaker than for P_new. For initially strongly deleterious a alleles and assuming that h_b=h_d, P_sv is mostly independent of dominance in outcrossers, the R ratio in equation (9) tends toward s_b/s_d (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 P_sv 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 N_e. As N_e is lower in selfing than in outcrossing species, P_sv decreases with selfing rate under most conditions, contrary to what is expected for P_new (compare Figs. 2, 3). Using equation (9), we can determine the threshold dominance coefficient above which P_sv is higher in outcrossers than in selfers by solving in h_b: . General expressions are given in Supporting information Material 1. For α= 1, strong selection (N_ehs >> 1), and an initially deleterious allele we obtained

(11a)

When considering an initially neutral allele we obtained:

(11b)

where γ≈ 0.577 is the Euler's constant. Even when α= 1, 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 N_e is reduced and (2) initially deleterious alleles are maintained at lower frequencies because of the purging process.

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

(12)

The general expression of T_adapt is given in Supporting information Material 2. To get an approximation of T_adapt, 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

(13)

P_sv is given by equation (9). Assuming that the occurrence of mutations destined to be fixed follows a Poisson process with mean 2NuP_new, the time until the first occurrence of such a mutation is exponentially distributed with mean

(14)

with P_new given by equation (6). Hermisson and Pennings (2005) gave an approximation for . However, their expression is not very accurate as far as h is far from ½—either close to 0 or 1–and it cannot be simply extended to partial selfing by substituting h_e 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)

(15)

Finally, noting T_fix(h, s, x), the time to fixation starting from frequency x is given by

(16)

Using results obtained by (Glémin 2012), equation (16) can be approximated by (see Supporting information Material 2)

(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 deleterious alleles using the deterministic frequency at mutation–selection balance

(18)

Note that , , and T_wait scale in 1/s_b and so does T_adapt. The total waiting time, (1 –P_sv)T_wait, is always lower in outcrossers for dominant beneficial mutations. When P_sv is substantial, higher than 0.5, the total waiting time is also lower in outcrossers for mildly recessive allele, especially if N_e is strongly reduced in selfers, α < 1: when N_e is small in selfers, adaptation from standing variation is less likely and the waiting time is longer. On the contrary, is always shorter in selfers than in outcrossers because N_e is lower and h_e(h) is higher (for details see Glémin 2012). 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). T_wait and are computed for a selfing population, P_sv is modified as explained above and is slightly modified: N_eu is replaced by Nu for initially neutral mutations and u/(h_d+F–h_d)s_d is replaced by u/h_ds_d 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 self-fertilizing 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 population 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, T_relax, is given by (see Supporting information Material 3)

(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 N₀, (2) selection is strong enough and initially acts mainly on heterozygotes in outcrossing populations (N_eh_e(h_b)s_b >> 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

(20)

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 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

(21)

When the mutation is initially neutral, we have

(22)

where Γ(z) is the Gamma function (Abramowitz and Stegun 1970). When there is no standing variation, equations (21) and (22) vanish to

(23)

These approximations are relatively good when compared to simulations for relatively weak population decline and selection (r= 0.001 and s_b= 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 s_b= 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 is higher in selfers than in outcrossers is given by

(24)

For α= 1, 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 and is lower than ½ when α= 1 (Fig. 6). To explain higher extinction rates in selfers compared to outcrossers as assumed by the dead-end hypothesis, N_e 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 by . 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 population 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.

Associate Editor: M. Johnston