Efficient Transposition of Tol2 in the Mouse Germline

Insertional mutagenesis screens play an integral part in the annotating of functional data for all sequenced genes in the postgenomic era. Chemical mutagenesis screens are highly efficient but identifying the causative gene can be a laborious task. Other mutagenesis platforms, such as transposable elements, have been successfully applied for insertional mutagenesis screens in both the mouse and rat. However, relatively low transposition efficiency has hampered their use as a high-throughput forward genetic mutagenesis screen. Here we report the first evidence of germline activity in the mouse using a naturally active DNA transposon derived from the medaka fish called Tol2, as an alternative system for high-throughput forward genetic mutagenesis screening tool.THE Tol2 (transposable element of Oryzias latipes, number 2) element belongs to the hAT family (hobo of Drosophilia, Activator of maize and Tam3 of snapdragon) of transposons and was the first known autonomously active vertebrate type II transposable element (Koga et al. 1996; Kawakami et al. 1998). Unlike other DNA-type transposons like Sleeping Beauty (SB) (Ivics et al. 1997) or piggyBac (PB) (Fraser et al. 1996), Tol2 does not exhibit any known strong site specificity for integration nor does it exhibit any significant overexpression inhibition activity (Kawakami and Noda 2004; Balciunas et al. 2006) as seen in SB (Geurts et al. 2003). Recently, Tol2 was shown to effectively carry large DNA cargo of up to 10 kb in human and mouse cells without affecting its transposition efficiency (Balciunas et al. 2006). To date, Tol2 has also been demonstrated to transpose efficiently in zebrafish, frog, chicken, mouse cells, and human cells (Kawakami et al. 2000, 2004; Koga et al. 2003; Kawakami and Noda 2004; Balciunas et al. 2006; Hamlet et al. 2006; Sato et al. 2007).Germline mutagenesis using the SB transposon system has been demonstrated in both the mouse (Dupuy et al. 2001; Horie et al. 2001) and rat (Kitada et al. 2007; Lu et al. 2007). In addition, PB germline mutagenesis in mice has also been demonstrated (Ding et al. 2005; Wu et al. 2007). However, the relatively low germline transposition efficiency of both transposon systems reported so far has hampered their use in a high-throughput forward genetic mutagenesis screen (Keng et al. 2005; Kitada et al. 2007).

TABLE 1

Germline transposition frequency in various transposon systems

Detecting major genetic loci controlling phenotypic variability in experimental crosses

Traditional methods for detecting genes that affect complex diseases in humans or animal models, milk production in livestock, or other traits of interest, have asked whether variation in genotype produces a change in that trait’s average value. But focusing on differences in the mean ignores differences in variability about that mean. The robustness, or uniformity, of an individual’s character is not only of great practical importance in medical genetics and food production but is also of scientific and evolutionary interest (e.g., blood pressure in animal models of heart disease, litter size in pigs, flowering time in plants). We describe a method for detecting major genes controlling the phenotypic variance, referring to these as vQTL. Our method uses a double generalized linear model with linear predictors based on probabilities of line origin. We evaluate our method on simulated F₂ and collaborative cross data, and on a real F₂ intercross, demonstrating its accuracy and robustness to the presence of ordinary mean-controlling QTL. We also illustrate the connection between vQTL and QTL involved in epistasis, explaining how these concepts overlap. Our method can be applied to a wide range of commonly used experimental crosses and may be extended to genetic association more generally.QUANTITATIVE trait locus (QTL) analysis has traditionally focused on detection of major genes controlling the expected mean of a phenotype. But there is substantial evidence that not only the mean but also the variance, that is, the stochastic variability of the phenotype about its average value, may itself be under genetic control. The identification of such variance-controlling loci, which we call vQTL, can be helpful in a variety of contexts, including selection of livestock for uniformity, evaluating predictability of response to medical treatment, identification of key biomolecular stabilizers, and assessment of population resilience in ecology and evolution.One way of interpreting an increase in variability is as a decrease in stability. Waddington (1942) described the concept of canalization, whereby natural selection favors the relative constancy of some attributes, for example, well-formed organs and limbs, and thereby leads to the evolution of heritable architectures that buffer the impact of environmental or background genetic variation that would otherwise cause development to go astray. These architectures create virtual “canals” down which developmental programs flow. For a canalized phenotype, which modern usage expands to include nondevelopmental traits, the “zone of canalization” is the range of underlying liability over which potentially disruptive variation may be absorbed without serious consequence to the expressed trait value (Lynch and Walsh 1998). A well-studied example of a stabilizing architecture is that provided by heat-shock protein 90 (Hsp90), which buffers genetic and stochastic variation in the development of plants and flies (Rutherford and Lindquist 1998; Queitsch et al. 2002; Sangster et al. 2008).But in absorbing variation, such stabilizing architectures also hide it from view, and a sensitizing change in the stabilizer that shifts liability outside the zone of canalization can have a dramatic effect on the phenotype. Such shifts release the combined effects of previously “cryptic” genetic variation: now decanalized, the phenotype is more sensitive to internal (including genetic) and external environment, and as a result varies more greatly between individuals (Dworkin 2005; Hornstein and Shomron 2006). In this vein, decanalization has been proposed to explain why the genetic architectures of some diseases in human populations seem more amenable than others to genetic dissection through genome-wide association (Gibson and Goldstein 2007). Specifically, whereas some disease phenotypes in homogeneous populations may be heavily canalized and thereby harder to dissect, others may have been decanalized by modern living conditions (e.g., inflammatory diseases) or modern admixture, while yet others are simply too recent in evolutionary history for buffering networks to have evolved (e.g., response to HIV).Increased variability can also be adaptive. In natural populations disruptive selection favors diversity, with increased “capacitance” (Rice 2008) or “bet-hedging” (Beaumont et al. 2009) spreading risk over a variable fitness landscape. Feinberg and Irizarry (2010) recently proposed a heritable and selectable mechanism for this based on stochastic epigenetic variation. In controlled populations, variability can be increased through directional selection. For example, in a Drosophila selection experiment Clayton and Robertson (1957) reported increased bristle number variance, which is consistent with the idea that genotypes associated with higher environmental variance have a greater chance of being selected under directional selection (Hill and Zhang 2004). Moreover, genetic differences have been observed for phenotypic variability in body weight for chickens (Rowe et al. 2006) and snails (Ros et al. 2004) and litter size in rabbits (Ibanez-Escriche et al. 2008), sheep (Sancristobal-Gaudy et al. 1998), and pigs (Sorensen and Waagepetersen 2003).In natural populations with stabilizing selection we should expect to find alleles minimizing variance for fitness traits (Lande 1980; Houle 1992), whereas directional selection during domestication will favor alleles that increase variance. One may therefore expect to find vQTL in experimental crosses between wild and domestic animals (see Andersson 2001). Nonetheless, genetic buffering that leads to phenotypic robustness need not require an evolutionary explanation to be observed, nor to be useful in medicine and agriculture. Plainly, detecting vQTL and inferring how they arose are separate questions; here we concentrate on the first.

Retrograde Intraflagellar Transport Mutants Identify Complex A Proteins With Multiple Genetic Interactions in Chlamydomonas reinhardtii

The intraflagellar transport machinery is required for the assembly of cilia. It has been investigated by biochemical, genetic, and computational methods that have identified at least 21 proteins that assemble into two subcomplexes. It has been hypothesized that complex A is required for retrograde transport. Temperature-sensitive mutations in FLA15 and FLA17 show defects in retrograde intraflagellar transport (IFT) in Chlamydomonas. We show that IFT144 and IFT139, two complex A proteins, are encoded by FLA15 and FLA17, respectively. The fla15 allele is a missense mutation in a conserved cysteine and the fla17 allele is an in-frame deletion of three exons. The flagellar assembly defect of each mutant is rescued by the respective transgenes. In fla15 and fla17 mutants, bulges form in the distal one-third of the flagella at the permissive temperature and this phenotype is also rescued by the transgenes. These bulges contain the complex B component IFT74/72, but not α-tubulin or p28, a component of an inner dynein arm, which suggests specificity with respect to the proteins that accumulate in these bulges. IFT144 and IFT139 are likely to interact with each other and other proteins on the basis of three distinct genetic tests: (1) Double mutants display synthetic flagellar assembly defects at the permissive temperature, (2) heterozygous diploid strains exhibit second-site noncomplemention, and (3) transgenes confer two-copy suppression. Since these tests show different levels of phenotypic sensitivity, we propose they illustrate different gradations of gene interaction between complex A proteins themselves and with a complex B protein (IFT172).CILIA and flagella are microtubule-based organelles that are found on most mammalian cells. They provide motility to cells and participate in many sensory processes. Defects in or loss of cilia/flagella cause a variety of human diseases that include polycystic kidney disease, retinal degeneration, infertility, obesity, respiratory defects, left–right axis determination, and polydactyly (Fliegauf et al. 2007). Mouse mutants demonstrate that cilia are essential for viability, neural tube closure, and bone development (Eggenschwiler and Anderson 2007; Fliegauf et al. 2007). Cilia and flagella are also present in protists, algae, moss, and some fungi.The assembly and maintenance of cilia and flagella require intraflagellar transport (IFT) (Kozminski et al. 1995). IFT involves the movement of 100- to 200-nm-long protein particles from the basal body located in the cell body to the tip of the flagella using the heterotrimeric kinesin-2 (anterograde movement) (Kozminski et al. 1995) and movement back to the cell body (retrograde movement) using the cytoplasmic dynein complex (Pazour et al. 1999; Porter et al. 1999). IFT particles change their direction of movement as well as their size, speed, and frequency at the ends of the flagella as they switch from anterograde to retrograde movement (Iomini et al. 2001). Biochemical isolation of IFT particles reveals that they are composed of at least 16 proteins and that these particles can be dissociated into two complexes in vitro by changing the salt concentration (Cole et al. 1998; Piperno et al. 1998). Recent genetic and bioinformatics analysis adds at least 7 more proteins to the IFT particle (Follit et al. 2009) (Eggenschwiler and Anderson 2007).

TABLE 1

Proteins and gene names for the intraflagellar transport particles in Chlamydomonas, C. elegans, and mouse

Variation in Genomic Recombination Rates Among Heterogeneous Stock Mice

We used a large panel of pedigreed, genetically admixed house mice to study patterns of recombination rate variation in a leading mammalian model system. We found considerable inter-individual differences in genomic recombination rates and documented a significant heritable component to this variation. These findings point to clear variation in recombination rate among common laboratory strains, a result that carries important implications for genetic analysis in the house mouse.THE rate of recombination—the amount of crossing over per unit DNA—is a key parameter governing the fidelity of meiosis. Recombination rates that are too high or too low frequently give rise to aneuploid gametes or prematurely arrest the meiotic cell cycle (Hassold and Hunt 2001). As a consequence, recombination rates should experience strong selective pressures to lie within the range defined by the demands of meiosis (Coop and Przeworski 2007). Nonetheless, classical genetic studies in Drosophila (Chinnici 1971; Kidwell 1972; Brooks and Marks 1986), crickets (Shaw 1972), flour beetles (Dewees 1975), and lima beans (Allard 1963) have shown that considerable inter-individual variation for recombination rate is present within populations. Recent studies examining the transmission of haplotypes in human pedigrees have corroborated these findings (Broman et al. 1998; Kong et al. 2002; Coop et al. 2008).Here, we use a large panel of heterogeneous stock (HS) mice to study variation in genomic recombination rates in a genetic model system. These mice are genetically admixed, derived from an initial generation of pseudorandom mating among eight common inbred laboratory strains (DBA/2J, C3H/HeJ, AKR/J, A/J, BALB/cJ, CBA/J, C57BL/6J, and LP/J), followed by >50 generations of pseudorandom mating in subsequent hybrid cohorts (Mott et al. 2000; Demarest et al. 2001). The familial relationships among animals in recent generations were tracked to organize the mice into pedigrees. In total, this HS panel includes ∼2300 animals comprising 85 families, 8 of which span multiple generations. The remainder consists of nuclear families (sibships) that range from 1 to 34 sibs, with an average of 9.6 sibs (Valdar et al. 2006) (Mott et al. 2000; Demarest et al. 2001; Shifman et al. 2006).

TABLE 1

Heterogeneous stock mouse pedigrees

Healing of Euchromatic Chromosome Breaks by Efficient de novo Telomere Addition in Drosophila melanogaster

Many arthropod species are infected with maternally inherited endosymbionts that induce a shift in the sex ratio of their hosts by feminizing or killing males (cytoplasmic sex-ratio distorters, or SRDs). These endosymbionts can have profound impacts on evolutionary processes of their hosts. Here, I derive analytical expressions for the coalescent effective size N_e of populations that are infected with SRDs. Irrespective of the type of SRD, N_e for mitochondrial genes is given by the number of infected females. For nuclear genes, the effective population size generally decreases with increasing prevalence of the SRD and can be considerably lower than the actual size of the population. For example, with male-killing bacteria that have near perfect maternal transmission, N_e is reduced by a factor that is given to a good approximation by the proportion of uninfected individuals in the population. The formulae derived here also yield the effective size of populations infected with mutualistic endosymbionts or maternally inherited bacteria that induce cytoplasmic incompatibility, although in these cases, the reduction in N_e is expected to be less severe than for cytoplasmic SRDs.SIMPLE null models are essential in science. In population genetics, this role is filled by the Wright–Fisher model and its retrospective counterpart, the Kingman coalescent. Both of these models have proven to be immensely useful in spite of the fact that natural populations usually violate the assumptions made in these models. The reason for this is that often, the Wright–Fisher model can be rescaled so that it behaves in many important respects like a more complex population model. This rescaling is achieved through the concept of the effective population size, N_e. Roughly speaking, a complex population model is said to have a certain N_e if the haploid Wright–Fisher model with population size N_e experiences the same amount of random genetic drift as the complex model. Reflecting the different ways in which drift can be measured, N_e can be defined in different ways, e.g., as the inbreeding, the variance, or the coalescent effective population size. Different definitions often produce the same value for N_e, but may also yield drastically different numbers (Kimura and Crow 1963).The coalescent effective population size is defined through the factor by which time needs to be rescaled in a complex population model to produce the standard coalescent with time scale given by the population size N (Nordborg and Krone 2002). It has been argued that this is the most useful definition for N_e because “the coalescent essentially embodies all of the information that can be found in sampled genetic data” (Sjödin et al. 2005). More recently, Wakeley and Sargsyan (2009) have proposed two extensions of the coalescent effective population size in which they advocate including a mutation parameter in the definition and also allowing for a nonlinear relationship between N_e and N.One frequently encountered feature in natural populations that complicates population genetics is infection with maternally inherited endosymbionts. In particular, many arthropod species harbor a great number of phylogenetically diverse microorganisms that influence their hosts'' biology in different ways (Bourtzis and Miller 2003; Bourtzis and Miller 2006; Bourtzis and Miller 2009). Because of their maternal transmission, many of these microorganisms—for example, the bacteria Wolbachia pipientis and Cardinium hertigii—have evolved intricate manipulations of their hosts'' reproductive system that allows them to spread in a host population through exploitation of male hosts (reproductive parasitism, reviewed in Engelstädter and Hurst 2009a). Most manipulations involve a shift in the sex ratio of their hosts (both primary and at the population level), and the inducing endosymbionts are consequently referred to as cytoplasmic sex-ratio distorters (SRDs). In some species, genetic males develop into females if they are infected (“feminization”: Martin et al. 1973; Rigaud 1997; Bouchon et al. 1998; Hiroki et al. 2002). More commonly, infected males are killed by the endosymbionts early in their development (male killing: reviewed in Hurst et al. 2003). The adaptive advantage of this strategy is seen in an early fitness boost in the surviving females in a brood, for example, through reduced sibling competition or cannibalism of the dead brothers (Hurst 1991; Hurst and Majerus 1993; Jaenike et al. 2003). Some examples for species infected with male-killing or feminizing SRDs are given in Huigens and Stouthamer 2003).

TABLE 1

Empirical examples for cytoplasmic SRDs with parameter estimates

Surprising Fitness Consequences of GC-Biased Gene Conversion: I. Mutation Load and Inbreeding Depression

GC-biased gene conversion (gBGC) is a recombination-associated process mimicking selection in favor of G and C alleles. It is increasingly recognized as a widespread force in shaping the genomic nucleotide landscape. In recombination hotspots, gBGC can lead to bursts of fixation of GC nucleotides and to accelerated nucleotide substitution rates. It was recently shown that these episodes of strong gBGC could give spurious signatures of adaptation and/or relaxed selection. There is also evidence that gBGC could drive the fixation of deleterious amino acid mutations in some primate genes. This raises the question of the potential fitness effects of gBGC. While gBGC has been metaphorically termed the “Achilles'' heel” of our genome, we do not know whether interference between gBGC and selection merely has practical consequences for the analysis of sequence data or whether it has broader fundamental implications for individuals and populations. I developed a population genetics model to predict the consequences of gBGC on the mutation load and inbreeding depression. I also used estimates available for humans to quantitatively evaluate the fitness impact of gBGC. Surprising features emerged from this model: (i) Contrary to classical mutation load models, gBGC generates a fixation load independent of population size and could contribute to a significant part of the load; (ii) gBGC can maintain recessive deleterious mutations for a long time at intermediate frequency, in a similar way to overdominance, and these mutations generate high inbreeding depression, even if they are slightly deleterious; (iii) since mating systems affect both the selection efficacy and gBGC intensity, gBGC challenges classical predictions concerning the interaction between mating systems and deleterious mutations, and gBGC could constitute an additional cost of outcrossing; and (iv) if mutations are biased toward A and T alleles, very low gBGC levels can reduce the load. A robust prediction is that the gBGC level minimizing the load depends only on the mutational bias and population size. These surprising results suggest that gBGC may have nonnegligible fitness consequences and could play a significant role in the evolution of genetic systems. They also shed light on the evolution of gBGC itself.GC-BIASED gene conversion (gBGC) is increasingly recognized as a widespread force in shaping genome evolution. In different species, gene conversion occurring during double-strand break recombination repair is thought to be biased toward G and C alleles. In heterozygotes, GC alleles undergo a kind of molecular meiotic drive that mimics selection (reviewed in Marais 2003). This process can rapidly increase the GC content, especially around recombination hotspots (Spencer et al. 2006), and, more broadly, can affect genome-wide nucleotide landscapes (Duret and Galtier 2009a). For instance, it is thought to play a role in shaping isochore structure evolution in mammals (Galtier et al. 2001; Meunier and Duret 2004; Duret et al. 2006) and birds (Webster et al. 2006). Direct experimental evidence of gBGC mainly comes from studies in yeast (Birdsell 2002; Mancera et al. 2008; but see Marsolier-Kergoat and Yeramian 2009) and humans (Brown and Jiricny 1987). However, associations between recombination and the nucleotide landscape and frequency spectra biased toward GC alleles provide indirect evidence in very diverse organisms (OrganismsDirect evidenceIndirect evidenceAchille''s heel evidenceReferencesYeastMeiotic segregation biasMancera et al. (2008)Mitotic and mitotic heteromismatch correction biasCorrelation between GC and recombinationBirdsell (2002)MammalsMitotic heteromismatch correction biasBrown and Jiricny (1987)Correlation between GC*/GC and recombinationDuret and Arndt (2008); Meunier and Duret (2004)Biased frequency spectrum toward GC allelesGaltier et al. (2001); Spencer et al. (2006)GC bias associated with high d_N/d_S near recombination hotspotBerglund et al. (2009; Galtier et al. (2009)BirdsCorrelation between GC and recombinationInternational Chicken Genome Sequencing Consortium (2004)TurtlesCorrelation between GC and chromosome sizeKuraku et al. (2006)DrosophilaCorrelation between GC and recombinationMarais et al. (2003)Biased frequency spectrum toward GC allelesGaltier et al. (2006)NematodesCorrelation between GC and recombinationMarais et al. (2001)GrassesCorrelation between GC and outcrossing/selfingGlémin et al. (2006)Correlation between GC* and recombination and outcrossing/selfingOutcrossing increases d_N/d_S for genes with high GC*Haudry et al. (2008)Green algaeCorrelation between GC and recombinationJancek et al. (2008)ParameciumCorrelation between GC and chromosome sizeDuret et al. (2008)Open in a separate windowThe impact of gBGC on noncoding sequences and synonymous sites has been studied in depth, especially because of confounding effects with selection on codon usage (Marais et al. 2001). More recently, Galtier and Duret (2007) pointed out that gBGC may also interfere with selection when affecting functional sequences. They argued that gBGC could leave spurious signatures of adaptive selection and proposed to extend the null hypothesis of molecular evolution. Indeed, gBGC can lead to a ratio of nonsynonymous (d_N) over synonymous (d_S) substitutions above one (Berglund et al. 2009; Galtier et al. 2009), i.e., a typical signature of positive selection (Nielsen 2005). This hypothesis has been widely debated for human-accelerated regions (HARs). These regions are extremely conserved across mammals but show evidence of accelerated evolution along the human lineage, which has been interpreted as evidence of positive selection (Pollard et al. 2006a,b; Prabhakar et al. 2006, 2008). On the contrary, other authors argued that patterns observed in HARs, such as the AT → GC substitution bias, the absence of a selective sweep signature, or the propensity to occur within or close to recombination hotspots, are more likely explained by gBGC rather than positive selection (Galtier and Duret 2007; Berglund et al. 2009; Duret and Galtier 2009b; but see also Pollard et al. 2006a who also suggested that gBGC might play a role in HARs evolution). It is thus crucial to take gBGC into account when interpreting genomic data.Moreover, Galtier and Duret (2007) initially suggested that gBGC hotspots could contribute to the fixation of slightly deleterious AT → GC mutations and could represent the Achilles'' heel of our genome. This hypothesis was reinforced later in primates, with evidence of gBGC-driven fixation of deleterious mutations in proteins (Galtier et al. 2009). A similar result was also found in some grass species, whose genomes are also supposed to be affected by gBGC (Glémin et al. 2006). Haudry et al. (2008) compared two outcrossing and two selfing grass species and showed that GC-biased genes exhibit higher d_N/d_S ratio in outcrossing than in selfing lineages. The reverse pattern would be expected under pure selective models because of the reduced selection efficacy in selfers (Charlesworth 1992; Glémin 2007). This pattern is in agreement with a genomic Achilles'' heel associated with outcrossing, while gBGC is inefficient in selfing species because they are mainly homozygous.Twenty years ago, Bengtsson (1990) already pointed out that biased conversion can generally affect the mutation load. The mutation load is the reduction in the mean fitness of a population due to mutation accumulation, which could lead to population extinction if it is too high (Lynch et al. 1995). At this time, Bengtsson concluded that “it is impossible to know if biased conversion plays a major role in determining the magnitude of the mutation load in organisms such as ourselves, but the possibility must be considered and further investigated (Bengtsson 1990, p. 186).” Now, one can propose gBGC could be such a widespread biased conversion process. It thus appears timely to thoroughly investigate the fitness consequences of gBGC through its potential effects on the dynamics of deleterious mutations. The fitness consequences of gBGC were also pointed out as a major future issue to be addressed by Duret and Galtier (2009a). In addition to the load, deleterious mutations have many other evolutionary consequences (for review see Charlesworth and Charlesworth 1998). They are thought to be the main determinant of inbreeding depression, i.e., the reduction in fitness of inbred individuals compared to outbred ones. They also play a key role in the evolution of genetic systems (sexual reproduction and recombination, inbreeding avoidance mechanisms, ploidy cycles), of senescence, or in the degeneration of nonrecombining regions, such as Y chromosomes. So far, we know little, if anything, about how gBGC might affect these processes.In his seminal work, Bengtsson (1990) did not address several important points. First, he did not include genetic drift in his model. Nearly neutral mutations, for which drift and selection are of similar intensities, are the most damaging ones because they can drift to fixation, unlike strongly deleterious mutations that are maintained at low frequency (Crow 1993; Lande 1994, 1998). While gBGC intensities are rather weak (Birdsell 2002; Spencer et al. 2006), they could markedly affect the fate of nearly neutral mutations (see also Galtier et al. 2009). Second, Bengtsson did not study the effect of gene conversion on inbreeding depression, while he showed that recessive mutations, mostly involved in inbreeding depression, are the most affected by gene conversion. Third, he did not envisage systematic GC bias with its opposite effects on A/T and G/C deleterious alleles. Fourth, while he noted that selfing affects both the efficacy of selection and that of conversion, he did not fully investigate the effect of mating systems. On one hand, selfing is efficient in purging strongly deleterious mutations causing inbreeding depression. However, since selfing is expected to increase drift, weakly deleterious mutations can fix in selfing species, contributing to the so-called “drift load” (Charlesworth 1992; Glémin 2007). Self-fertilizing populations are thus expected to exhibit low inbreeding depression and high drift load. On the other hand, gBGC, and thus its cost, vanishes as the selfing rate and homozygosity increase (Marais et al. 2004). gBGC could thus challenge classical views on mating systems and it was even speculated that gBGC could affect their evolution (Haudry et al. 2008).Here I present a population genetics model that includes mutation, selection, drift, and gBGC, which extends previous studies (Gutz and Leslie 1976; Lamb and Helmi 1982; Nagylaki 1983a,b; Bengtsson 1990). I specifically examine how gBGC can affect inbreeding depression and the mutation load. I also focus on the effect of mating system, which is especially interesting with regard to the interaction between biased conversion and selection. Finally, I discuss how these results could give insight into how gBGC evolved.

Impacts of gBGC on inbreeding depression:

Inbreeding depression is defined as the reduction in fitness of selfed (and more generally inbred) individuals compared to outcrossed individuals,(15)where and are the mean fitness of outcrosses and selfcrosses, respectively (Charlesworth and Charlesworth 1987; Charlesworth and Willis 2009). The approximation is very good in most conditions, because under weak (s ≪ 1) and strong selection (x ≪ 1) (see Glémin et al. 2003). Similar to the load, considering both sites for which either S or W alleles are deleterious, in proportion q and 1 – q, respectively, we get(16)

gBGC and the genetic basis of inbreeding depression in panmictic populations:

In infinite panmictic populations without gBGC, inbreeding depression depends only on mutation rates and dominance levels. Partially recessive mutations () contribute only to inbreeding depression, and the more recessive they are, the higher the inbreeding depression (Charlesworth and Charlesworth 1987). In finite populations, deterministic results hold for strongly deleterious mutations (s ≫ 1/N_e), which contribute mostly to inbreeding depression. Contrary to the load, weakly deleterious mutations (∼s ≤ 1/N_e) contribute little to inbreeding depression (Figure 4, a and c, and see Bataillon and Kirkpatrick 2000).Open in a separate windowFigure 4.—Inbreeding depression (×10⁶) as a function of s without (a and c) or with (b and d) gBGC (b = 0.0002). (a and b) h = 0.2: thick lines, N = 5000; thin lines, N = 10,000; dashed lines, N = 50,000; dotted lines, N = 100,000. (c and d) N = 10,000: thick lines, h = 0.4; thin lines, h = 0.2; dashed lines, h = 0.1; dotted lines, h = 0.05. u = 10⁻⁶, λ = 2.Like the load, gBGC affects both the magnitude and the structure of inbreeding depression. In infinite populations, and more generally for strongly deleterious alleles (N_es ≫ 1), replacing x by x_eq given by Equations 4 in Equations 15 and 16 leads to(17a)(17b)(17c)The effect of gBGC on inbreeding depression is not monotonic. Like the load, gBGC increases inbreeding depression if b > hs(1 − 2q/(q + λ − qλ)). However, contrary to the load, a strong gBGC decreases inbreeding depression, which tends to 0 as b increases, while the load tends to qs (Equation 10c). An analysis of Equation 17b shows that mutations that maximize inbreeding depression are those that also maximize the load, i.e., S deleterious mutations with s ≈ 2b.In finite populations, inbreeding depression must be integrated over the Φ distribution, which leads to(18)(see also Glémin et al. 2003). While it is not possible to get an analytical expression of (18), numerical computations (see appendix b) show that S deleterious mutations with s ≈ 2b also maximize inbreeding depression in finite populations (Figure 4). More broadly, inbreeding depression is maximal under the overdominant-like selection regime (gray area in Figure 2). Once again, even low to moderate gBGC markedly affects the genetic structure of inbreeding depression. First, mutations of intermediate effects contribute the most to inbreeding depression, i.e., up to one order of magnitude higher than strongly deleterious mutations (compare Figure 4a with 4b). Second, even nearly additive mutations can have a substantial effect (compare Figure 4c with 4d).Since little is known about the distribution of dominance coefficients, especially the dominance of mildly deleterious mutations (of the order of b), it is difficult to quantitatively predict the full impact of gBGC on inbreeding depression. We can conclude that, on average, gBGC should increase inbreeding depression. However, further insight into mutational parameters is crucial to assess the quantitative impact of gBGC.

Joint effect of gBGC and mating system on the load and inbreeding depression:

Selfing, or more generally inbreeding, slightly reduces the segregating load through the purging of recessive mutations (Ohta and Cockerham 1974), but can substantially increase the fixation load because of the effective population size reduction under inbreeding: (see above and Pollak 1987; Nordborg 1997; Glémin 2007). In numerical examples, I assumed that α decreases with F according to the background selection model (Charlesworth et al. 1993; Nordborg et al. 1996), as in Glémin (2007). With gBGC, selfing thus has two opposite effects on the fixation load. Selfing increases the drift load sensu stricto but decreases the fixation load due to gBGC. A surprising consequence is that the load can be higher in outcrossing than in selfing populations (Figure 5). Quantitatively this is also expected, even with a gBGC hotspot affecting just 3% of the genome (Figure 5 and Open in a separate windowFigure 5.—Effective population size (a and b) and the load (×10⁶) (c–f) as a function of F for different gBGC intensities (thick lines, b = 0; thin lines, b = 0.0001; dashed lines, b = 0.0002; dotted lines, b = 0.0005). The effective population size depends on F under the background selection (BS) model (Charlesworth et al. 1993), using Equations 16 and 17 in Glémin (2007): , where U is the genomic deleterious mutation rate, R is the genomic recombination rate, s_d is the mean selection coefficient against strongly deleterious mutations, and h_d is their dominance coefficient. N = 10,000, U = 0.2, h_d = 0.1, and s_d = 0.05. (a, c, and e) R = 5, “weak” BS; (b, d, and f) R = 0.5, “strong” BS. (c and d) Load averaged over half GC and half AT deleterious alleles, with a bias in favor of AT alleles. (e and f) Load averaged over 10% of GC deleterious alleles and 90% of AT deleterious alleles with a bias in favor of AT alleles; see Figure 3. h = 0.5, u = 10⁻⁶, and λ = 2.Generally, the effect of selfing is simpler for inbreeding depression. Purging, N_e reduction, and suppression of gBGC contribute to decreasing inbreeding depression in selfing populations (Figure 6a). However, there are special cases in which maximum inbreeding depression is reached for intermediate selfing rates (Figure 6b). In such cases, in outcrossing populations, gBGC is strong enough to sweep polymorphism out and reduce inbreeding depression (b > s, regime 1 in Figure 2). As the selfing rate increases, gBGC declines, and the selection dynamics become overdominant-like (regime 2, Figure 2), thus maximizing inbreeding depression. For high selfing rates, gBGC vanishes (regime 3 in Figure 2) and deleterious alleles are either purged or fixed if there is substantial drift. This is similar to the effect of selfing on inbreeding depression caused by asymmetrical overdominance, where inbreeding depression also peaks for intermediate selfing rates (Ziehe and Roberds 1989; Charlesworth and Charlesworth 1990). In the present case, the range of parameters leading to this peculiar behavior is narrow because the overdominant-like region depends on the selfing rates and can vanish either for low or for high selfing rates (Figure 2).Open in a separate windowFigure 6.—Inbreeding depression (×10⁶) as a function of F for different gBGC intensities (thick lines, b = 0; thin lines, b = 0.0001; dashed lines, b = 0.0002; dotted lines, b = 0.0005). Inbreeding depression is averaged over half GC and half AT deleterious alleles. The effective population size depends on F as in Figure 5 (same parameters). (a) s = 0.002; (b) s = 0.0005; (c) s = 0.0002. h = 0.2, u = 10⁻⁶, and λ = 2.

Minimum load and the evolution of gBGC and recombination landscapes:

Although gBGC may have deleterious fitness consequences, it is surprising that it evolved in many taxa (Duret and Galtier 2009a). Birdsell (2002) initially suggested that gBGC may have evolved as a response to mutational bias toward AT (λ > 1, here). Indeed, I show that a minimum load is reached for weak gBGC (b ≈ ln(λ)/4N, Equation 14). This result is very general whatever the distribution of fitness effects of mutations (appendix d). However, the range of optimal gBGC is narrow, and gBGC increases the load as far as b > ln(λ)/2N (appendix c). In humans, using N = 10,000 and λ = 2, gBGC levels that minimize the load are ∼1.17 × 10⁻⁵, i.e., one order of magnitude lower than the average bias observed in recombination hotspots (Myers et al. 2005). However, selection on conversion modifiers will not necessarily minimize the load because of gametic disequilibrium generated between modifiers and fitness loci (Bengtsson and Uyenoyama 1990). Selection for limitation of somatic AT-biased mutations could also have selected for GC-biased mismatch repair machinery (Brown and Jiricny 1987). If the bias level that would be selected for somatic reasons is >ln(λ)/2N, a side effect would be the generation of a substantial load at the population level. Finally, it is interesting to note that when synonymous codon positions are under selection for translation accuracy, optimal gBGC levels can be higher than gBGC levels that minimize the protein load, especially when most optimal codons end in G or C ().Conversely, gBGC could also affect the evolution of recombination landscapes, which could evolve to reduce the gBGC load. Surprisingly, for a given recombination/conversion level, the hotspot distribution does not appear to be optimal (Nishant and Rao 2005), one can speculate that the hotspot localization outside genes could be a response to avoid the deleterious effects of gBGC.Up to now, these verbal arguments have not been assessed theoretically (but see Bengtsson and Uyenoyama 1990 for a different kind of conversion bias). Population genetics models are necessary to test these hypotheses concerning the evolution of gBGC and recombination landscapes and to pinpoint the key parameters that might govern their evolution.

gBGC and the evolution of mating systems:

Deleterious mutations also play a crucial role in the evolution of mating systems. They are the main source of inbreeding depression, which balances the automatic advantage of selfing. The drift load is also thought to contribute to the extinction of selfing species. Since they are mainly homozygous, selfing species are mostly free from gBGC and its deleterious impacts. I discuss below how this might affect the evolution of mating systems.

Inbreeding depression and the shift in mating systems:

Inbreeding depression plays a key role in the evolution of mating systems (Charlesworth and Charlesworth 1987; Charlesworth 2006b). Since it balances the automatic advantage of selfing, high inbreeding depression favors outcrossing, while selfing can evolve when it is low. Moreover, selfing helps to purge strongly deleterious mutations, thus decreasing inbreeding depression. This positive feedback reinforces the disruptive selection on the selfing rate and prevents the transition from selfing to outcrossing (Lande and Schemske 1985).Theoretical results suggest that, in most conditions, gBGC would reinforce inbreeding depression in outcrossing populations (Figure 6), which would prevent the evolution of selfing. In reverse, if selfing is initially selected for, recurrent selfing would reduce the load through both purging and avoidance of gBGC. Under this scenario, gBGC would reinforce disruptive selection on mating systems. However, under some conditions (see Figure 6), inbreeding depression peaks at intermediate selfing rates, as observed for asymmetrical overdominance (Ziehe and Roberds 1989; Charlesworth and Charlesworth 1990). In theory, this could prevent the shift toward complete selfing and maintain stable mixed mating systems (Charlesworth and Charlesworth 1990; Uyenoyama and Waller 1991). However, this pattern is observed under restrictive conditions and it is very unlikely on the whole-genome scale. Dominance patterns are crucial for predicting inbreeding depression, especially with gBGC. Contrary to the load, it is thus difficult to evaluate the quantitative impact of gBGC on inbreeding depression. However, increased inbreeding depression in outcrossing species subject to gBGC seems to be the most likely scenario.

gBGC and the long-term evolution of mating systems:

In the long term, the gBGC-induced load also challenges the “dead-end hypothesis,” which posits that, because of the reduction of selection efficacy, self-fertilizing species would accumulate weakly deleterious mutations in the long term, eventually leading to extinction (Takebayashi and Morrell 2001). Because of gBGC, not drift, outcrossing species could also accumulate a load of weakly deleterious mutations (Figure 7), and they could suffer from a higher load than highly self-fertilizing species (Haudry et al. (2008) found that in two outcrossing grass species, but not in two self-fertilizing ones, the d_N/d_S ratio is significantly higher for genes exhibiting GC enrichment. They speculated that substitutions in these genes might contribute to increasing the load in these two outcrossing grass species. Such results are still very sparse. In plants, evidence of strong gBGC is mainly restricted to grasses (but see Wright et al. 2007). It will be necessary to conduct more in-depth studies to assess the phylogenetic distribution of gBGC in plants and other hermaphrodite organisms and to further test the genomic Achilles'' heel hypothesis in relation to mating systems. While theoretically possible, the quantitative effect of gBGC on the evolution of mating systems remains a new, open, and challenging question.

Conclusion:

I showed that the interaction between gBGC and selection might have surprising qualitative consequences on load and inbreeding depression patterns. Given the few quantitative data available on gBGC levels and selection intensities (mainly in humans), it turns out that even weak genome-wide gBGC can have significant fitness impacts. gBGC should be taken into account not only for sequence analyses (Berglund et al. 2009; Galtier et al. 2009), but also for its potential fitness consequences, for instance concerning genetic diseases. Interferences between gBGC and selection also give rise to new questions on the evolution of mating systems. However, most of the challenging conclusions given here have yet to be quantitatively evaluated. Quantification of gBGC and its interaction with selection in various organisms will be crucial in the future.     

Polymorphic Genes of Major Effect: Consequences for Variation,Selection and Evolution in Arabidopsis thaliana

The importance of genes of major effect for evolutionary trajectories within and among natural populations has long been the subject of intense debate. For example, if allelic variation at a major-effect locus fundamentally alters the structure of quantitative trait variation, then fixation of a single locus can have rapid and profound effects on the rate or direction of subsequent evolutionary change. Using an Arabidopsis thaliana RIL mapping population, we compare G-matrix structure between lines possessing different alleles at ERECTA, a locus known to affect ecologically relevant variation in plant architecture. We find that the allele present at ERECTA significantly alters G-matrix structure—in particular the genetic correlations between branch number and flowering time traits—and may also modulate the strength of natural selection on these traits. Despite these differences, however, when we extend our analysis to determine how evolution might differ depending on the ERECTA allele, we find that predicted responses to selection are similar. To compare responses to selection between allele classes, we developed a resampling strategy that incorporates uncertainty in estimates of selection that can also be used for statistical comparisons of G matrices.THE structure of the genetic variation that underlies phenotypic traits has important consequences for understanding the evolution of quantitative traits (Fisher 1930; Lande 1979; Bulmer 1980; Kimura 1983; Orr 1998; Agrawal et al. 2001). Despite the infinitesimal model''s allure and theoretical tractability (see Orr and Coyne 1992; Orr 1998, 2005a,b for reviews of its influence), evidence has accumulated from several sources (artificial selection experiments, experimental evolution, and QTL mapping) to suggest that genes of major effect often contribute to quantitative traits. Thus, the frequency and role of genes of major effect in evolutionary quantitative genetics have been a subject of intense debate and investigation for close to 80 years (Fisher 1930; Kimura 1983; Orr 1998, 2005a,b). Beyond the conceptual implications, the prevalence of major-effect loci also affects our ability to determine the genetic basis of adaptations and species differences (e.g., Bradshaw et al. 1995, 1998).Although the existence of genes of major effect is no longer in doubt, we still lack basic empirical data on how segregating variation at such genes affects key components of evolutionary process (but see Carrière and Roff 1995). In other words, How does polymorphism at genes of major effect alter patterns of genetic variation and covariation, natural selection, and the likely response to selection? The lack of data stems, in part, from the methods used to detect genes of major effect: experimental evolution (e.g., Bull et al. 1997; Zeyl 2005) and QTL analysis (see Erickson et al. 2004 for a review) often detect such genes retrospectively after they have become fixed in experimental populations or the species pairs used to generate the mapping population. The consequences of polymorphism at these genes on patterns of variation, covariation, selection, and the response to selection—which can be transient (Agrawal et al. 2001)—are thus often unobserved.A partial exception to the absence of data on the effects of major genes comes from artificial selection experiments, in which a substantial evolutionary response to selection in the phenotype after a plateau is often interpreted as evidence for the fixation of a major-effect locus (Frankham et al. 1968; Yoo 1980a,b; Frankham 1980; Shrimpton and Robertson 1988a,b; Caballero et al. 1991; Keightley 1998; see Mackay 1990 and Hill and Caballero 1992 for reviews). However, many of these experiments report only data on the selected phenotype (e.g., bristle number) or, alternatively, the selected phenotype and some measure of fitness (e.g., Frankham et al. 1968, Yoo 1980b; Caballero et al. 1991; Mackay et al. 1994; Fry et al. 1995; Nuzhdin et al. 1995; Zur Lage et al. 1997), making it difficult to infer how a mutation will affect variation, covariation, selection, and evolutionary responses for a suite of traits that might affect fitness themselves. One approach is to document how variation at individual genes of major effect affects the genetic variance–covariance matrix (“G matrix”; Lande 1979), which represents the additive genetic variance and covariance between traits.Although direct evidence for variation at major-effect genes altering patterns of genetic variation, covariation, and selection is rare, there is abundant evidence for the genetic mechanisms that could produce these dynamics. A gene of major effect could have these consequences due to any of at least three genetic mechanisms: (1) pleiotropy, where a gene of major effect influences several traits, including potentially fitness, simultaneously, (2) physical linkage or linkage disequilibrium (LD), in which a gene of major effect is either physically linked or in LD with other genes that influence other traits under selection, and (3) epistasis, in which the allele present at a major-effect gene alters the phenotypic effect of other loci and potentially phenotypes under selection. Evidence for these three evolutionary genetic mechanisms leading to changes in suites of traits comes from a variety of sources, including mutation accumulation experiments (Clark et al. 1995; Fernandez and Lopez-Fanjul 1996), mutation induction experiments (Keightley and Ohnishi 1998), artificial selection experiments (Long et al. 1995), and transposable element insertions (Rollmann et al. 2006). For pleiotropy in particular, major-effect genes that have consequences on several phenotypic traits are well known from the domestication and livestock breeding literature [e.g., myostatin mutations in Belgian blue cattle and whippets (Arthur 1995; Grobet et al. 1997; Mosher et al. 2007), halothane genes in pigs (Christian and Rothschild 1991; Fujii et al. 1991), and Booroola and Inverdale genes in sheep (Amer et al. 1999; Visscher et al. 2000)]. While these data suggest that variation at major-effect genes could—and probably does—influence variation, covariation, and selection on quantitative traits, data on the magnitude of these consequences remain lacking.Recombinant inbred line (RIL) populations are a promising tool for investigating the influence of major-effect loci. During advancement of the lines from F₂''s to RILs, alternate alleles at major-effect genes (and most of the rest of the genome) will be made homozygous, simplifying comparisons among genotypic classes. Because of the high homozygosity, individuals within RILs are nearly genetically identical, facilitating phenotyping of many genotypes under a range of environments. In addition, because of recombination, alternative alleles are randomized across genetic backgrounds—facilitating robust comparisons between sets of lines differing at a major-effect locus.Here we investigate how polymorphism at an artificially induced mutation, the erecta locus in Arabidopsis thaliana, affects the magnitude of these important evolutionary genetic parameters under ecologically realistic field conditions. We use the Landsberg erecta (Ler) × Columbia (Col) RIL population of A. thaliana to examine how variation at a gene of major effect influences genetic variation, covariation, and selection on quantitative traits in a field setting. The Ler × Col RIL population is particularly suitable, because it segregates for an artificially induced mutation at the erecta locus, which has been shown to influence a wide variety of plant traits. The Ler × Col population thus allows a powerful test of the effects of segregating variation at a gene—chosen a priori—with numerous pleiotropic effects. The ERECTA gene is a leucine-rich receptor-like kinase (LRR-RLK) (Torii et al. 1996) and has been shown to affect plant growth rates (El-Lithy et al. 2004), stomatal patterning and transpiration efficiency (Masle et al. 2005; Shpak et al. 2005), bacterial pathogen resistance (Godiard et al. 2003), inflorescence and floral organ size and shape (Douglas et al. 2002; Shpak et al. 2003, 2004), and leaf polarity (Xu et al. 2003; Qi et al. 2004).Specifically, we sought to answer the following questions: (1) Is variation at erecta significantly associated with changes to the G matrix? (2) Is variation at erecta associated with changes in natural selection on genetically variable traits? And (3) is variation at erecta associated with significantly different projected evolutionary responses to selection?     

The Genealogical Consequences of Fecundity Variance Polymorphism

The genealogical consequences of within-generation fecundity variance polymorphism are studied using coalescent processes structured by genetic backgrounds. I show that these processes have three distinctive features. The first is that the coalescent rates within backgrounds are not jointly proportional to the infinitesimal variance, but instead depend only on the frequencies and traits of genotypes containing each allele. Second, the coalescent processes at unlinked loci are correlated with the genealogy at the selected locus; i.e., fecundity variance polymorphism has a genomewide impact on genealogies. Third, in diploid models, there are infinitely many combinations of fecundity distributions that have the same diffusion approximation but distinct coalescent processes; i.e., in this class of models, ancestral processes and allele frequency dynamics are not in one-to-one correspondence. Similar properties are expected to hold in models that allow for heritable variation in other traits that affect the coalescent effective population size, such as sex ratio or fecundity and survival schedules.THE population genetics of within-generation fecundity variance has been studied from two perspectives. Beginning with Wright (1938), several authors have investigated the relationship between the effective size of a panmictic population with seasonal reproduction and the variance of the number of offspring born to each adult within a season (Crow and Denniston 1988; Nunney 1993, 1996; Waples 2002; Hedrick 2005; Engen et al. 2007). Although the precise form of this relationship depends on other biological factors such as the mating system and the manner in which population regulation operates, each of these studies shows that the effective population size is a decreasing function of fecundity variance. Furthermore, provided that the variance and the coalescent effective population sizes coincide (Ewens 1982; Nordborg and Krone 2002; Sjodin et al. 2005), these results imply that both the rate at which neutral allele frequencies fluctuate from generation to generation and the rate at which lineages coalesce will be positively correlated with within-generation fecundity variance. For example, it has been suggested that the shallow genealogies that have been documented in many marine organisms are a consequence of the high variance of reproductive success in the recruitment sweepstakes operating in these species (Hedgecock 1994; Árnason 2004; Eldon and Wakeley 2006).These results hold in models in which all individuals have the same within-generation (or within-season) fecundity variance. However, the evolutionary genetics of populations that are polymorphic for alleles that influence demographic traits have also been investigated. The first results of this kind were derived by Gillespie (1974, 1975, 1977), who used diffusion theory to show that natural selection can act directly on within-generation fecundity variance in a haploid population with nonoverlapping generations. By studying a simple model of a population composed of two genotypes, say A₁ and A₂, Gillespie (1974) showed that the fluctuations in the frequency of allele A₁ can be approximated by a diffusion process with the following drift and variance coefficients,where p is the frequency of A₁, N is the number of adults, and 1 + μ_i and are the mean and the variance, respectively, of the number of offspring produced by an individual of type A_i. Most discussions of this class of models have focused on the fitness consequences of differences in fecundity variance, which are summarized by the drift coefficient, m(p), of the diffusion approximation. There are two main conclusions. The first is that because m(p) is an increasing function of the difference − , selection can favor alleles that reduce within-generation fecundity variance even if these have lower mean fecundity. Such variance–mean trade-offs can be interpreted as a kind of bet hedging and could explain the evolution of certain risk-spreading traits such as insect oviposition onto multiple host plants (Root and Kareiva 1986) or multiple mating by females (Sarhan and Kokko 2007). On the other hand, because the strength of selection on fecundity variance is inversely proportional to population size, selection for mean–variance trade-offs will usually be dominated by changes in mean fecundity. For this reason, it has been suggested that within-generation bet hedging will be favored only in very small populations (Seger and Brockman 1987; Hopper et al. 2003), although recent theoretical studies have shown that bet hedging can evolve under less restrictive conditions in subdivided populations (Shpak 2005; Lehmann and Balloux 2007; Shpak and Proulx 2007).Less consideration has been given to the diffusion coefficient, v(p), which differs from the familiar quadratic term, p(1 − p), of the Wright–Fisher diffusion. Because the variance effective population size of a monomorphic population depends on the fecundity variance, it is not surprising that v(p) has an additional dependence on the frequency of A₁ whenever the two alleles have different offspring variances. However, as noted by Gillespie (1974), the relationship between allele frequency fluctuations and the allelic composition of the population is counterintuitive. For example, when p is close to 1, so that the population is composed mainly of A₁-type individuals, the rate of allele frequency fluctuations is dominated by the variance of the A₂ genotype. In particular, if we define the variance effective population size by the expression Np(1 − p)/v(p) (Ewens 1982), then not only is this quantity frequency dependent, but also it depends on the life history traits of the missing genotype whenever the population is fixed for one of the two alleles. In contrast, the coalescent effective population size of a monomorphic population depends only on the offspring distribution of the fixed allele. The discrepancy between these two quantities raises the following question: namely, How does fecundity variance polymorphism affect the statistical properties of the genealogy of a random sample of individuals?The answer to this question is of interest for several reasons. First, although the effects of selection on genealogies have received considerable attention (Przeworski et al. 1999; Williamson and Orive 2002; Barton and Etheridge 2004), little is known about the genealogical consequences of variation in traits that alter the coalescent rate. Extrapolating from models in which the effective population size varies under the control of external factors, we might expect the coalescent process in a model with fecundity variance polymorphism to be a stochastic time change of Kingman''s coalescent. However, the results derived in the next section show that this intuition is usually wrong. The second motivation is more practical. Even if changes in fecundity variance are usually controlled by selection on other traits, the existence of interspecific differences in fecundity variance suggests that there must be periods when populations are polymorphic for alleles that alter the fecundity variance. In these instances, it might be possible to use sequence data to identify the loci responsible for these changes, but to do so will require the development of methods that exploit patterns that are unique to models in which the effective population size depends on the genetic composition of the population. For example, whereas the effects of genetic hitchhiking are usually restricted to linked sites (Maynard Smith and Haigh 1974; Kim and Stephan 2002; Przeworski 2002; Przeworski et al. 2005), we will see later that selective sweeps by mutations that affect fecundity variance would have a genomewide impact on polymorphism.Kingman (1982a,b) showed that the genealogy of a sample of individuals from a panmictic, neutrally evolving population of constant size can be described by a simple stochastic process known as the coalescent (or Kingman''s coalescent). One of the most important properties of Kingman''s coalescent is that it is a Markov process, a fact that is heavily exploited in mathematical analyses and that also allows for efficient simulations of genealogies. Unfortunately, this property generally does not hold in populations composed of nonexchangeable individuals. For example, if there are selective differences between individuals, then although the genealogy of a sample of individuals can still be regarded as a stochastic process, selective interactions between individuals cause this process to also depend on the history of nonancestral lineages. The key to overcoming this difficulty is to embed the genealogical process in a larger process that does satisfy the Markov property. This can be done in two ways. One approach is to embed the coalescent tree within a graphical process called the ancestral selection graph (Krone and Neuhauser 1997; Neuhauser and Krone 1997; Donnelly and Kurtz 1999) in which lineages can either branch, giving rise to pairs of potential ancestors, or coalesce. The intuition behind this construction is that the effects of selection on the genealogy can be accounted for by keeping track of a pool of potential ancestors that includes lineages that have failed to persist due to being outcompeted by individuals of higher fitness. Because the branching rates are linear in the number of lineages, while the coalescence rates are quadratic, this process is certain to reach an ultimate ancestor in finite time. The process can be stopped at this time, and both the ancestral and the genotypic status of individual branches can be resolved by assigning random mutations to the graph and then traversing it from the root to the leaves.The second approach is due to Kaplan et al. (1988), who showed that the genealogical history of a sample of genes under selection can be represented by a structured coalescent process. Here we think of the population as being subdivided into several demes, or genetic backgrounds, consisting of individuals that share the same genotype at the selected locus. Because individuals with the same genotype are exchangeable, the rate of coalescence within a background depends only on the size of the background and the number of ancestral lineages sharing that genotype. In addition, mutations at the selected site will move lineages between backgrounds. To obtain a Markov process, we need to keep track of two kinds of information: (i) the types of the ancestral lineages and (ii) the frequencies of the alleles segregating at the selected locus. Fortunately, because one-dimensional diffusion processes are reversible with respect to their stationary distributions (i.e., the detailed balance conditions are satisfied), the ancestral process of allele frequencies at a locus segregating two alleles has the same law as the forward process. Subsequently, Hudson and Kaplan (1988) showed that the genealogy at a linked neutral locus can be described by a structured coalescent defined in terms of the genetic backgrounds at the selected locus; in this case, recombination between the selected and neutral loci can also move lineages between backgrounds.The objective of this article is to extend the structured coalescent to population genetic models in which within-generation fecundity variance is genotype dependent. (The genealogical consequences of polymorphism affecting between-generation fecundity variance will be described in a separate article.) In these models, exchangeability is violated not only by selective differences between individuals, but also by differences in life history traits that affect coalescent rates and allele frequency fluctuations. Nonetheless, because lineages are exchangeable within backgrounds, the coalescence and substitution rates can still be calculated conditional on the types of the lineages and the genetic composition of the population. In the next two sections, I derive structured coalescent processes that describe the genealogy at a neutral marker locus that is linked to a second locus (the “selected locus”) that affects fecundity variance. This is first done for a haploid model and then extended to a diploid model in which there may be both sex- and genotype-specific differences in fecundity variance. Results for both models are summarized in Rates

---

TransitionHaploid modelDiploid modeln₁μ₁q/pn₁μ₁q/pn₂μ₂p/qn₂μ₂p/qn₁rqn₁rqn₂rpn₂rpOpen in a separate windowThis work shows that coalescent processes in populations with fecundity variance polymorphism differ from the structured coalescent in a monomorphic population in three ways. One difference is that in populations with fecundity variance polymorphism, the coalescent rates in the different genetic backgrounds are not inversely proportional to the variance effective population size. Instead, coalescence within each allelic background depends only on the frequencies and fecundity distributions of genotypes containing that allele. The second difference is that the genealogies at the marker and selected loci are correlated even when these loci are unlinked; i.e., fecundity variance polymorphism has a genomewide impact on genealogies and genetic variation. This follows from the calculations leading up to Equation 28, which show that the genealogical process at an unlinked marker locus can be represented as a stochastic time change of Kingman''s coalescent dependent on the ancestral process of allele frequencies at the selected locus. The third and most surprising difference is that the correspondence between ancestral processes and allele frequency processes is many-to-one in diploid models with fecundity variance polymorphism. In fact, there are infinitely many combinations of genotype-dependent fecundity distributions (satisfying Equation 24) that have the same diffusion approximation but different genealogical processes. These results are illustrated numerically using simulations of the structured coalescent under directional and balancing selection. Finally, I examine the scope of the theory and some possible applications in the discussion.     

Adaptive Divergence in Experimental Populations of Pseudomonas fluorescens. IV. Genetic Constraints Guide Evolutionary Trajectories in a Parallel Adaptive Radiation

The capacity for phenotypic evolution is dependent upon complex webs of functional interactions that connect genotype and phenotype. Wrinkly spreader (WS) genotypes arise repeatedly during the course of a model Pseudomonas adaptive radiation. Previous work showed that the evolution of WS variation was explained in part by spontaneous mutations in wspF, a component of the Wsp-signaling module, but also drew attention to the existence of unknown mutational causes. Here, we identify two new mutational pathways (Aws and Mws) that allow realization of the WS phenotype: in common with the Wsp module these pathways contain a di-guanylate cyclase-encoding gene subject to negative regulation. Together, mutations in the Wsp, Aws, and Mws regulatory modules account for the spectrum of WS phenotype-generating mutations found among a collection of 26 spontaneously arising WS genotypes obtained from independent adaptive radiations. Despite a large number of potential mutational pathways, the repeated discovery of mutations in a small number of loci (parallel evolution) prompted the construction of an ancestral genotype devoid of known (Wsp, Aws, and Mws) regulatory modules to see whether the types derived from this genotype could converge upon the WS phenotype via a novel route. Such types—with equivalent fitness effects—did emerge, although they took significantly longer to do so. Together our data provide an explanation for why WS evolution follows a limited number of mutational pathways and show how genetic architecture can bias the molecular variation presented to selection.UNDERSTANDING—and importantly, predicting—phenotypic evolution requires knowledge of the factors that affect the translation of mutation into phenotypic variation—the raw material of adaptive evolution. While much is known about mutation rate (e.g., Drake et al. 1998; Hudson et al. 2002), knowledge of the processes affecting the translation of DNA sequence variation into phenotypic variation is minimal.Advances in knowledge on at least two fronts suggest that progress in understanding the rules governing the generation of phenotypic variation is possible (Stern and Orgogozo 2009). The first stems from increased awareness of the genetic architecture underlying specific adaptive phenotypes and recognition of the fact that the capacity for evolutionary change is likely to be constrained by this architecture (Schlichting and Murren 2004; Hansen 2006). The second is the growing number of reports of parallel evolution (e.g., Pigeon et al. 1997; ffrench-Constant et al. 1998; Allender et al. 2003; Colosimo et al. 2004; Zhong et al. 2004; Boughman et al. 2005; Shindo et al. 2005; Kronforst et al. 2006; Woods et al. 2006; Zhang 2006; Bantinaki et al. 2007; McGregor et al. 2007; Ostrowski et al. 2008)—that is, the independent evolution of similar or identical features in two or more lineages—which suggests the possibility that evolution may follow a limited number of pathways (Schluter 1996). Indeed, giving substance to this idea are studies that show that mutations underlying parallel phenotypic evolution are nonrandomly distributed and typically clustered in homologous genes (Stern and Orgogozo 2008).While the nonrandom distribution of mutations during parallel genetic evolution may reflect constraints due to genetic architecture, some have argued that the primary cause is strong selection (e.g., Wichman et al. 1999; Woods et al. 2006). A means of disentangling the roles of population processes (selection) from genetic architecture is necessary for progress (Maynard Smith et al. 1985; Brakefield 2006); also necessary is insight into precisely how genetic architecture might bias the production of mutations presented to selection.Despite their relative simplicity, microbial populations offer opportunities to advance knowledge. The wrinkly spreader (WS) morphotype is one of many different niche specialist genotypes that emerge when experimental populations of Pseudomonas fluorescens are propagated in spatially structured microcosms (Rainey and Travisano 1998). Previous studies defined, via gene inactivation, the essential phenotypic and genetic traits that define a single WS genotype known as LSWS (Spiers et al. 2002, 2003) (Figure 1). LSWS differs from the ancestral SM genotype by a single nonsynonymous nucleotide change in wspF. Functionally (see Figure 2), WspF is a methyl esterase and negative regulator of the WspR di-guanylate cyclase (DGC) (Goymer et al. 2006) that is responsible for the biosynthesis of c-di-GMP (Malone et al. 2007), the allosteric activator of cellulose synthesis enzymes (Ross et al. 1987). The net effect of the wspF mutation is to promote physiological changes that lead to the formation of a microbial mat at the air–liquid interface of static broth microcosms (Rainey and Rainey 2003).Open in a separate windowFigure 1.—Outline of experimental strategy for elucidation of WS-generating mutations and their subsequent identity and distribution among a collection of independently evolved, spontaneously arising WS genotypes. The strategy involves, first, the genetic analysis of a specific WS genotype (e.g., LSWS) to identify the causal mutation, and second, a survey of DNA sequence variation at specific loci known to harbor causal mutations among a collection of spontaneously arising WS genotypes. For example, suppressor analysis of LSWS using a transposon to inactivate genes necessary for expression of the wrinkly morphology delivered a large number of candidate genes (top left) (Spiers et al. 2002). Genetic and functional analysis of these candidate genes (e.g., Goymer et al. 2006) led eventually to the identity of the spontaneous mutation (in wspF) responsible for the evolution of LSWS from the ancestral SM genotype (Bantinaki et al. 2007). Subsequent analysis of the wspF sequence among 26 independent WS genotypes (bottom) showed that 50% harbored spontaneous mutations (of different kinds; see Open in a separate windowFigure 2.—Network diagram of DGC-encoding pathways underpinning the evolution of the WS phenotype and their regulation. Overproduction of c-di-GMP results in overproduction of cellulose and other adhesive factors that determine the WS phenotype. The ancestral SBW25 genome contains 39 putative DGCs, each in principle capable of synthesizing the production of c-di-GMP, and yet WS genotypes arise most commonly as a consequence of mutations in just three DGC-containing pathways: Wsp, Aws, and Mws. In each instance, the causal mutations are most commonly in the negative regulatory component: wspF, awsX, and the phosphodiesterase domain of mwsR (see text).To determine whether spontaneous mutations in wspF are a common cause of the WS phenotype, the nucleotide sequence of this gene was obtained from a collection of 26 spontaneously arising WS genotypes (WS_A-Z) taken from 26 independent adaptive radiations, each founded by the same ancestral SM genotype (Figure 1): 13 contained mutations in wspF (Bantinaki et al. 2007). The existence of additional mutational pathways to WS provided the initial motivation for this study.

TABLE 1

Mutational causes of WS

Estimating Selection Intensity on Synonymous Codon Usage in a Nonequilibrium Population

Codon usage bias is the nonrandom use of synonymous codons for the same amino acid. Most population genetic models of codon usage evolution assume that the population is at mutation–selection–drift equilibrium. Natural populations, however, frequently deviate from equilibrium, often because of recent demographic changes. Here, we construct a matrix model that includes the effects of a recent change in population size on estimates of selection on preferred vs. unpreferred codons. Our results suggest that patterns of synonymous polymorphisms affecting codon usage can be quite erratic after such a change; statistical methods that fail to take demographic effects into account can then give incorrect estimates of important parameters. We propose a new method that can accurately estimate both demographic and codon usage parameters. The method also provides a simple way of testing for the effects of covariates such as gene length and level of gene expression on the intensity of selection, which we apply to a large Drosophila melanogaster polymorphism data set. Our analyses of twofold degenerate codons reveal that (i) selection acts in favor of preferred codons, (ii) there is mutational bias in favor of unpreferred codons, (iii) shorter genes and genes with higher expression levels are under stronger selection, and (iv) there is little evidence for a recent change in population size in the Zimbabwe population of D. melanogaster.CODONS specifying the same amino acid are called synonymous codons. These are often used nonrandomly, with some codons appearing more frequently than others. This biased usage of synonymous codons has been found in many organisms such as Drosophila, yeast, and bacteria (Ikemura 1985; Duret and Mouchiroud 1999; Hershberg and Petrov 2008). Conventionally, synonymous codons for a given amino acid are divided into two classes: preferred and unpreferred codons (Ikemura 1985; Akashi 1994; Duret and Mouchiroud 1999). Several observations indicate that codon usage is affected by natural selection. First, in species with codon usage bias, preferred codons generally correspond to the most abundant tRNA species (Ikemura 1981). Second, highly expressed genes usually have higher codon usage bias than genes with low expression (Sharp and Li 1986; Duret and Mouchiroud 1999; Hey and Kliman 2002). Third, the synonymous substitution rate of a gene has been shown to be negatively correlated with its degree of codon usage bias (Sharp and Li 1986; Bierne and Eyre-Walker 2006). The most commonly cited explanations of the apparent fitness differences between preferred and unpreferred codons are selection for translation efficiency, translational accuracy, and mRNA stability (Ikemura 1985; Eyre-Walker and Bulmer 1993; Akashi 1994; Drummond et al. 2005). Recently, it has been proposed that exon splicing also affects codon usage bias (Warnecke and Hurst 2007).From a population genetics perspective, the extent of codon usage bias is ultimately a product of the joint effects of mutation, selection, genetic drift, recombination, and demographic history. The Li–Bulmer model of drift, selection, and reversible mutation between preferred and unpreferred codons at a site is the most widely used model (Li 1987; Bulmer 1991; McVean and Charlesworth 1999). Applications of this model generally assume that the population is at mutation–selection–drift equilibrium. However, empirical studies have suggested that changes in the strengths of various driving forces may not be unusual. For example, in Drosophila melanogaster, there is evidence that the population size (Li and Stephan 2006; Thornton and Andolfatto 2006; Keightley and Eyre-Walker 2007; Stephan and Li 2007), recombinational landscape (Takano-Shimizu 1999), and mutational process (Takano-Shimizu 2001; Kern and Begun 2005) may have changed significantly over the species'' evolutionary history.Such changes cause departures from equilibrium. Theoretical models show that it takes a very long time, proportional to the reciprocal of the mutation rate, for the population to approach a new equilibrium state (Tachida 2000; Comeron and Kreitman 2002). Before reaching equilibrium, the population often shows counterintuitive patterns of evolution (Eyre-Walker 1997; Takano-Shimizu 1999, 2001; Comeron and Kreitman 2002; Comeron and Guthrie 2005; Charlesworth and Eyre-Walker 2007). Despite these theoretical results, details of the patterns of polymorphism and substitution rates following a recent change in population size, and their effects on estimates of strength of selection, have not been determined.The above findings point to the importance of incorporating nonequilibrium factors into the study of codon usage bias. To this end, we extend the Li–Bulmer model to allow population size to vary over time, by representing the evolutionary process by a transition matrix. By analyzing this matrix model, we show that a recent change in population size can result in erratic patterns of codon usage and that methods failing to take into account these demographic effects can give false estimates of the intensity of selection.To solve these problems, we propose a new method, which does not require polarizing ancestral vs. derived states using outgroup data (cf. Cutter and Charlesworth 2006), but requires only knowledge of preferred vs. unpreferred states defined by patterns of codon usage. We use information on both polymorphic and fixed sites, which enables both mutational bias and the strength of selection to be estimated, in contrast to previous methods that use information on polymorphisms alone. Simulations indicate that this method can accurately estimate both demographic and codon usage parameters and can distinguish between selection and demography. We use the new method to analyze a large D. melanogaster polymorphism data set (Shapiro et al. 2007) and find evidence for natural selection on synonymous codons. We use our approach to show that genes with shorter coding sequences and higher levels of expression are under significantly stronger selection than longer genes with lower expression.     

The Genetic Basis of Phenotypic Adaptation II: The Distribution of Adaptive Substitutions in the Moving Optimum Model

We consider a population that adapts to a gradually changing environment. Our aim is to describe how ecological and genetic factors combine to determine the genetic basis of adaptation. Specifically, we consider the evolution of a polygenic trait that is under stabilizing selection with a moving optimum. The ecological dynamics are defined by the strength of selection, , and the speed of the optimum, ; the key genetic parameters are the mutation rate Θ and the variance of the effects of new mutations, ω. We develop analytical approximations within an “adaptive-walk” framework and describe how selection acts as a sieve that transforms a given distribution of new mutations into the distribution of adaptive substitutions. Our analytical results are complemented by individual-based simulations. We find that (i) the ecological dynamics have a strong effect on the distribution of adaptive substitutions and their impact depends largely on a single composite measure , which combines the ecological and genetic parameters; (ii) depending on γ, we can distinguish two distinct adaptive regimes: for large γ the adaptive process is mutation limited and dominated by genetic constraints, whereas for small γ it is environmentally limited and dominated by the external ecological dynamics; (iii) deviations from the adaptive-walk approximation occur for large mutation rates, when different mutant alleles interact via linkage or epistasis; and (iv) in contrast to predictions from previous models assuming constant selection, the distribution of adaptive substitutions is generally not exponential.AN important aim for both empirical and theoretical evolutionary biologists is to better understand the genetics of adaptation (e.g., Orr 2005a). For example, among the multitude of mutations that arise in a population, which ones are eventually fixed and contribute to evolutionary change? That is, given a distribution of new mutations, what is the distribution of adaptive substitutions (or fixed mutations)? Here, distribution means the probability distribution of the effects of mutations on either the phenotype or the fitness of their carriers. In principle, both the distribution of new mutations and the distribution of adaptive substitutions can be measured empirically, the former from mutation accumulation experiments (Eyre-Walker and Keightley 2007) and the latter from QTL (e.g., Bradshaw et al. 1998) or experimental evolution (Elena and Lenski 2003) studies. However, as only a small subset of all mutations is beneficial, such measurements are difficult. Therefore, a large role in studying the genetics of adaptation has to be played by theoretical modeling.In recent years, several different approaches have emerged for modeling the process of adaptation. Considerable work exists, in particular, in the context of Fisher''s geometric model (e.g., Fisher 1930; Kimura 1983; Orr 1998; Welch and Waxman 2005; Martin and Lenormand 2006), Gillespie''s mutational landscape model (e.g., Gillespie 1983, 1984; Orr 2002), various models of so-called “adaptive walks” on rugged fitness landscapes (e.g., Kauffman and Levin 1987; Kauffman 1993), and models of clonal interference in asexual populations (e.g., Gerrish and Lenski 1998; Park and Krug 2007). Together, these models have yielded several robust predictions. For example, both Fisher''s geometric model and the mutational landscape model predict that the distribution of adaptive substitutions should be approximately exponential (with respect to either phenotype or fitness) (Orr 1998, 2002, 2005a,b). This means that most substitutions have little effect, but that a significant fraction of the overall evolutionary change is due to a small number of substitutions with large effects. These results are in qualitative agreement with empirical data (Orr 2005a; Elena and Lenski 2003) and have shed new light on the classical debate about micro- vs. macromutationalism (Fisher 1930; Provine 2001).One way to look at adaptation is to view selection as a sieve that transforms the distribution of new mutations into the distribution of adaptive substitutions (Turner 1981; Orr and Betancourt 2001). This perspective emphasizes the role of environmental factors and directly leads to the question of how different selective regimes (sieves) affect the adaptive process. Yet, almost all studies to date have focused on the simplest possible ecological scenario: a population that, after a sudden change in the environment, is now under constant stabilizing selection.In reality, however, environmental change is often gradual rather than sudden (e.g., Hairston et al. 2005; Thompson 2005; Parmesan 2006; Perron et al. 2008). To account for this possibility, several authors (Bello and Waxman 2006; Collins et al. 2007; Kopp and Hermisson 2007; Sato and Waxman 2008; Kopp and Hermisson 2009) have recently turned to the so-called moving optimum model, which was originally devised in the field of quantitative genetics (e.g., Lynch et al. 1991; Lynch and Lande 1993; Bürger and Lynch 1995; Bürger 1999; Waxman and Peck 1999; Bürger and Gimelfarb 2002; Nunney 2003; Jones et al. 2004). In this model, the selectively favored value of a quantitative trait changes over time, such that the trait is under a mixture of stabilizing and directional selection. An important aspect of the moving optimum model is that it introduces an additional timescale (the timescale of environmental change), which is absent in the previous models.In a recent article (Kopp and Hermisson 2009) and a previous note (Kopp and Hermisson 2007), we have used the moving optimum model to investigate the time to fixation of a single mutation and the order in which mutations of different phenotypic effect go to fixation. However, the fastest mutations in the short term are not necessarily those that dominate evolution in the long term. The present article focuses on this long-term evolution, which can be characterized by the distribution of adaptive substitutions.     

On the Classification of Epistatic Interactions

Modern genomewide association studies are characterized by the problem of “missing heritability.” Epistasis, or genetic interaction, has been suggested as a possible explanation for the relatively small contribution of single significant associations to the fraction of variance explained. Of particular concern to investigators of genetic interactions is how to best represent and define epistasis. Previous studies have found that the use of different quantitative definitions for genetic interaction can lead to different conclusions when constructing genetic interaction networks and when addressing evolutionary questions. We suggest that instead, multiple representations of epistasis, or epistatic “subtypes,” may be valid within a given system. Selecting among these epistatic subtypes may provide additional insight into the biological and functional relationships among pairs of genes. In this study, we propose maximum-likelihood and model selection methods in a hypothesis-testing framework to choose epistatic subtypes that best represent functional relationships for pairs of genes on the basis of fitness data from both single and double mutants in haploid systems. We gauge the performance of our method with extensive simulations under various interaction scenarios. Our approach performs reasonably well in detecting the most likely epistatic subtype for pairs of genes, as well as in reducing bias when estimating the epistatic parameter (ɛ). We apply our approach to two available data sets from yeast (Saccharomyces cerevisiae) and demonstrate through overlap of our identified epistatic pairs with experimentally verified interactions and functional links that our results are likely of biological significance in understanding interaction mechanisms. We anticipate that our method will improve detection of epistatic interactions and will help to unravel the mysteries of complex biological systems.UNDERSTANDING the nature of genetic interactions is crucial to obtaining a more complete picture of complex biological systems and their evolution. The discovery of genetic interactions has been the goal of many researchers studying a number of model systems, including but not limited to Saccharomyces cerevisiae, Caenorhabditis elegans, and Escherichia coli (You and Yin 2002; Burch et al. 2003; Burch and Chao 2004; Tong et al. 2004; Drees et al. 2005; Sanjuán et al. 2005; Segre et al. 2005; Pan et al. 2006; Zhong and Sternberg 2006; Jasnos and Korona 2007; St. Onge et al. 2007; Decourty et al. 2008). Recently, high-throughput experimental approaches, such as epistatic mini-array profiles (E-MAPs) and genetic interaction analysis technology for E. coli (GIANT-coli), have enabled the study of epistasis on a large scale (Schuldiner et al. 2005, 2006; Collins et al. 2006, 2007; Typas et al. 2008). However, it remains unclear whether the computational and statistical methods currently in use to identify these interactions are indeed the most appropriate.The study of genetic interaction, or “epistasis,” has had a long and somewhat convoluted history. Bateson (1909) first used the term epistasis to describe the ability of a gene at one locus to “mask” the mutational influence of a gene at another locus (Cordell 2002). The term “epistacy” was later coined by Fisher (1918) to denote the statistical deviation of multilocus genotype values from an additive linear model for the value of a phenotype (Phillips 1998, 2008).These origins are the basis for the two main current interpretations of epistasis. The first, as introduced by Bateson (1909), is the “biological,” “physiological,” or “compositional” form of epistasis, concerned with the influence of an individual''s genetic background on an allele''s effect on phenotype (Cheverud and Routman 1995; Phillips 1998, 2008; Cordell 2002; Moore and Williams 2005). The second interpretation, attributed to Fisher, is “statistical” epistasis, which in its linear regression framework places the phenomenon of epistasis in the context of a population (Wagner et al. 1998; Wade et al. 2001; Wilke and Adami 2001; Moore and Williams 2005; Phillips 2008). Each of these approaches is equally valid in studying genetic interactions; however, confusion still exists about how to best reconcile the methods and results of the two (Phillips 1998, 2008; Cordell 2002; Moore and Williams 2005; Liberman and Feldman 2006; Aylor and Zeng 2008).Aside from the distinction between the statistical and the physiological definitions of epistasis, inconsistencies exist when studying solely physiological epistasis. For categorical traits, physiological epistasis is clear as a “masking” effect. When noncategorical or numerical traits are measured, epistasis is defined as the deviation of the phenotype of the multiple mutant from that expected under independence of the underlying genes.The “expectation” of the phenotype under independence, that is, in the absence of epistasis, is not defined consistently between studies. For clarity, consider epistasis between pairs of genes and, without loss of generality, consider fitness as the phenotype. The first commonly used definition of independence, originating from additivity, defines the effect of two independent mutations to be equal to the sum of the individual mutational effects. A second, motivated by the use of fitness as a phenotype, defines the effect of the two mutations as the product of the individual effects (Elena and Lenski 1997; Desai et al. 2007; Phillips 2008). A third definition of independence has been referred to as “minimum,” where alleles at two loci are independent if the double mutant has the same fitness as the less-fit single mutant. Mani et al. (2008) claim that this has been used when identifying pairwise epistasis by searching for synthetic lethal double mutants (Tong et al. 2001, 2004; Pan et al. 2004, 2006; Davierwala et al. 2005). A fourth is the “Log” definition presented by Mani et al. (2008) and Sanjuan and Elena (2006). The less-frequently used “scaled ɛ” (Segre et al. 2005) measure of epistasis takes the multiplicative definition of independence with a scaling factor.These different definitions of independence are partly due to distinct measurement “scales.” For some traits, a multiplicative definition of independence may be necessary to identify epistasis between two genes, whereas for other traits, additivity may be appropriate (Falconer and Mackay 1995; Wade et al. 2001; Mani et al. 2008; Phillips 2008). An interaction found under one independence definition may not necessarily be found under another, leading to different biological conclusions (Mani et al. 2008).Mani et al. (2008) suggest that there may be an “ideal” definition of independence for all gene pairs for identifying functional relationships. However, it is plausible that different representations of independence for two genes may reflect different biological properties of the relationship (Kupper and Hogan 1978; Rothman et al. 1980). “Two categories of general interest [the additive and multiplicative definitions, respectively] are those in which etiologic factors act interchangeably in the same step in a multistep process, or alternatively act at different steps in the process” (Rothman et al. 1980, p. 468). In some cases, the discovery of epistasis may merely be an artifact of using an incorrect null model (Kupper and Hogan 1978). It may be necessary to represent “independence” differently, resulting in different statistical measures of interactions, for different pairs of genes depending on their functions.Previous studies have suggested that different pairs of loci may have different modes of interaction and have attempted to subclassify genetic interactions into regulatory hierarchies and mutually exclusive “interaction subtypes” to elucidate underlying biological properties (Avery and Wasserman 1992; Drees et al. 2005; St. Onge et al. 2007). We suggest that epistatic relationships can be divided into several subtypes, or forms, corresponding to the aforementioned definitions of independence. As a particular gene pair may deviate from independence according to several criteria, we do not claim that these subtypes are necessarily mutually exclusive. We attempt to select the most likely epistatic subtype that is the best statistical representation of the relationship between two genes. To further subclassify interactions, epistasis among deleterious mutations can take one of two commonly used forms: positive (equivalently alleviating, antagonistic, or buffering) epistasis, where the phenotype of the double mutant is less severe than expected under independence, and negative (equivalently aggravating, synergistic, or synthetic), where the phenotype is more severe than expected (Segre et al. 2005; Collins et al. 2006; Desai et al. 2007; Mani et al. 2008).Another objective of such distinctions is to reduce the bias of the estimator of the epistatic parameter (ɛ), which measures the extent and direction of epistasis for a given gene pair. Mani et al. (2008), assuming that the overall distribution of ɛ should be centered around 0, find that inaccurately choosing a definition of independence can result in increased bias when estimating ɛ. For example, using the minimum definition results in the most severe bias when single mutants have moderate fitness effects, and the additive definition results in the largest positive bias when at least one gene has an extreme fitness defect (Mani et al. 2008). Therefore, it is important to select an optimal estimator for ɛ for each pair of genes from among the subtypes of epistatic interactions.Epistasis may be important to consider in genomic association studies, as a gene with a weak main effect may be identified only through its interaction with another gene or other genes (Frankel and Schork 1996; Culverhouse et al. 2002; Moore 2003; Cordell 2009; Moore and Williams 2009). Epistasis has also been studied extensively in the context of the evolution of sex and recombination. The mutational deterministic hypothesis proposes that the evolution of sex and recombination would be favored by negative epistatic interactions (Feldman et al. 1980; Kondrashov 1994); many other studies have also studied the importance of the form of epistasis (Elena and Lenski 1997; Otto and Feldman 1997; Burch and Chao 2004; Keightley and Otto 2006; Desai et al. 2007; MacCarthy and Bergman 2007). Indeed, according to Mani et al. (2008, p. 3466), “the choice of definition [of epistasis] alters conclusions relevant to the adaptive value of sex and recombination.”Given fitness data from single and double mutants in haploid organisms, we implement a likelihood method to determine the subtype that is the best statistical representation of the epistatic interaction for pairs of genes. We use maximum-likelihood estimation and the Bayesian information criteria (BIC) (Schwarz 1978) with a likelihood-ratio test to select the most appropriate null or epistatic model for each putative interaction. We conduct extensive simulations to gauge the performance of our method and demonstrate that it performs reasonably well under various interaction scenarios. We apply our method to two data sets with fitness measurements obtained from yeast (Jasnos and Korona 2007; St. Onge et al. 2007), whose authors assume only multiplicative epistasis for all interactions. By examining functional links and experimentally validated interactions among epistatic pairs, we demonstrate that our results are biologically meaningful. Studying a random selection of genes, we find that minimum epistasis is more prevalent than both additive and multiplicative epistasis and that the overall distribution of ɛ is not significantly different from zero (as Jasnos and Korona 2007 suggest). For genes in a particular pathway, we advise selecting among fewer epistatic subtypes. We believe that our method of epistatic subtype classification will aid in understanding genetic interactions and their properties.

St. Onge et al. (2007) data set:

St. Onge et al. (2007) examined 26 nonessential genes known to confer resistance to MMS, constructed double-deletion strains for 323 double-mutant strains (all but two of the total possible pairs), and assumed the multiplicative form of epistasis for all interactions (see Methods: Analysis of experimental data). Following these authors, we focus on single- and double-mutant fitnesses measured in the presence of MMS. (For results in the absence of MMS, see File S1 and File S1_2.)Using the resampling method described in Analysis of experimental data and File S1, 222 gene pairs pass the cutoff of having epistasis inferred in at least 900 of 1000 replicates. This does not include 5 synthetic lethal gene pairs. Hypothesis testing and a multiple-testing procedure (for 222 simultaneous hypotheses) are necessary to determine the final epistatic pairs.To select one among the three multiple-testing procedures, we follow St. Onge et al. (2007) and examine gene pairs that share specific functional links (see Analysis of experimental data). The Bonferroni method is likely too conservative, yielding only 25 significantly epistatic pairs with only one functional link among them; alternatively, the pFDR procedure appears to be too lenient in rejecting independence for all 222 pairs. Therefore, we use the FDR procedure (although the number of functional links is not significant) and detect 193 epistatic pairs, of which 5 (2.6%) are synthetic lethals, 19 (9.8%) have additive epistasis, 33 (17.1%) have multiplicative epistasis, and 136 (70.5%) have minimum epistasis (File S1_1). We find 29 gene pairs with positive (alleviating) epistasis and 159 gene pairs with negative (aggravating) epistasis.

TABLE 2

Summary of gene pairs with the indicated epistatic subtypes, inferred using the FDR procedure with the BIC method that considers all three epistatic subtypes and their corresponding null models

Estimating the Parameters of Selection on Nonsynonymous Mutations in Drosophila pseudoobscura and D. miranda

We present the results of surveys of diversity in sets of >40 X-linked and autosomal loci in samples from natural populations of Drosophila miranda and D. pseudoobscura, together with their sequence divergence from D. affinis. Mean silent site diversity in D. miranda is approximately one-quarter of that in D. pseudoobscura; mean X-linked silent diversity is about three-quarters of that for the autosomes in both species. Estimates of the distribution of selection coefficients against heterozygous, deleterious nonsynonymous mutations from two different methods suggest a wide distribution, with coefficients of variation greater than one, and with the average segregating amino acid mutation being subject to only very weak selection. Only a small fraction of new amino acid mutations behave as effectively neutral, however. A large fraction of amino acid differences between D. pseudoobscura and D. affinis appear to have been fixed by positive natural selection, using three different methods of estimation; estimates between D. miranda and D. affinis are more equivocal. Sources of bias in the estimates, especially those arising from selection on synonymous mutations and from the choice of genes, are discussed and corrections for these applied. Overall, the results show that both purifying selection and positive selection on nonsynonymous mutations are pervasive.SURVEYS of DNA sequence diversity and divergence are shedding light on a number of questions in evolutionary genetics (for recent reviews, see Akey 2009; Sella et al. 2009). Two of the most important questions of this kind concern the distribution of selection coefficients against deleterious mutations affecting protein sequences and the proportion of amino acid sequence differences between related species that have been fixed by positive selection. Several different methods have been proposed for studying each of these questions, using different features of data on polymorphism and divergence at nonsynonymous and silent sites.For example, the parameters of the distribution of selection coefficients against deleterious amino acid mutations have been estimated by contrasting the numbers of nonsynonymous and silent within-species polymorphisms and fixed differences between species (Sawyer and Hartl 1992; Bustamante et al. 2002; Piganeau and Eyre-Walker 2003; Sawyer et al. 2007); by fitting the frequency spectra of nonsynonymous and silent variants to models of selection, mutation, and drift (Akashi 1999; Eyre-Walker et al. 2006; Keightley and Eyre-Walker 2007; Kryukov et al. 2007; Boyko et al. 2008; Eyre-Walker and Keightley 2009); or by comparing levels of nonsynonymous and silent diversities between species with different population sizes (Loewe and Charlesworth 2006; Loewe et al. 2006). The results of these different approaches generally agree in suggesting that there is a wide distribution of selection coefficients against nonsynonymous mutations and that the mean selection coefficient against heterozygous carriers of such mutations is very small. The results imply that a typical individual from a human population carries several hundred weakly deleterious mutations (Eyre-Walker et al. 2006; Kryukov et al. 2007; Boyko et al. 2008); for a typical Drosophila population, with its much higher level of variability, the number is probably an order of magnitude greater (Loewe et al. 2006; Keightley and Eyre-Walker 2007).The presence of this large load of slightly deleterious mutations in human and natural populations, most of which are held at low frequencies by natural selection, has many implications. From the point of view of understanding human genetic disease, it means that we have to face the likelihood that susceptibility to a disease can be influenced by variants at many loci, each with small effects (Kryukov et al. 2007). The pervasive presence of deleterious mutations throughout the genome contributes to inbreeding depression (Charlesworth and Willis 2009) and may mean that the effective population size is reduced by background selection effects, even in regions of the genome with normal levels of genetic recombination (Loewe and Charlesworth 2007). Their presence may contribute so strongly to Hill–Robertson effects (Hill and Robertson 1966; Felsenstein 1974) that they cause severely reduced levels of diversity and adaptation in low-recombination regions of the genome (Charlesworth et al. 2010) and create a selective advantage to maintaining nonzero levels of recombination (Keightley and Otto 2006; Charlesworth et al. 2010). In addition, having an estimate of the distribution of selection coefficients against deleterious nonsynonymous mutations allows their contribution to between-species divergence to be predicted, providing a way of estimating the fraction of fixed nonsynonymous differences caused by positive selection (Loewe et al. 2006; Boyko et al. 2008; Eyre-Walker and Keightley 2009).It is thus important to collect data that shed light on the properties of selection against nonsynonymous mutations in a wide range of systems and also to compare the results from different methods of estimation, since they are subject to different sources of difficulty and biases. In a previous study, we proposed the use of a comparison between two related species with different effective population sizes for this purpose (Loewe and Charlesworth 2006; Loewe et al. 2006), using Drosophila miranda and D. pseudoobscura as material. These are well suited for this type of study, as they are closely related, live together in similar habitats, and yet have very different levels of silent nucleotide diversity, indicating different effective population sizes (N_e). This study was hampered by our inability to compare the same set of loci across the two species and by the small number of loci that could be used. We here present the results of a much larger study of DNA variation at X-linked and autosomal loci for these two species, using D. affinis as a basis for estimating divergence. We compare the results, applying the method of Loewe et al. (2006) with that of Eyre-Walker and Keightley (2009) for estimating the distribution of deleterious selection coefficients and with McDonald–Kreitman test-based methods for estimating the proportion of nonsynonymous differences fixed by positive selection. While broadly confirming the conclusions from earlier studies, we note some possible sources of bias and describe methods for minimizing their effects.     

Alternative Splicing Modulates Ubx Protein Function in Drosophila melanogaster

Polyploidy is an important aspect of the evolution of flowering plants. The potential of gene copies to diverge and evolve new functions is influenced by meiotic behavior of chromosomes leading to segregation as a single locus or duplicated loci. Switchgrass (Panicum virgatum) linkage maps were constructed using a full-sib population of 238 plants and SSR and STS markers to access the degree of preferential pairing and the structure of the tetraploid genome and as a step toward identification of loci underlying biomass feedstock quality and yield. The male and female framework map lengths were 1645 and 1376 cM with 97% of the genome estimated to be within 10 cM of a mapped marker in both maps. Each map coalesced into 18 linkage groups arranged into nine homeologous pairs. Comparative analysis of each homology group to the diploid sorghum genome identified clear syntenic relationships and collinear tracts. The number of markers with PCR amplicons that mapped across subgenomes was significantly fewer than expected, suggesting substantial subgenome divergence, while both the ratio of coupling to repulsion phase linkages and pattern of marker segregation indicated complete or near complete disomic inheritance. The proportion of transmission ratio distorted markers was relatively low, but the male map was more extensively affected by distorted transmission ratios and multilocus interactions, associated with spurious linkages.POLYPLOIDY is common among plants (Masterson 1994; Levin 2002) and is an important aspect of plant evolution. Widespread paleopolyploidy in flowering plant lineages suggests that ancient polyploidization events have contributed to the radiation of angiosperms (Soltis et al. 2009; Van de Peer et al. 2009a). Whole genome duplications are thought to be the sources of evolutionary novelty (Osborn et al. 2003; Freeling and Thomas 2006; Chen 2007; Hegarty and Hiscock 2008; Flagel and Wendel 2009; Leitch and Leitch 2008). Other attributes of polyploids considered to promote evolutionary success include increased vigor, masking of recessive alleles, and reproductive barriers arising from loss of one of the duplicate genes (Soltis and Soltis 2000; Comai 2005; Otto 2007; Van de Peer et al. 2009b). Among crop species, polyploidy likely contributed to trait improvement under artificial selection (Paterson 2005; Udall and Wendell 2006; Dubcovsky and Dvorak 2007; Hovav et al. 2008).Disomic inheritance in polyploids, in contrast to polysomic inheritance, presents opportunities for duplicated genes to diverge and evolve new functions. The relative age of whole genome duplications and the extent of homology between subgenomes greatly influence chromosomal pairing at meiosis (Soltis and Soltis 1995; Wolfe 2001; Ramsey and Schemske 2002). Polysomic inheritance resulting from random chromosome pairing is associated with doubling of a single set of chromosomes. Disomic inheritance resulting from preferential pairing is often associated with polyploidy arising from combinations of divergent genomes. The evolutionary process of diploidization leads to a shift from random to preferential pairing that is not well understood but is genetically defined in systems such as Ph1 of wheat (Triticum aestivum) and PrBn of Brassica napus (Riley and Chapman 1958; Vega and Feldman 1998; Jenczewski et al. 2003). The degree of preferential pairing also affects allelic diversity and the ability to detect linkage. Accurate information about chromosome pairing and whole or partial genome duplications is thus important for both evolutionary studies and in linkage analysis.Such information is extremely limited in the C4 panicoid species Panicum virgatum (switchgrass), which is now viewed as a promising energy crop in the United States and Europe (Lewandowski et al. 2003; McLaughlin and Kszos 2005) and is planted extensively for forage and soil conservation (Vogel and Jung 2001). Little is known about either its genome structure or inheritance. Much current bioenergy feedstock development is focused on tetraploid cytotypes (2n = 4x = 36) due to their higher yield potentials, and an initial segregation study indicated a high degree of preferential pairing in a single F1 mapping population (Missaoui et al. 2005). A once-dominant component of the tallgrass prairie in North America, switchgrass is largely self-incompatible (Martinez-Reyna and Vogel 2002) with predominantly tetraploid or octoploid cytotypes (Hultquist et al. 1997; Lu et al. 1998). Limited gene flow appears possible between different cytotypes suggested by DNA content variation within collection sites and seed lots (Nielsen 1944; Hultquist et al. 1997; Narasimhamoorthy et al. 2008). True diploids appear to be rare (Nielsen 1944; Young et al. 2010). Multivalents in meiosis have not been observed in tetraploids or F1 hybrids between upland and lowland tetraploids, although rare univalents occurred (Barnett and Carver 1967; Martinez-Reyna et al. 2001). However, polysomic inheritance may occur with random bivalent pairing (Howard and Swaminathan 1953).Sustainable production of switchgrass for bioenergy to meet the goal of reducing greenhouse gas emissions will require advances in feedstock production that include improvements in yield (Carroll and Somerville 2009). Switchgrass has extensive genetic diversity and potential for genetic improvements, but each cycle of phenotypic selection can take several years (McLaughlin and Kszos 2005; Parrish and Fike 2005; Bouton 2007). Detailed understanding of genome structure to enable efficient marker-assisted selection (MAS) can speed this process considerably. Complete linkage maps are therefore required to both understand chromosome pairing and allow MAS.We report the construction of the first complete linkage maps of two switchgrass genotypes. The linkage maps provide genetic evidence for disomic inheritance in lowland, tetraploid switchgrass. Gene-derived markers enabled a comparative analysis to sorghum, revealing syntenic relationships between the diploid sorghum genome and the tetraploid switchgrass subgenomes. Transmission ratio distortion and multilocus interactions were analyzed in detail to document their potential influence on map accuracy and map-based studies in switchgrass.