Genome Changes After Gene Duplication: Haploidy vs. Diploidy

Since genome size and the number of duplicate genes observed in genomes increase from haploid to diploid organisms, diploidy might provide more evolutionary probabilities through gene duplication. It is still unclear how diploidy promotes genomic evolution in detail. In this study, we explored the evolution of segmental gene duplication in haploid and diploid populations by analytical and simulation approaches. Results show that (1) under the double null recessive (DNR) selective model, given the same recombination rate, the evolutionary trajectories and consequences are very similar between the same-size gene-pool haploid vs. diploid populations; (2) recombination enlarges the probability of preservation of duplicate genes in either haploid or diploid large populations, and haplo-insufficiency reinforces this effect; and (3) the loss of duplicate genes at the ancestor locus is limited under recombination while under complete linkage the loss of duplicate genes is always random at the ancestor and newly duplicated loci. Therefore, we propose a model to explain the advantage of diploidy: diploidy might facilitate the increase of recombination rate, especially under sexual reproduction; more duplicate genes are preserved under more recombination by originalization (by which duplicate genes are preserved intact at a special quasi-mutation-selection balance under the DNR or haplo-insufficient selective model), so genome sizes and the number of duplicate genes in diploid organisms become larger. Additionally, it is suggested that small genomic rearrangements due to the random loss of duplicate genes might be limited under recombination.USUALLY genome size becomes larger from haploid to diploid organisms (Lynch and Conery 2003), and so does the number of duplicate genes observed in genomes (Zhang 2003). It is extensively hypothesized that diploidy might facilitate the preservation and accumulation of duplicate genes, but it is still unclear how diploidy supports the evolution of duplicate genes in detail. The superiority of diploidy is classically attributed to preventing expression of deleterious mutations (Crow and Kimura 1965), but it is also argued that the sheltering of deleterious mutations cannot adequately explain the advantages of diploidy (Perrot et al. 1991).Recombination is a common phenomenon in all three kingdoms of life, Bacteria, Eukarya, and Archaea. It has been reported that recombination influences the loss of duplicate genes (Zhang and Kishino 2004; Xue et al. 2010). In diploid organisms, if recombination between the ancestor locus and the newly duplicated locus is free, the rate of recombination is maximally 0.5, which is commonly observed especially when the two loci are located on different chromosomes. Although recombination should not be regarded as an exception in haploid organisms (Fraser et al. 2007), recombination events usually occur more frequently in diploid populations than they do in haploid populations. In other words, diploidy might facilitate the occurrence of recombination. The difference of recombination behaviors between haploid and diploid organisms is an obvious and important feature during genomic evolution.In our recent studies of genomic duplication, we proposed a new possible way of preserving and accumulating duplicate genes in genomes—originalization (Xue and Fu 2009a). As is well known, for a locus in an infinite diploid population, the frequencies of wild-type and degenerative alleles will move to an equilibrium under purifying selection and mutation, which is known as the mutation–selection balance. After genomic duplication, under two simple selective models, double null recessive (DNR, under which valid individuals require at least one active wild-type allele on the ancestor and newly duplicated loci) and haplo-insufficient (HI or partial dominant, under which valid individuals require at least two active wild-type alleles on both loci) models, a special equilibrium of allele frequencies at the ancestor and newly duplicated loci will be reached under recombination, in which the frequency of wild-type allele is kept high at both loci. Under the HI selective model this balance becomes so stable and flexible that the fixation of a degenerative allele at one of these two loci (or the balance being broken) becomes very difficult even in a modest population (Xue and Fu 2009a,b). However, if the two loci are tightly linked (recombination rate r = 0), this balance of allele frequencies does not appear. As r increases, the balance becomes more stable and the frequency of the wild-type allele at two loci becomes higher. High frequency of the wild-type allele at both loci means that duplicate genes are preserved intact in genomes, so this phenomenon was named originalization.Although many duplicate genes originated from genomic duplications in some species, such as yeast, maize, and fish (Li et al. 2005), those from segmental duplications are also very popular (Zhang et al. 2000; Leister 2004). In haploid populations, most duplication events are small segmental duplications. Therefore, to understand genomic evolution comprehensively, it is necessary to explore the evolution of segmental genomic duplication.Lynch et al. (2001) and Tanaka et al. (2009) have studied the evolution of segmental gene duplication in diploid populations theoretically. However, in this study, we further compared the evolution of segmental gene duplication in haploid vs. diploid populations by numerical and simulation approaches under the DNR and HI selective models. We observed that haploid and diploid populations with the same-size gene pool are very similar under the DNR model and the same recombination rate. Recombination enlarges the probability of preservation of duplicate genes in either haploid or diploid populations via originalization, and haplo-insufficiency reinforces this effect. The loss of duplicate genes at the ancestor locus might be limited under recombination, while under complete linkage, the loss of duplicate genes is random at the ancestor and newly duplicated loci. According to these results, we propose a model with which to explain the revolutionary genomic transition from haploidy to diploidy.     

Coalescent Simulation of Intracodon Recombination

The coalescent with recombination is a very useful tool in molecular population genetics. Under this framework, genealogies often represent the evolution of the substitution unit, and because of this, the few coalescent algorithms implemented for the simulation of coding sequences force recombination to occur only between codons. However, it is clear that recombination is expected to occur most often within codons. Here we have developed an algorithm that can evolve coding sequences under an ancestral recombination graph that represents the genealogies at each nucleotide site, thereby allowing for intracodon recombination. The algorithm is a modification of Hudson''s coalescent in which, in addition to keeping track of events occurring in the ancestral material that reaches the sample, we need to keep track of events occurring in ancestral material that does not reach the sample but that is produced by intracodon recombination. We are able to show that at typical substitution rates the number of nonsynonymous changes induced by intracodon recombination is small and that intracodon recombination does not generally result in inflated estimates of the overall nonsynonymous/synonymous substitution ratio (ω). On the other hand, recombination can bias the estimation of ω at particular codons, resulting in apparent rate variation among sites and in the spurious identification of positively selected sites. Importantly, in this case, allowing for variable synonymous rates across sites greatly reduces the false-positive rate and recovers statistical power. Finally, coalescent simulations with intracodon recombination could be used to better represent the evolution of nuclear coding genes or fast-evolving pathogens such as HIV-1.We have implemented this algorithm in a computer program called NetRecodon, freely available at http://darwin.uvigo.es.THE coalescent (Kingman 1982; Hudson 1990) provides an efficient sampling of genealogical histories from a theoretical population evolving under a neutral Wright–Fisher model (Ewens 1979; Kingman 1982; Hudson 1990). Coalescent simulations are commonly used in molecular population genetics to understand the behavior and interactions among evolutionary processes under different scenarios (Innan et al. 2005), such as hypothesis testing (DeChaine and Martin 2006), evaluation and comparison of different analytical methods (Carvajal-Rodriguez et al. 2006), or estimation of population genetic parameters (Beaumont et al. 2002). Indeed, to obtain meaningful biological inferences from these simulations, it is very important that the underlying model is as realistic as possible. In this regard, a number of models have been developed during the last decade that consider different evolutionary processes such as recombination (Simonsen and Churchill 1997; Wiuf and Posada 2003), gene conversion (Wiuf and Hein 2000), selection (Hudson and Kaplan 1988, 1995), and gene flow or demographic history (Slatkin 1987; Pybus and Rambaut 2002).Despite these advances, and in the face of a plethora of coalescent simulators (Excoffier et al. 2000; Hudson 2002; Posada and Wiuf 2003; Spencer and Coop 2004; Mailund et al. 2005; Schaffner et al. 2005; Marjoram and Wall 2006; Arenas and Posada 2007; Hellenthal and Stephens 2007; Liang et al. 2007), it was not possible until very recently to simulate recombining protein-coding DNA sequences within this framework (Anisimova et al. 2003; Arenas and Posada 2007). Importantly, to our knowledge, the algorithms described or implemented so far allow recombination only between codons, not within them. The reason for this unrealistic constraint is that standard codon models describe the probabilities of change along a lineage from one codon to another (Yang 2006), whereas recombination can occur between any two nucleotides, potentially resulting in one or more lineages not being shared by all the positions of the codon. In other words, although the unit for substitution in coding sequences is the codon, the unit for recombination in these sequences is still the nucleotide. Here we describe a new algorithm that overcomes this limitation by allowing for the evolution of different positions of the same codon in distinct genealogies. Furthermore, we use this algorithm to evaluate the effect of intracodon recombination on the generation of nonsynonymous (NS) diversity and on the estimation of the ratio of nonsynonymous-to-synonymous substitution rates (ω or d_N/d_S) (Li and Gojobori 1983) and the hypotheses derived from it.     

GC Content and Recombination: Reassessing the Causal Effects for the Saccharomyces cerevisiae Genome

Recombination plays a crucial role in the evolution of genomes. Among many chromosomal features, GC content is one of the most prominent variables that appear to be highly correlated with recombination. However, it is not yet clear (1) whether recombination drives GC content (as proposed, for example, in the biased gene conversion model) or the converse and (2) what are the length scales for mutual influences between GC content and recombination. Here we have reassessed these questions for the model genome Saccharomyces cerevisiae, for which the most refined recombination data are available. First, we confirmed a strong correlation between recombination rate and GC content at local scales (a few kilobases). Second, on the basis of alignments between S. cerevisiae, S. paradoxus, and S. mikatae sequences, we showed that the inferred AT/GC substitution patterns are not correlated with recombination, indicating that GC content is not driven by recombination in yeast. These results thus suggest that, in S. cerevisiae, recombination is determined either by the GC content or by a third parameter, also affecting the GC content. Third, we observed long-range correlations between GC and recombination for chromosome III (for which such correlations were reported experimentally and were the model for many structural studies). However, similar correlations were not detected in the other chromosomes, restraining thus the generality of the phenomenon. These results pave the way for further analyses aimed at the detailed untangling of drives involved in the evolutionary shaping of the yeast genome.THE architecture of genomes is the result of various evolutionary forces, which can exert concerted or opposing effects. Recombination is considered to represent one such fundamental drive. Indeed, correlations with recombination were reported for a large number of structural or functional properties, such as the length of genes, the length of introns for split genes (Comeron and Kreitman 2000; Prachumwat et al. 2004), or even gene order, with the clustering of essential genes in regions of low recombination (Pal and Hurst 2003). GC content represents perhaps the most prominent property for which strong correlations with recombination were reported for the genomes of many organisms including mammals, Drosophila melanogaster, Caenorhabditis elegans, and Saccharomyces cerevisiae (Gerton et al. 2000; Marais et al. 2001; Birdsell 2002; Kong et al. 2002; Meunier and Duret 2004). On the other hand it was recently demonstrated that in Arabidopsis thaliana rate of crossover and GC content are not correlated (Drouaud et al. 2006). However, despite these numerous results, it is not clear as yet (1) whether recombination drives GC content or the converse and (2) what are the length scales for the correlations between GC and recombination.Correlations between recombination and GC content have been detected both at local scales [typically in the kilobase range (see Gerton et al. 2000)] and at much larger ones (Kong et al. 2002). Arguments were advanced in favor of context-dependent recombinational activities, with the idea that such activities could be regulated, at least in part, by global features of chromosome structure, characterized more or less directly by the GC content (for a general overview, see, for example, Eyre-Walker and Hurst 2001). In this direction, in terms of evolutionary models, mutual influences between recombination and GC were even considered at the highest organizational levels, with the proposal that the large-scale organization of mammalian genomes in terms of GC-rich isochores could be accounted for to a large extent by the integral of past recombinational activities (Duret et al. 2006; Duret and Arndt 2008).Regarding the causality relationship between recombination and GC, the biased gene conversion model (see Eyre-Walker 1993 for original formulations) proposes that recombination represents a driving force for GC variations, from local to genomewide scales (in terms of isochore structures). In this model a basic role is attributed to allelic gene conversions during meiotic recombination, as a consequence of the repair of mismatches in heteroduplex DNA. This process is supposed to be biased toward GC, leading to an increase of overall GC contents in regions with high recombination activity (Brown and Jiricny 1989; Eyre-Walker 1993; Galtier et al. 2001; Marais et al. 2001; Birdsell 2002). On the contrary, with analyses mainly based on the Saccharomyces cerevisiae genome, the supporters of the opposite causality model have suggested that it is rather high GC content that promotes recombination (Gerton et al. 2000; Petes 2001; Blat et al. 2002; Petes and Merker 2002).In this general background we here reassess various questions concerning the relationships between recombination and GC for the S. cerevisiae model system. Surprisingly, whereas S. cerevisiae has served as the system of choice for many of the original questions and models concerning recombination, it appears that various questions, debated notably in the context of mammalian genomes, were not further put to test in the S. cerevisiae genome for which the most accurate recombination data of any system have become recently available (Blitzblau et al. 2007; Buhler et al. 2007; Mancera et al. 2008).We first addressed the causality question at local scales, using the same approach as the one that was implemented in the case of mammalian genomes. At such scales, with the new recombination data for S. cerevisiae, we confirmed the strong correlations between GC and recombination. We then analyzed the patterns of substitutions that occurred in the S. cerevisiae strain S288C lineage under two evolutionary perspectives: (1) after the divergence between the S288C lineage and the lineage of another strain of S. cerevisiae, YJM789, and (2) after the divergence between the S. cerevisiae and the S. paradoxus lineages. The rationale behind such substitution analyses (Meunier and Duret 2004; Webster et al. 2005; Khelifi et al. 2006; Duret and Arndt 2008) is to address the possible effect of recombination on GC content, through the determination of the relative rates of AT to GC and GC to AT substitutions. On the basis of such analyses, we found that recombination is not directly correlated to the patterns of AT/GC substitutions in S. cerevisiae, which indicates that recombination has no detectable influence on GC content in this case.Beyond the local scales, we then considered the ranges of mutual influences between recombination and GC content in S. cerevisiae. We first extended the substitution analyses at significantly larger scales, to test the possibility that the local result could hide long-range correlations. Indeed, results demonstrating the effect of recombination on GC content in the human genome could be observed only at the megabase scale (Duret and Arndt 2008). In S. cerevisiae, however, we found no evidence for a significant effect of recombination on GC content at any scale. Concerning the large-scale influences, we tested then a model developed by Petes and Merker (2002), following which, in S. cerevisiae, recombinational activity at one given locus could be determined by the GC content of the surrounding region, over large distances. This model was elaborated on the basis of the analysis of chromosome III, but our results did not allow us to validate the generality of the hypothesis for all S. cerevisiae chromosomes.     

A Principled Approach to Deriving Approximate Conditional Sampling Distributions in Population Genetics Models with Recombination

The multilocus conditional sampling distribution (CSD) describes the probability that an additionally sampled DNA sequence is of a certain type, given that a collection of sequences has already been observed. The CSD has a wide range of applications in both computational biology and population genomics analysis, including phasing genotype data into haplotype data, imputing missing data, estimating recombination rates, inferring local ancestry in admixed populations, and importance sampling of coalescent genealogies. Unfortunately, the true CSD under the coalescent with recombination is not known, so approximations, formulated as hidden Markov models, have been proposed in the past. These approximations have led to a number of useful statistical tools, but it is important to recognize that they were not derived from, though were certainly motivated by, principles underlying the coalescent process. The goal of this article is to develop a principled approach to derive improved CSDs directly from the underlying population genetics model. Our approach is based on the diffusion process approximation and the resulting mathematical expressions admit intuitive genealogical interpretations, which we utilize to introduce further approximations and make our method scalable in the number of loci. The general algorithm presented here applies to an arbitrary number of loci and an arbitrary finite-alleles recurrent mutation model. Empirical results are provided to demonstrate that our new CSDs are in general substantially more accurate than previously proposed approximations.THE probability of observing a sample of DNA sequences under a given population genetics model—which is referred to as the sampling probability or likelihood—plays an important role in a wide range of problems in a genetic variation study. When recombination is involved, however, obtaining an analytic formula for the sampling probability has hitherto remained a challenging open problem (see Jenkins and Song 2009, 2010 for recent progress on this problem). As such, much research (Griffiths and Marjoram 1996; Kuhner et al. 2000; Nielsen 2000; Stephens and Donnelly 2000; Fearnhead and Donnelly 2001; De Iorio and Griffiths 2004a,b; Fearnhead and Smith 2005; Griffiths et al. 2008; Wang and Rannala 2008) has focused on developing Monte Carlo methods on the basis of the coalescent with recombination (Griffiths 1981; Kingman 1982a,b; Hudson 1983), a well-established mathematical framework that models the genealogical history of sample chromosomes. These Monte Carlo-based full-likelihood methods mark an important development in population genetics analysis, but a well-known obstacle to their utility is that they tend to be computationally intensive. For a whole-genome variation study, approximations are often unavoidable, and it is therefore important to think of ways to minimize the trade-off between scalability and accuracy.A popular likelihood-based approximation method that has had a significant impact on population genetics analysis is the following approach introduced by Li and Stephens (2003): Given a set Φ of model parameters (e.g., mutation rate, recombination rate, etc.), the joint probability p(h₁, … , h_n | Φ) of observing a set {h₁, … , h_n} of haplotypes sampled from a population can be decomposed as a product of conditional sampling distributions (CSDs), denoted by π,(1)where π(h_k+1|h₁, …, h_k, Φ) is the probability of an additionally sampled haplotype being of type h_k+1, given a set of already observed haplotypes h₁, …, h_k. In the presence of recombination, the true CSD π is unknown, so Li and Stephens proposed using an approximate CSD in place of π, thus obtaining the following approximation of the joint probability:(2)Li and Stephens referred to this approximation as the product of approximate conditionals (PAC) model. In general, the closer is to the true CSD π, the more accurate the PAC model becomes. Notable applications and extensions of this framework include estimating crossover rates (Li and Stephens 2003; Crawford et al. 2004) and gene conversion parameters (Gay et al. 2007; Yin et al. 2009), phasing genotype data into haplotype data (Stephens and Scheet 2005; Scheet and Stephens 2006), imputing missing data to improve power in association mapping (Stephens and Scheet 2005; Li and Abecasis 2006; Marchini et al. 2007; Howie et al. 2009), inferring local ancestry in admixed populations (Price et al. 2009), inferring human colonization history (Hellenthal et al. 2008), inferring demography (Davison et al. 2009), and so on.Another problem in which the CSD plays a fundamental role is importance sampling of genealogies under the coalescent process (Stephens and Donnelly 2000; Fearnhead and Donnelly 2001; De Iorio and Griffiths 2004a,b; Fearnhead and Smith 2005; Griffiths et al. 2008). In this context, the optimal proposal distribution can be written in terms of the CSD π (Stephens and Donnelly 2000), and as in the PAC model, an approximate CSD may be used in place of π. The performance of an importance sampling scheme depends critically on the proposal distribution and therefore on the accuracy of the approximation . Often in conjunction with composite-likelihood frameworks (Hudson 2001; Fearnhead and Donnelly 2002), importance sampling has been used in estimating fine-scale recombination rates (McVean et al. 2004; Fearnhead and Smith 2005; Johnson and Slatkin 2009).So far, a significant scope of intuition has gone into choosing the approximate CSDs used in these problems (Marjoram and Tavaré 2006). In the case of completely linked loci, Stephens and Donnelly (2000) suggested constructing an approximation by assuming that the additional haplotype h_k+1 is an imperfect copy of one of the first k haplotypes, with copying errors corresponding to mutation. Fearnhead and Donnelly (2001) generalized this construction to include crossover recombination, assuming that the haplotype h_k+1 is an imperfect mosaic of the first k haplotypes (i.e., h_k+1 is obtained by copying segments from h₁, …, h_k, where crossover recombination can change the haplotype from which copying is performed). The associated CSD, which we denote by , can be interpreted as a hidden Markov model and so admits an efficient dynamic programming solution. Finally, Li and Stephens (2003) proposed a modification to Fearnhead and Donnelly''s model that limits the hidden state space, thereby providing a computational simplification; we denote the corresponding approximate CSD by .Although these approaches are computationally appealing, it is important to note that they are not derived from, though are certainly motivated by, principles underlying typical population genetics models, in particular the coalescent process (Griffiths 1981; Kingman 1982a,b; Hudson 1983). The main objective of this article is to develop a principled technique to derive an improved CSD directly from the underlying population genetics model. Rather than relying on intuition, we base our work on mathematical foundation. The theoretical framework we employ is the diffusion process. De Iorio and Griffiths (2004a,b) first introduced the diffusion-generator approximation technique to obtain an approximate CSD in the case of a single locus (i.e., no recombination). Griffiths et al. (2008) later extended the approach to two loci to include crossover recombination, assuming a parent-independent mutation model at each locus. In this article, we extend the framework to develop a general algorithm that applies to an arbitrary number of loci and an arbitrary finite-alleles recurrent mutation model.Our work can be summarized as follows. Using the diffusion-generator approximation technique, we derive a recursion relation satisfied by an approximate CSD. This recursion can be used to construct a closed system of coupled linear equations, in which the conditional sampling probability of interest appears as one of the unknown variables. The system of equations can be solved using standard numerical analysis techniques. However, the size of the system grows superexponentially with the number of loci and, consequently, so does the running time. To remedy this drawback, we introduce additional approximations to make our approach scalable in the number of loci. Specifically, the recursion admits an intuitive genealogical interpretation, and, on the basis of this interpretation, we propose modifications to the recursion, which then can be easily solved using dynamic programming. The computational complexity of the modified algorithm is polynomial in the number of loci, and, importantly, the resulting CSD has little loss of accuracy compared to that following from the full recursion.The accuracy of approximate CSDs has not been discussed much in the literature, except in the application-specific context for which they are being employed. In this article, we carry out an empirical study to explicitly test the accuracy of various CSDs and demonstrate that our new CSDs are in general substantially more accurate than previously proposed approximations. We also consider the PAC framework and show that our approximations also produce more accurate PAC-likelihood estimates. We note that for the maximum-likelihood estimation of recombination rates, the actual value of the likelihood may not be so important, as long as it is maximized near the true recombination rate. However, in many other applications—e.g., phasing genotype data into haplotype data, imputing missing data, importance sampling, and so on—the accuracy of the CSD and PAC-likelihood function over a wide range of parameter values may be important. Thus, we believe that the theoretical work presented here will have several practical implications; our method can be applied in a wide range of statistical tools that use CSDs, improving their accuracy.The remainder of this article is organized as follows. To provide intuition for the ensuing mathematics, we first describe a genealogical process that gives rise to our CSD. Using our genealogical interpretation, we consider two additional approximations and relate these to previously proposed CSDs. Then, in the following section, we derive our CSD using the diffusion-generator approach and provide mathematical statements for the additional approximations; some interesting limiting behavior is also described there. This section is self-contained and may be skipped by the reader uninterested in mathematical details. Finally, in the subsequent section, we carry out a simulation study to compare the accuracy of various approximate CSDs and demonstrate that ours are generally the most accurate.     

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

Reproductive Value and Fluctuating Selection in an Age-Structured Population

Fluctuations in age structure caused by environmental stochasticity create autocorrelation and transient fluctuations in both population size and allele frequency, which complicate demographic and evolutionary analyses. Following a suggestion of Fisher, we show that weighting individuals of different age by their reproductive value serves as a filter, removing temporal autocorrelation in population demography and evolution due to stochastic age structure. Assuming weak selection, random mating, and a stationary distribution of environments with no autocorrelation, we derive a diffusion approximation for evolution of the reproductive value weighted allele frequency. The expected evolution obeys an adaptive topography defined by the long-run growth rate of the population. The expected fitness of a genotype is its Malthusian fitness in the average environment minus the covariance of its growth rate with that of the population. Simulations of the age-structured model verify the accuracy of the diffusion approximation. We develop statistical methods for measuring the expected selection on the reproductive value weighted allele frequency in a fluctuating age-structured population.THE evolutionary dynamics of age-structured populations were formalized by Charlesworth (1980, 1994) and Lande (1982) on the basis of earlier ideas of Fisher (1930, 1958), Medawar (1946, 1952), and Hamilton (1966), showing that the strength of selection on genes affecting the vital rates of survival or fecundity depends on their age of action (reviewed by de Jong 1994; Charlesworth 2000). Fisher defined the reproductive value of individuals of a given age as their expected contribution to future population growth, determined by the age-specific vital rates. This has the property that in a constant environment the total reproductive value in a population always increases at a constant rate. The total population size, however, undergoes transient fluctuations as the stable age distribution is approached, and the total population size only asymptotically approaches a constant growth rate (Caswell 2001).Environmental stochasticity creates continual fluctuations in age structure, producing temporal autocorrelation in population size and in allele frequencies, which seriously complicate demographic and evolutionary analyses. Fisher (1930, 1958, p. 35) suggested for analysis of genetic evolution that individuals should be weighted by their reproductive value to compensate for deviations from the stable age distribution. Here we apply this suggestion to study weak fluctuating selection in an age-structured population in a stochastic environment.One of the central conceptual paradigms of evolutionary biology was described by Wright (1932). His adaptive topography represents a population as a point on a surface of population mean fitness as a function of allele frequencies. Assuming weak selection, random mating, and loose linkage (implying approximate Hardy–Weinberg equilibrium within loci and linkage eqilibrium among loci), natural selection in a constant environment causes the population to evolve uphill of the mean fitness surface (Wright 1937, 1945, 1969; Arnold et al. 2001; Gavrilets 2004). Evolution by natural selection thus tends to increase the mean fitness of a population in a constant environment.Lande (2007, 2008) generalized Wright''s adaptive topography to a stochastic environment, allowing density-dependent population growth but assuming density-independent selection, showing that the expected evolution maximizes the long-run growth rate of the population at low density, . Here r is population growth rate at low density in the average environment and is the environmental variance in population growth rate among years, which are standard parameters in stochastic demography (Cohen 1977, 1979; Tuljapurkar 1982; Caswell 2001; Lande et al. 2003). In this model of stochastic evolution the adaptive topography describing the expected evolution is derived by expressing r and as functions of allele frequencies with parameters being the mean Malthusian fitnesses of the genotypes and their temporal variances and covariances. These results are based on diffusion approximations for the coupled stochastic processes of population size and allele frequencies in a fluctuating environment.Diffusion approximations are remarkably accurate for many problems in evolution and ecology (Crow and Kimura 1970; Lande et al. 2003). Because a diffusion process is subject to white noise with no temporal autocorrelation, the approximation is most accurate if the noise in the underlying biological process is approximately uncorrelated among years. Despite temporal autocorrelation in total population size produced by age-structure fluctuations, the stochastic demography of age-structured populations over timescales of a generation or more can nevertheless be accurately approximated by a diffusion process (Tuljapurkar 1982; Lande and Orzack 1988; Engen et al. 2005a, 2007). The success of the diffusion approximation for total population size occurs because the noise in the total reproductive value is nearly white, with no temporal autocorrelation to first order, and the log of total population size fluctuates around the log of reproductive value with a return time to equilibrium on the order of a few generations (Engen et al. 2007). Hence the diffusion approximation is well suited to describe the stochastic dynamics of total reproductive value as well as total population size.This article extends Lande''s (2008) model of fluctuating selection without age structure by deriving a diffusion approximation for the evolution of an age-structured population in a stochastic environment. Assuming weak selection at all ages, random mating, and a stationary distribution of environments with no temporal autocorrelation, we show that the main results of the model remain valid, provided that the model parameters are expressed in terms of means, variances, and covariances of age-specific vital rates and that allele frequencies are defined by weighting individuals of different age by their reproductive value, as suggested by Fisher (1930, 1958). We perform simulations to verify the accuracy of the diffusion approximation and outline statistical methods for estimating the expected selection acting on the reproductive value weighted allele frequency.     

Rate of Adaptation in Large Sexual Populations

Adaptation often involves the acquisition of a large number of genomic changes that arise as mutations in single individuals. In asexual populations, combinations of mutations can fix only when they arise in the same lineage, but for populations in which genetic information is exchanged, beneficial mutations can arise in different individuals and be combined later. In large populations, when the product of the population size N and the total beneficial mutation rate U_b is large, many new beneficial alleles can be segregating in the population simultaneously. We calculate the rate of adaptation, v, in several models of such sexual populations and show that v is linear in NU_b only in sufficiently small populations. In large populations, v increases much more slowly as log NU_b. The prefactor of this logarithm, however, increases as the square of the recombination rate. This acceleration of adaptation by recombination implies a strong evolutionary advantage of sex.IN asexual populations, beneficial mutations arising on different genotypes compete against each other and in large populations most of the beneficial mutations are lost because they arise on mediocre genetic backgrounds or acquire further beneficial mutations less rapidly than their peers—the combined effects of clonal interference and multiple mutations (Gerrish and Lenski 1998; Desai and Fisher 2007). Exchange of genetic material between individuals allows the combination of beneficial variants that arose in different lineages and can thereby speed up the process of adaptation (Fisher 1930; Muller 1932). Indeed, most life forms engage in some form of recombination, e.g., lateral gene transfer or competence for picking up DNA in bacteria, facultative sexual reproduction in yeast and plants, or obligate sexual reproduction in most animals. Some benefits of recombination for the rate of adaptation have recently been demonstrated experimentally in Caenorhabditis reinhardtii (Colegrave 2002), Escherichia coli (Cooper 2007), and Saccharomyces cerevisiae (Goddard et al. 2005); for a review of older experiments, see Rice (2002).Yet the benefits of sex become less obvious when one considers its disadvantageous effects: recombination can separate well-adapted combinations of alleles and sexual reproduction is more costly than asexual reproduction due to resources spent for mating and, in some cases, the necessity of males. The latter—in animals often termed the twofold cost of sex—implies that sexual populations can be unstable to the invasion of asexual variants. As a result, the pros and cons of sex have been the subject of many decades of debate in the theoretical literature (Crow and Kimura 1965; Maynard Smith 1968; Felsenstein 1974; Barton 1995a; Barton and Charlesworth 1998), and several different potentially beneficial aspects of sex have been identified, including the pruning of detrimental mutations (Peck 1994; Rice 1998) and host–parasite coevolution or otherwise changing environments (Charlesworth 1993; Ladle et al. 1993; Bürger 1999; Waxman and Peck 1999; Gandon and Otto 2007; Callahan et al. 2009). In the opposite situation of relatively static populations, it has been proposed that recombination is favored in the presence of negative epistasis (Feldman et al. 1980; Kondrashov 1984, 1988)—a situation when the combined detrimental effect of two unfavorable alleles is greater than the sum of the individual effects. While this may sometimes be a significant effect, most populations, especially microbes, are likely to be under continuing selection and the benefits of sex for speeding up adaptation are likely to dominate.The Fisher–Muller hypothesis is that sex speeds up adaptation by combining beneficial variants. Moreover, it has been demonstrated by Hill and Robertson (1966) that linkage decreases the efficacy of selection. This detrimental effect of linkage, known as the “Hill–Robertson effect,” causes selection for higher recombination rates, which has been shown by analyzing recombination modifier alleles at a locus linked to two competing segregating loci (Otto and Barton 1997; Iles et al. 2003; Barton and Otto 2005; Roze and Barton 2006; Martin et al. 2006). Hitchhiking of the allele that increases the recombination rates with the sweeping linked loci results in effective selection for increased recombination.Experiments and simulation studies suggest that the Hill–Roberston effect is more pronounced and selection for recombination modifiers is stronger in large populations with many sweeping loci (Felsenstein 1974; Colegrave 2002; Iles et al. 2003). However, the quantitative understanding of the effect of recombination in large populations is limited. Rouzine and Coffin have studied the role of recombination in the context of evolution of drug resistance in human immunodeficiency virus, finding that recombination of standing variation speeds up adaptation by producing anomalously fit individuals at the high fitness edge of the distribution (Rouzine and Coffin 2005; Gheorghiu-Svirschevski et al. 2007). The effects of epistatic interactions between polymorphisms and recombination on the dynamics of selection have recently been analyzed by Neher and Shraiman (2009). Yet none of these works consider the effects of new beneficial mutations. In the absence of new mutations (and in the absence of heterozygous advantage that can maintain polymorphisms) the fitness soon saturates as most alleles become extinct and standing variation disappears. Thus the crucial point that must be addressed is the balance between selection and recombination of existing variation and the injection of additional variation by new mutations.Here, we study the dynamics of continual evolution via new mutations, selection, and recombination using several models of recombination. Our primary models most naturally apply when periods of asexual reproduction occur between matings, so that they approximate the life style of facultatively outcrossing species such as S. cerevisiae, some plants, and C. elegans, which reproduce asexually most of the time but undergo extensive recombination when outcrossing. The models enable us to study analytically the explicit dependence of the rate of adaptation and of the dynamics of the beneficial alleles on the important parameters such as the outcrossing rate and population size. In an independent study N. H. Barton and J. Coe (personal communication) calculate the rate of adaptation for obligate sexual organisms using several different multilocus models of recombination, including the free recombination model studied here. The relation of our work to theirs, as well as to that of Cohen et al. (2005, 2006) who have also studied the effects of recombination with multiple new mutations, is commented on in the discussion.When deleterious mutations can be neglected, the rate of adaptation is the product of the rate of production of favorable mutations NU_b (N being the population size and U_b the genomewide beneficial mutation rate), the magnitude of their effect, and their fixation probability. The fixation probability is dominated by the probability that the allele becomes established, i.e., that it rises to high enough numbers in the population that it is very unlikely to die out by further stochastic fluctuations. In a homogeneous population a single beneficial mutation with selective advantage s has a probability of establishment and eventual fixation of (in discrete generation models, P_e≈2s) (Moran 1959). In a heterogeneous population, however, a novel beneficial mutation can arise on different genetic backgrounds and its establishment probability will thus vary, being greater if it arises in a well-adapted individual. But even well-adapted genotypes soon fall behind due to sweeps of other beneficial mutations and combinations. To avoid extinction, descendants of the novel mutation thus have to move to fitter genetic backgrounds via recombination in outcrossing events (Rice 2002). As a result the establishment probability decreases as the rate of average fitness gain, v, in the population increases. But the rate of average fitness gain or, equivalently, the rate of adaptation itself depends on the establishment probability. These two quantities therefore have to be determined self-consistently.In this article we analyze several models via self-consistent calculations of the fixation probability of new mutations. For a given production rate of beneficial mutations NU_b, we find that interference between mutations is of minor importance if the recombination rate r exceeds . In this regime, the rate of adaption is v ≈ NU_bs² as found for sequential mutations or in the absence of linkage. At recombination rates below , however, v grows only logarithmically with log NU_b. We find this behavior in all our models and argue that it obtains more generally. The prefactor of the log NU_b increases with the square of the recombination rate, implying a strong benefit of recombination in large populations.     

Modeling Multiallelic Selection Using a Moran Model

We present a Moran-model approach to modeling general multiallelic selection in a finite population and show how it may be used to develop theoretical models of biological systems of balancing selection such as plant gametophytic self-incompatibility loci. We propose new expressions for the stationary distribution of allele frequencies under selection and use them to show that the continuous-time Markov chain describing allele frequency change with exchangeable selection and Moran-model reproduction is reversible. We then use the reversibility property to derive the expected allele frequency spectrum in a finite population for several general models of multiallelic selection. Using simulations, we show that our approach is valid over a broader range of parameters than previous analyses of balancing selection based on diffusion approximations to the Wright–Fisher model of reproduction. Our results can be applied to any model of multiallelic selection in which fitness is solely a function of allele frequency.NATURAL selection has long been a topic of interest in population genetics, yet the stochastic theory of genes under selection remains underdeveloped compared to the theory of neutral genes. Due to the interplay of stochastic and deterministic forces, models of selection present analytical challenges beyond those of neutral models, although a great deal of progress has been made with models that use diffusion approximations to a Wright–Fisher model of reproduction. Diffusion approximations with selection are, however, sometimes difficult to employ and always require assumptions about population parameters for tractability. These limitations suggest that there may be value in developing new methods of solving the problem of selection in a finite population, and here we do so using a Moran model of reproduction in place of the familiar Wright–Fisher model. Our approach has two major advantages over previous models: general applicability to a wide variety of selection models and accuracy over a broad range of parameter values. In this work, we propose new expressions for the full stationary distributions of allele frequencies under multiallelic selection, as well as expressions for average allele frequency distributions.We restrict our attention to exchangeable models of selection, meaning that relabeling the alleles will not change selective outcomes and thus that selection will be a function of allele frequency rather than allele identity. Many models of selection can be transformed into frequency-dependent forms (Denniston and Crow 1990), and some common models of selection have the desired property of exchangeability. For example, symmetric overdominant selection, in which heterozygotes have a selective advantage over homozygotes but the specific genotype of homozygote or heterozygote has no further selective effect, can be expressed as frequency-dependent selection on individual (exchangeable) alleles, although the direct selection is actually on diploid genotypes. Many other proposed models of multiallelic balancing selection, in which substantial variation is maintained by selection, can be viewed in this way. Such models have been of particular interest because of the potential application to highly multiallelic systems found in nature, such as self-incompatibility (SI) loci in plants and the major histocompatibility complex (MHC) loci in vertebrates, and the desire to analyze these systems is a motivation for the present work. We now review some of the population genetic theory related to these systems.Early in the history of population genetics, Wright (1939) presented a somewhat controversial stochastic model of gametophytic self-incompatibility (GSI) genes, sparking much further theoretical and empirical work. An analytic theory of multiallelic symmetric overdominance was developed along similar lines to this early model (Kimura and Crow 1964; Takahata 1990) and has been used as an approximation to the unknown mode of selection in the MHC (Takahata et al. 1992). Drawing insights from these first two applications, other biological systems where balancing selection was posited, including sex determination in honeybees (Yokoyama and Nei 1979), fungal mating systems (May et al. 1999), and heterokaryon incompatibility in fungi (Muirhead et al. 2002), have also been modeled successfully using closely related approaches. Progress has been made in using these models to address genealogical (Takahata 1990; Vekemans and Slatkin 1994) and demographic (Muirhead 2001) questions, as well as extending the models into more complex modes of selection (Uyenoyama 2003) and reproduction (Vallejo-Marin and Uyenoyama 2008).Models of genetic variation under balancing selection have traditionally been focused on specific systems, such that extensions require entirely new analyses, and have also included a number of simplifying assumptions in the interest of mathematical tractability. For example, the symmetric overdominance model has been strongly criticized as an unrealistic approximation of MHC evolution (Paterson et al. 1998; Hedrick 2002; Penn et al. 2002; Ilmonen et al. 2007; Stoffels and Spencer 2008), and yet it has proved difficult to make finite-population models of any of the more realistic frequency dependence schemes using the same approaches. A constraint on further progress is the fact that the standard model of stochastic population genetics, the Wright–Fisher model, is in fact quite difficult to analyze.The Wright–Fisher model of reproduction employs nonoverlapping generations, so that for a diploid population of size N, all 2N allele copies are chosen simultaneously when forming a new generation of individuals. While it is straightforward to describe this reproduction scheme mathematically as a discrete-time Markov chain, that chain unfortunately appears intractable even in simple cases (Ewens 2004). Traditionally, then, diffusion approximations have been used to obtain quantities of interest, such as the equilibrium expected number of alleles, allele frequency spectra, and fixation probabilities and times. Diffusion approximations are derived in the limit , but are applicable to problems of finite N, provided that the strengths of other forces such as mutation and selection can be assumed to be weak, of O(N⁻¹) (Ewens 2004). Watterson (1977) derived such a diffusion approximation for multiallelic symmetric overdominance using these assumptions. More recently, as interest in population genetics has turned to problems of inference, Grote and Speed (2002) considered sampling probabilities under the diffusion approximation for symmetric overdominance, while Donnelly et al. (2001) and Stephens and Donnelly (2003) proposed computational methods for some asymmetric models.Although strong selection can be modeled using diffusion approximations by making the product of the population size and the selection coefficient (Ns) large, the assumption of weak selection is not in fact appropriate for the canonical biological systems of balancing selection. Specifically, selection coefficients are defined by the differences in fitness (the expected number of offspring) among individuals in the population at a given time. These differences may be large in systems such as GSI, where the fitness of a very common allele may be very small while the fitness of other alleles may be greater than one.In an attempt to deal with the extremely strong selection of gametophytic self-incompatibility, Wright''s (1939) original model focused attention on the dynamics of a single representative allele. He collapsed the influence of all other alleles into a single summary statistic: the homozygosity, F, which is a function of the frequencies of all alleles, and which Wright (1939) assumed to be constant. The analysis is essentially that of a two-allele system, using a one-dimensional diffusion analysis. This approach, while shown by simulation to be very effective in the appropriate parameter range (Ewens and Ewens 1966), received substantial criticism on mathematical grounds (Fisher 1958; Moran 1962; Ewens 1964b). Ewens (1964b), in particular, objected to the use of diffusion theory for GSI, pointing out that strong frequency-dependent selection violates the diffusion requirement that both the mean and the variance of the change in allele frequencies be small and of O(N⁻¹). Ewens (1964a) then applied Wright''s basic one-dimensional diffusion approach to modeling symmetric overdominance, but assumed that selection was weak and of O(N⁻¹) to stay within the strict limits of the diffusion approximation.Kimura and Crow (1964) and Wright (1966), on the other hand, presented alternative one-dimensional diffusion approximations to symmetric overdominance, closer in spirit to Wright''s original model of GSI, that did not make the weak-selection assumption. Watterson (1977) was concerned about both the inconsistencies of the approximations used in these models and the treatment of F as a constant rather than as a random variable dependent upon allele frequencies. Using his own multiallelic diffusion approximation for symmetric overdominance (Watterson 1977), he derived an alternative (small-Ns) approximation to the frequency of a single representative allele. We consider this approximation, as well as the best-known one-dimensional symmetric overdominance diffusion, the strong-selection approximation of Kimura and Crow (1964), in comparison with our alternative approach to deriving allele frequency spectra under general multiallelic selection with exchangeable alleles.To avoid the approximations required to employ Wright–Fisher/diffusion-based methods, we turn to an alternative model of reproduction in a finite population: the overlapping-generations model of Moran (1962). In the Moran model, a single allele copy dies and another reproduces in each time step, rather than all 2N allele copies simultaneously being replaced by offspring each generation. As in the Wright–Fisher model, this reproduction scheme is represented mathematically by a Markov chain. Unlike the Wright–Fisher model, however, the Moran model can sometimes yield tractable, exact solutions to the underlying Markov chain, without the need to resort to diffusion approximations. We exploit this trait to develop a new stochastic theory of multiallelic selection with minimal dependence on assumptions about population parameter values. Our method has the additional benefit of being flexible: it can accommodate any exchangeable model of multiallelic selection and either of two general models of parent-independent mutation, the infinite-alleles and k-allele models of mutation. Our Moran-model predictions agree well with the results of Wright–Fisher simulations.     

Drosophila Transposon Insertions as Unknowns for Structured Inquiry Recombination Mapping Exercises in an Undergraduate Genetics Course

Structured inquiry approaches, in which students receive a Drosophila strain of unknown genotype to analyze and map the constituent mutations, are a common feature of many genetics teaching laboratories. The required crosses frustrate many students because they are aware that they are participating in a fundamentally trivial exercise, as the map locations of the genes are already established and have been recalculated thousands of times by generations of students. We modified the traditional structured inquiry approach to include a novel research experience for the students in our undergraduate genetics laboratories. Students conducted crosses with Drosophila strains carrying P[lacW] transposon insertions in genes without documented recombination map positions, representing a large number of unique, but equivalent genetic unknowns. Using the eye color phenotypes associated with the inserts as visible markers, it is straightforward to calculate recombination map positions for the interrupted loci. Collectively, our students mapped 95 genetic loci on chromosomes 2 and 3. In most cases, the calculated 95% confidence interval for meiotic map location overlapped with the predicted map position based on cytology. The research experience evoked positive student responses and helped students better understand the nature of scientific research for little additional cost or instructor effort.INQUIRY-BASED learning in which students are engaged in open-ended, student-centered, hands-on activities is an important tool for training undergraduates to think like scientists (Colburn 2000; Handelsman et al. 2004). With this approach, students learn scientific subjects by interpreting and discussing experimental results in a fashion similar to that used by scientific researchers (NRC 2003). There are three main approaches to instruction via inquiry. In open inquiry, students formulate their own problem, as well as the procedures to investigate the problem. In guided inquiry, the instructor provides the problem and necessary materials, but the students devise an experimental procedure to investigate the problem. Finally, in structured inquiry, the instructor provides the problem, the materials, and the procedure, but the students are required to gather and interpret the experimental data independently, coming to their own conclusions (Welch et al. 2006). In each case, the instructor does not provide “the answer” to the problem. In the ideal case, the instructor does not even know what the answer will be prior to the student experiment, forcing the students to grapple with the information themselves. Inquiry-based laboratories can even be extended so that students are participating in novel research as part of their coursework (DebBurman 2002; Buckner et al. 2007), which been shown to improve undergraduate retention and student performance in biology lecture courses (Marcus et al. 2009).The process of inquiry has been identified as central to training students to understand fundamental approaches used in the field of genetics such as the design of controlled crosses and interpretation of experimental data (Cartier and Stewart 2000). Pukkila (2004) discusses effective methods by which inquiry-based learning can be incorporated into undergraduate genetics lecture courses with large enrollments and into recitation sections. However, the implementation of inquiry-based approaches in undergraduate genetics laboratories has not been discussed extensively.Teaching laboratories offer some advantages for inquiry learning because they generally contain small groups of students, facilitating a flexible and intimate learning environment with many interactions between students and the instructor, as well as among classmates. However, teaching laboratories associated with large lecture courses also offer some challenges, in particular how to deliver substantially similar experiences to laboratory sections taught by multiple instructors, as well as how to provide inquiry-based learning in a logistically manageable and cost-effective manner. For these reasons, most inquiry-based genetics laboratory exercises have used the structured inquiry approach, for example, using many Drosophila melanogaster strains with similar mutant phenotypes (e.g., white eyes and black bodies), but a variety of genotypes, in a series of standardized genetic mapping crosses to familiarize students with the collection and interpretation of classical genetic data (MacIntyre 1974; Pye 1980). The difficulty with contrived genetic unknowns carrying well-mapped genetic mutations is that many students become frustrated that their hard work evaluating the crosses over a period of several months is devoted to a fundamentally trivial exercise, as the recombination map locations of the genes are already established in the scientific literature and have been recalculated thousands of times by generations of genetics students.We have expanded upon the structured inquiry approach to genetics to include novel research experiences for the students in our undergraduate genetics laboratories. They conduct mapping crosses with Drosophila strains carrying P-element transposon insertions in genes without documented recombination map positions. The stock centers maintain very large collections of P-element transposon stocks with known insertion sites on the cytological and genome maps (Spradling et al. 1999). However, in spite of the cytology to recombination map equivalence table available in FlyBase (2009), very few of the transposon inserts have been formally placed on the recombination map. By using the eye color phenotypes associated with many transposon inserts as visible markers in genetic crosses (Marcus 2003), it is straightforward to calculate recombination map positions for the interrupted loci. The stock collections contain many stocks with identical transposons inserted at different chromosomal locations, providing a large number of unique, but equivalent genetic unknowns that can be used for recombination mapping exercises. At the same time, this approach provides students with the opportunity to map genes that have never been mapped before, allowing them to make small but useful contributions to the field of Drosophila genetics.     

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.     

The Dot1 Histone Methyltransferase and the Rad9 Checkpoint Adaptor Contribute to Cohesin-Dependent Double-Strand Break Repair by Sister Chromatid Recombination in Saccharomyces cerevisiae

Genomic integrity is threatened by multiple sources of DNA damage. DNA double-strand breaks (DSBs) are among the most dangerous types of DNA lesions and can be generated by endogenous or exogenous agents, but they can arise also during DNA replication. Sister chromatid recombination (SCR) is a key mechanism for the repair of DSBs generated during replication and it is fundamental for maintaining genomic stability. Proper repair relies on several factors, among which histone modifications play important roles in the response to DSBs. Here, we study the role of the histone H3K79 methyltransferase Dot1 in the repair by SCR of replication-dependent HO-induced DSBs, as a way to assess its function in homologous recombination. We show that Dot1, the Rad9 DNA damage checkpoint adaptor, and phosphorylation of histone H2A (γH2A) are required for efficient SCR. Moreover, we show that Dot1 and Rad9 promote DSB-induced loading of cohesin onto chromatin. We propose that recruitment of Rad9 to DSB sites mediated by γH2A and H3K79 methylation contributes to DSB repair via SCR by regulating cohesin binding to damage sites. Therefore, our results contribute to an understanding of how different chromatin modifications impinge on DNA repair mechanisms, which are fundamental for maintaining genomic stability.IN eukaryotic cells, genomic integrity is ensured by the action of the DNA damage checkpoint. This checkpoint coordinates the cellular response to DNA damage, triggering cell cycle arrest and activating DNA repair mechanisms, thus providing time for the cell to repair the damage before resuming cell cycle progression (Harrison and Haber 2006). DNA double-strand breaks (DSBs) are among the most dangerous genomic lesions and, if they are not properly repaired, they can lead to fatal consequences. DSBs can be repaired either by homologous recombination (HR) or by nonhomologous end joining (NHEJ), but only HR with the sister chromatid ensures that the fidelity of genetic information is mantained. Thus, sister chromatid recombination (SCR) is the preferred mechanism of DSB repair in mitotic cells (Kadyk and Hartwell 1992; Johnson and Jasin 2000; González-Barrera et al. 2003). Since SCR occurs between identical DNA molecules, its analysis by genetic or physical methods is difficult but, recently, a physical assay to monitor the repair by SCR of a single DSB generated during replication has been developed in budding yeast (González-Barrera et al. 2003; Cortes-Ledesma and Aguilera 2006). This SCR assay is based on a circular minichromosome harboring an internal mini-HO site, which is cleaved mainly in one strand producing ∼10% DSBs during replication, in contrast to the direct and efficient DSB induction at the full-length HO site. In this way, upon HO induction, the DSB occurs only in one chromatid and the other one remains intact and available for repair (see Figure 1A). Although this assay has been used mainly to monitor unequal SCR events, it has been demonstrated that it is an accurate indicator of the proficiency in total SCR (González-Barrera et al. 2003; Cortes-Ledesma and Aguilera 2006). Using this physical assay, it has been established that Rad52, Rad59, Rad51, and Rad54, but not Rdh54/Tid1, are involved in SCR (Cortes-Ledesma et al. 2007b). Also, SMC (structural maintenance of chromosomes) proteins including the cohesin complex and the Smc5/6 complex are required for efficient SCR (Cortes-Ledesma and Aguilera 2006; De Piccoli et al. 2006; Cortes-Ledesma et al. 2007a).Open in a separate windowFigure 1.—Dot1 is required for efficient SCR. (A) Schematic of the physical assay used to monitor repair by SCR of an HO-induced DSB in the centromeric plasmid pRS316-TINV. Fragments generated after XhoI–SpeI digestion, detected by the LEU2 probe (line with asterisks) are indicated with their corresponding sizes. Since other recombination events can also lead to the 2.9-kb fragment, only the 4.7-kb band is used to measure SCR. (B) Kinetics of HO-induced DSB formation and its repair in wild-type (MKOS-3C) and dot1 (YP764) cells incubated in galactose for the indicated times. A representative Southern blot is presented showing the different fragments detected. The 3.8-kb band corresponds to the intact plasmid and equal SCR events, the 1.4-kb and 2.4-kb fragments arise after HO cut, the 2.9-kb band results from unequal SCR and IC-BIR and the 4.7-kb band is specific for unequal SCR. (C) Quantification of DSBs (1.4-kb plus 2.4-kb bands) and SCR (4.7-kb band) relative to the total DNA. Averages and standard deviations are shown. In some cases, such as the dot1 SCR values, the error bars are hidden by the graph symbols.Detection, signaling and repair of genomic lesions occur in the context of chromatin; therefore, factors regulating chromatin structure, such as histone modifications and chromatin remodelers, play important roles in the DNA damage response (Peterson and Cote 2004; Lydall and Whitehall 2005; van Attikum and Gasser 2005; Downs et al. 2007). Mec1- and Tel1-dependent phosphorylation of histone H2A at serine 129 (hereafter referred to as γH2A) is required for DSB repair by NHEJ and likely HR (Downs et al. 2000) and also mediates recruitment of cohesin to DSB sites (Unal et al. 2004). Another chromatin modification involved in the DNA damage response is the methylation of lysine 79 of histone H3 (H3K79) mediated by Dot1 (van Leeuwen et al. 2002). During meiosis, Dot1 is required for the meiotic recombination checkpoint (San-Segundo and Roeder 2000) and, in mitotic cells, Dot1-dependent H3K79 methylation is involved in the Rad9-mediated activation of the Rad53 checkpoint kinase (Giannattasio et al. 2005; Wysocki et al. 2005). Moreover, genetic analyses of the response to different DNA damaging agents, such as ionizing radiation (IR), methyl methanesulfonate (MMS), and UV, have suggested that Dot1 modulates multiple DNA repair pathways (Game et al. 2006; Toh et al. 2006; Bostelman et al. 2007; Conde and San-Segundo 2008) and also controls DSB resection (Lazzaro et al. 2008). To gain further insight in the molecular mechanisms of DNA repair impacted by Dot1 function we have used a physical assay to monitor DSB repair by SCR as a manifestation of HR repair. We provide molecular and genetic evidence indicating that Dot1, together with γH2A, promotes SCR by Rad9-mediated recruitment of cohesin to DSB sites.     

The Genetics of Postmating,Prezygotic Reproductive Isolation Between Drosophila virilis and D. americana

Many studies have demonstrated the rapid diversification of reproductive genes that function after mating but before fertilization. This process might lead to the evolution of postmating, prezygotic barriers between species. Here, I investigate the phenotypic and genetic basis of postmating, prezygotic isolation between two closely related species of Drosophila, Drosophila virilis and D. americana. I show that a strong barrier to interspecific fertilization results in a 99% reduction in progeny production. A genetic interaction among maternal and paternal alleles at only a few loci prevents the fertilization of D. virilis females by D. americana males. These loci are autosomal and isolation acts recessively; the fertilization incompatibility is caused by at least two loci in the maternal D. virilis parent in combination with at least three loci in the paternal D. americana parent. These findings, together with results from classical experiments, suggest that male–female coevolution within D. americana may have driven postmating, prezygotic isolation between species.AN understanding of speciation requires insight into the origins and mechanisms of reproductive isolation. Divergent selection on traits that facilitate mating or fertilization might eventually lead to incompatibilities between males and females of incipient species. In animals, it has long been recognized that sexual selection can promote the evolution of specialized courtship rituals or elaborate phenotypic displays to attract mates (Darwin 1871). Similarly, sexual selection can be a powerful evolutionary force during or after mating by affecting the many biochemical, physiological, and morphological mechanisms involved in fertilization (Eberhard 1996). Postmating reproductive traits might also be subject to sexually antagonistic coevolution, whereby a difference in the reproductive interests of males and females leads to an evolutionary arms race between the sexes (Rice 1996). Just as divergent sexual selection on mate signals and preferences might give rise to premating (sexual) isolation (reviewed in Ritchie 2007), postcopulatory sexual selection and sexual conflict might promote the evolution of postmating barriers to fertilization or hybrid incompatibilities (Howard 1999; Wu and Davis 1993). Indeed, these evolutionary forces have apparently led to competitive gametic isolation (Price 1997; Price et al. 2000; Fishman et al. 2008) and sperm–egg incompatibilities (Galindo et al. 2003). Moreover, because sexual selection and antagonistic coevolution can act rapidly (Fisher 1930; Rice 1996), they might be particularly important in the early stages of speciation.In diverse animal taxa, sexual selection and/or sexual conflict are thought to drive rapid evolution of a variety of postmating reproductive traits, including male genital morphology (Eberhard 1996), length of sperm and female sperm-storage organs (Pitnick et al. 1997; Miller and Pitnick 2002), ejaculate composition (e.g., Swanson et al. 2001a; Dorus et al. 2004), female reproductive tract proteins (e.g., Lawniczak and Begun 2007; Kelleher et al. 2007), and gamete recognition molecules (e.g., Wyckoff et al. 2000; Swanson et al. 2001b). In recent years, many studies have also documented strong signatures of positive selection in the rapid evolution of reproductive genes (e.g., Haerty et al. 2007; Turner et al. 2008; reviewed in Swanson and Vacquier 2002; Clark et al. 2006). For internally fertilizing species, coevolution between the female reproductive tract and the male ejaculate is particularly dynamic (Pitnick et al. 2007). For example, in Drosophila, hundreds of nonsperm seminal fluid proteins are transferred during mating, including many fast-evolving accessory gland proteins (ACPs) (Swanson et al. 2001a; Wagstaff and Begun 2005). As expected, there is evidence for coordinated evolution of female reproductive tract genes, which also show elevated rates of evolution in Drosophila (Panhuis and Swanson 2006; Prokupek et al. 2008). But what are the consequences of such rapid rates of diversification? How many of these fast-evolving reproductive genes contribute to isolating barriers? Major progress toward addressing these questions would require identifying and characterizing individual loci that cause postmating, prezygotic isolation.A large body of classical work suggests that the Drosophila virilis species group might represent an ideal model for studying the genetics of reproductive isolation (Patterson and Stone 1952); and importantly, the D. virilis genome sequence is now available. There is also evidence that postmating, prezygotic isolation may be significant among D. virilis and the closely related North American species, D. americana and D. novamexicana. Patterson et al. (1942) describe reproductive isolation due to “gamete mortality” in reciprocal crosses between D. virilis and D. americana. In later studies, these authors discovered that very few eggs from interspecific crosses become fertilized or hatch and speculate that sperm become “immobilized in the reproductive tract of the alien female” (Patterson and Stone 1952). Moreover, a recent study has found a similar problem with fertilization in crosses between D. americana and D. novamexicana (Y. Ahmed and B. McAllister, personal communication). Consistent with the evolution of these interspecific barriers, male and female reproductive tract proteins have been shown to evolve rapidly in the D. virilis species group (Civetta and Singh 1995; Haerty et al. 2007). In addition, females of both D. virilis and D. americana produce a large opaque vaginal mass in response to mating (the “insemination reaction”; Wheeler 1947), which almost certainly reflects an evolutionary history of interaction between the female reproductive tract and male ejaculate (Knowles and Markow 2001).Despite the potential importance of postmating, prezygotic isolation in D. virilis group divergence, almost nothing is known about its genetic architecture. On the basis of the results from their crosses between D. virilis and D. americana, Patterson et al. (1942) infer that postmating isolation involves recessive autosomal genes. However, their experiments often cannot distinguish between the effects of the apparent fertilization incompatibility and premating isolation, the latter also being strong between D. americana females and D. virilis males (Stalker 1942). Their genetic mapping studies were also crude.In this study, I have two main objectives. First, I characterize the phenotypic basis of postmating isolation between D. virilis and D. americana. To do so, I perform a series of crosses within and between species. I find that low F₁ hybrid production between D. virilis and D. americana is due primarily to a reduction in interspecific fertilization; females presented with heterospecific males almost always become inseminated, but very few eggs are fertilized. Second, I perform a detailed genetic analysis of the fertilization incompatibility between D. virilis females and D. americana males. Using the D. virilis genome assembly, I developed molecular markers targeted to genomic regions of interest for high-resolution genetic mapping of both the maternal and paternal components of isolation. This study is a first step toward understanding the genetic and evolutionary mechanisms of postmating, prezygotic reproductive isolation in Drosophila.