Effect of recombination on the accuracy of the likelihood method for detecting positive selection at amino acid sites

Maximum-likelihood methods based on models of codon substitution accounting for heterogeneous selective pressures across sites have proved to be powerful in detecting positive selection in protein-coding DNA sequences. Those methods are phylogeny based and do not account for the effects of recombination. When recombination occurs, such as in population data, no unique tree topology can describe the evolutionary history of the whole sequence. This violation of assumptions raises serious concerns about the likelihood method for detecting positive selection. Here we use computer simulation to evaluate the reliability of the likelihood-ratio test (LRT) for positive selection in the presence of recombination. We examine three tests based on different models of variable selective pressures among sites. Sequences are simulated using a coalescent model with recombination and analyzed using codon-based likelihood models ignoring recombination. We find that the LRT is robust to low levels of recombination (with fewer than three recombination events in the history of a sample of 10 sequences). However, at higher levels of recombination, the type I error rate can be as high as 90%, especially when the null model in the LRT is unrealistic, and the test often mistakes recombination as evidence for positive selection. The test that compares the more realistic models M7 (beta) against M8 (beta and omega) is more robust to recombination, where the null model M7 allows the positive selection pressure to vary between 0 and 1 (and so does not account for positive selection), and the alternative model M8 allows an additional discrete class with omega = d(N)/d(S) that could be estimated to be >1 (and thus accounts for positive selection). Identification of sites under positive selection by the empirical Bayes method appears to be less affected than the LRT by recombination.     

Recombination Detection Under Evolutionary Scenarios Relevant to Functional Divergence

Recombination can negatively impact methods designed to detect divergent gene function that rely on explicit knowledge of a gene tree. However, we know little about how recombination detection methods perform under evolutionary scenarios encountered in studies of functional molecular divergence. We use simulation to evaluate false positive rates for six recombination detection methods (GENECONV, MaxChi, Chimera, RDP, GARD-SBP, GARD-MBP) under evolutionary scenarios that might increase false positives. Broadly, these scenarios address: (i) asymmetric tree topology and sequence divergence, (ii) non-stationary codon bias and selection pressure, and (iii) positive selection. We also evaluate power to detect recombination under truly recombinant history. As with previous studies, we find that power increases with sequence divergence. However, we also find that accuracy to correctly infer the number of breakpoints is extremely low. When recombination is absent, increased sequence divergence leads to increased false positives. Furthermore, one method (GARD-SBP) is sensitive to tree shape, with higher false positive rates under an asymmetric tree topology. Somewhat surprisingly, all methods are robust to the simulated heterogeneity in codon bias, shifts in selection pressure and presence of positive selection. Based on these findings, we recommend that studies of functional divergence in systems where recombination is plausible can, and should, include a pre-test for recombination. Application of all methods to the core genome of Prochlorococcus reveals a substantial lack of concordance among results. Based on analysis of both real and simulated datasets we present some guidelines for the investigation of recombination in genes that may have experienced functional divergence.     

Robust inference of positive selection from recombining coding sequences

MOTIVATION: Accurate detection of positive Darwinian selection can provide important insights to researchers investigating the evolution of pathogens. However, many pathogens (particularly viruses) undergo frequent recombination and the phylogenetic methods commonly applied to detect positive selection have been shown to give misleading results when applied to recombining sequences. We propose a method that makes maximum likelihood inference of positive selection robust to the presence of recombination. This is achieved by allowing tree topologies and branch lengths to change across detected recombination breakpoints. Further improvements are obtained by allowing synonymous substitution rates to vary across sites. RESULTS: Using simulation we show that, even for extreme cases where recombination causes standard methods to reach false positive rates >90%, the proposed method decreases the false positive rate to acceptable levels while retaining high power. We applied the method to two HIV-1 datasets for which we have previously found that inference of positive selection is invalid owing to high rates of recombination. In one of these (env gene) we still detected positive selection using the proposed method, while in the other (gag gene) we found no significant evidence of positive selection. AVAILABILITY: A HyPhy batch language implementation of the proposed methods and the HIV-1 datasets analysed are available at http://www.cbio.uct.ac.za/pub_support/bioinf06. The HyPhy package is available at http://www.hyphy.org, and it is planned that the proposed methods will be included in the next distribution. RDP2 is available at http://darwin.uvigo.es/rdp/rdp.html     

Natural selection affects multiple aspects of genetic variation at putatively neutral sites across the human genome

A major question in evolutionary biology is how natural selection has shaped patterns of genetic variation across the human genome. Previous work has documented a reduction in genetic diversity in regions of the genome with low recombination rates. However, it is unclear whether other summaries of genetic variation, like allele frequencies, are also correlated with recombination rate and whether these correlations can be explained solely by negative selection against deleterious mutations or whether positive selection acting on favorable alleles is also required. Here we attempt to address these questions by analyzing three different genome-wide resequencing datasets from European individuals. We document several significant correlations between different genomic features. In particular, we find that average minor allele frequency and diversity are reduced in regions of low recombination and that human diversity, human-chimp divergence, and average minor allele frequency are reduced near genes. Population genetic simulations show that either positive natural selection acting on favorable mutations or negative natural selection acting against deleterious mutations can explain these correlations. However, models with strong positive selection on nonsynonymous mutations and little negative selection predict a stronger negative correlation between neutral diversity and nonsynonymous divergence than observed in the actual data, supporting the importance of negative, rather than positive, selection throughout the genome. Further, we show that the widespread presence of weakly deleterious alleles, rather than a small number of strongly positively selected mutations, is responsible for the correlation between neutral genetic diversity and recombination rate. This work suggests that natural selection has affected multiple aspects of linked neutral variation throughout the human genome and that positive selection is not required to explain these observations.     

Development of an efficient agrobacterium-mediated gene targeting system for rice and analysis of rice knockouts lacking granule-bound starch synthase (Waxy) and β1,2-xylosyltransferase

We have developed a high-frequency method for Agrobacterium-mediated gene targeting by combining an efficient transformation system using rice suspension-cultured calli and a positive/negative selection system. Compared with the conventional transformation system using calli on solid medium, transformation using suspension-cultured calli resulted in a 5- to 10-fold increase in the number of resistant calli per weight of starting material after positive/negative selection. Homologous recombination occurred in about 1.5% of the positive/negative selected calli. To evaluate the efficacy of our method, we show in this report that knockout rice plants containing either a disrupted Waxy (granule-bound starch synthase) or a disrupted Xyl (β1,2-xylosyltransferase) gene can be easily obtained by homologous recombination. Study of gene function using homologous recombination in higher plants can now be considered routine work as a direct result of this technical advance.     

Genetic recombination and adaptation to fluctuating environments: selection for geotaxis in Drosophila melanogaster

Heritable variation in fitness is the fuel of adaptive evolution, and sex can generate new adaptive combinations of alleles. If the generation of beneficial combinations drives the evolution of recombination, then the level of recombination should result in changes in the response to selection. Three types of lines of Drosophila melanogaster varying in their level of genetic recombination were selected over 38 generations for geotaxis. The within-chromosome recombination level of these lines was controlled for 60% of the genome: chromosome X and chromosome II. The full recombination lines had normal, unmanipulated levels of recombination on these two chromosomes. Conversely, nonrecombination lines had recombination effectively eliminated within the X and second chromosomes. Finally, partial recombination lines had the effective rate of within-chromosome recombination lowered to 10% of natural levels for these two chromosomes. The rate of response to selection was measured for continuous negative geotaxis and for a fluctuating environment (alternating selection for negative and positive geotaxis). All selected Drosophila lines responded to selection and approximately 36% of the response to selection was because of the X and second chromosomes. However, recombination did not accelerate adaptation during either directional or fluctuating selection for geotaxis.     

Positive correlation between evolutionary rate and recombination rate in Drosophila genes with male-biased expression

Previous studies have shown that genes that are expressed predominantly or exclusively in males tend to evolve rapidly in comparison to other genes. In most cases, however, it is unknown whether this rapid evolution is the result of increased positive (or sexual) selection on male-expressed traits or if it is due to a relaxation of selective constraints. To distinguish between these two possibilities, we analyzed the relationship between the nonsynonymous substitution rate (dN) and local recombination rate for 343 Drosophila genes that were classified as male, female, or nonsex biased in their expression. For the male-biased genes, a positive correlation between dN and recombination rate was observed. This can be explained by an increased rate of adaptive evolution in regions of higher recombination due to a reduction of Hill-Robertson interference. In contrast, the correlation between dN and recombination rate was negative for both female- and nonsex-biased genes, suggesting that these genes are primarily subject to purifying selection, which is expected to be less effective in regions of reduced recombination.     

Hitchhiking under positive Darwinian selection

Positive selection can be inferred from its effect on linked neutral variation. In the restrictive case when there is no recombination, all linked variation is removed. If recombination is present but rare, both deterministic and stochastic models of positive selection show that linked variation hitchhikes to either low or high frequencies. While the frequency distribution of variation can be influenced by a number of evolutionary processes, an excess of derived variants at high frequency is a unique pattern produced by hitchhiking (derived refers to the nonancestral state as determined from an outgroup). We adopt a statistic, H, to measure an excess of high compared to intermediate frequency variants. Only a few high-frequency variants are needed to detect hitchhiking since not many are expected under neutrality. This is of particular utility in regions of low recombination where there is not much variation and in regions of normal or high recombination, where the hitchhiking effect can be limited to a small (<1 kb) region. Application of the H test to published surveys of Drosophila variation reveals an excess of high frequency variants that are likely to have been influenced by positive selection.     

The evolution of recombination in a heterogeneous environment

Most models describing the evolution of recombination have focused on the case of a single population, implicitly assuming that all individuals are equally likely to mate and that spatial heterogeneity in selection is absent. In these models, the evolution of recombination is driven by linkage disequilibria generated either by epistatic selection or drift. Models based on epistatic selection show that recombination can be favored if epistasis is negative and weak compared to directional selection and if the recombination modifier locus is tightly linked to the selected loci. In this article, we examine the joint effects of spatial heterogeneity in selection and epistasis on the evolution of recombination. In a model with two patches, each subject to different selection regimes, we consider the cases of mutation-selection and migration-selection balance as well as the spread of beneficial alleles. We find that including spatial heterogeneity extends the range of epistasis over which recombination can be favored. Indeed, recombination can be favored without epistasis, with negative and even with positive epistasis depending on environmental circumstances. The selection pressure acting on recombination-modifier loci is often much stronger with spatial heterogeneity, and even loosely linked modifiers and free linkage may evolve. In each case, predicting whether recombination is favored requires knowledge of both the type of environmental heterogeneity and epistasis, as none of these factors alone is sufficient to predict the outcome.     

The implications of a low rate of horizontal transfer in Borrelia.

The nature and rate of recombination can be studied by comparing the sequences of multiple genes across a set of strains. When this approach is applied to Borrelia burgdorferi, four results emerge: (1) chromosomal genes are clonal; (2) there is little or no plasmid exchange; (3) the major mode of horizontal transfer of genetic material inserts a small fragment of DNA, typically <1 kb, during recombination; and (4) the level of horizontal transfer in Borrelia is so low that there is evidence for horizontal transfer only in genes where there is positive selection for diversity, that is, positive selection for the recombinant. Thus, Borrelia can serve as a model of a low recombination taxon. The implications of these results lead us to postulate that an unknown agent that is part of the Borrelia genome mediates the horizontal transfer of small fragments of DNA; the rare transfer of small fragments of DNA excludes both DNA parasites and virulence factors from the genome.     

Selection on recombination in clines

Computer runs have been done to examine Slatkin's (1975) model for selection on recombination rates in linear sets of populations with environmental changes affecting two loci. In order to determine whether the suggested selection pressures on recombination do, in fact, exist, we follow the changes in frequency at a third locus that is polymorphic for alleles affecting the recombination rate between the two selected loci. With haploid or diploid selection models, there can be selection for increased recombination if the parameter values are chosen suitably, but changes in parameter values often lead to changes in the direction of selection, so that decreased recombination is favored. The selection for increased recombination is usually weak, while that for decreased recombination is frequently much stronger. Weaker selection on the selected loci often leads to increasing selection for decreased recombination.     

The genetic architecture of disease resistance in plants and the maintenance of recombination by parasites

Parasites represent strong selection on host populations because they are ubiquitous and can drastically reduce host fitness. It has been hypothesized that parasite selection could explain the widespread occurrence of recombination because it is a coevolving force that favours new genetic combinations in the host. A review of deterministic models for the maintenance of recombination reveals that for recombination to be favoured, multiple genes that interact with each other must be under selection. To evaluate whether parasite selection can explain the maintenance of recombination, we review 85 studies that investigated the genetic architecture of plant disease resistance and discuss whether they conform to the requirements that emerge from theoretical models. General characteristics of disease resistance in plants and problems in evaluating resistance experimentally are also discussed. We found strong evidence that disease resistance in plants is determined by multiple loci. Furthermore, in most cases where loci were tested for interactions, epistasis between loci that affect resistance was found. However, we found weak support for the idea that specific allelic combinations determine resistance to different host genotypes and there was little data on whether epistasis between resistance genes is negative or positive. Thus, the current data indicate that it is possible that parasite selection can favour recombination, but more studies in natural populations that specifically address the nature of the interactions between resistance genes are necessary. The data summarized here suggest that disease resistance is a complex trait and that environmental effects and fitness trade-offs should be considered in future models of the coevolutionary dynamics of host and parasites.     

Dynamics of Genetic Variability in Two-Locus Models of Stabilizing Selection

We study a two locus model, with additive contributions to the phenotype, to explore the dynamics of different phenotypic characteristics under stabilizing selection and recombination. We demonstrate that the interaction of selection and recombination results in constraints on the mode of phenotypic evolution. Let V(g) be the genic variance of the trait and C(L) be the contribution of linkage disequilibrium to the genotypic variance. We demonstrate that, independent of the initial conditions, the dynamics of the system on the plane (V(g), C(L)) are typically characterized by a quick approach to a straight line with slow evolution along this line afterward. We analyze how the mode and the rate of phenotypic evolution depend on the strength of selection relative to recombination, on the form of fitness function, and the difference in allelic effect. We argue that if selection is not extremely weak relative to recombination, linkage disequilibrium generated by stabilizing selection influences the dynamics significantly. We demonstrate that under these conditions, which are plausible in nature and certainly the case in artificial stabilizing selection experiments, the model can have a polymorphic equilibrium with positive linkage disequilibrium that is stable simultaneously with monomorphic equilibria.     

Recombination and Response to Selection in DROSOPHILA MELANOGASTER

Most biologists beleive that recombination speeds response to selection for traits determined by polygenic loci. To test this hypothesis, sixteen Drosophila melanogaster populations were selected for positive phototaxis for twenty-one generations. In some populations, balancer chromosomes were used to suppress autosomal recombination, and in others the autosomes were free to recombine. Suppression of recombination had no effect on mean rate of response to selection, though it may have increased variability in the rate of response among replicate lines. Suppressed recombination lines did not shift selection response to the freely recombining X chromosomes, despite fairly large increased in X chromosome recombination. The results suggest that in populations of moderate size, sex does not accelerate short term response to selection.     

Effect of varying epistasis on the evolution of recombination

Whether recombination decelerates or accelerates a population's response to selection depends, at least in part, on how fitness-determining loci interact. Realistically, all genomes likely contain fitness interactions both with positive and with negative epistasis. Therefore, it is crucial to determine the conditions under which the potential beneficial effects of recombination with negative epistasis prevail over the detrimental effects of recombination with positive epistasis. Here, we examine the simultaneous effects of diverse epistatic interactions with different strengths and signs in a simplified model system with independent pairs of interacting loci and selection acting only on the haploid phase. We find that the average form of epistasis does not predict the average amount of linkage disequilibrium generated or the impact on a recombination modifier when compared to results using the entire distribution of epistatic effects and associated single-mutant effects. Moreover, we show that epistatic interactions of a given strength can produce very different effects, having the greatest impact when selection is weak. In summary, we observe that the evolution of recombination at mutation-selection balance might be driven by a small number of interactions with weak selection rather than by the average epistasis of all interactions. We illustrate this effect with an analysis of published data of Saccharomyces cerevisiae. Thus to draw conclusions on the evolution of recombination from experimental data, it is necessary to consider the distribution of epistatic interactions together with the associated selection coefficients.     

A weak effect of background selection on trinucleotide microsatellites in maize

Artificial selection during the domestication of maize is thought to have been predominantly positive and to have had little effect on the surrounding neutral diversity because linkage disequilibrium breaks down rapidly when physical distance increases. However, the degree to which indirect selection has shaped neutral diversity in the maize genome during domestication remains unclear. In this study, we investigate the relationship between local recombination rate and neutral polymorphism in maize and in teosinte using both sequence and microsatellite data. To quantify diversity, we estimate 3 parameters expected to differentially reflect the effects of indirect selection and mutation. We find no general correlation between diversity and recombination, indicating that indirect selection has had no genome-wide impact on maize diversity. However, we detect a weak correlation between heterozygosity and recombination for trinucleotide microsatellites deviating from the stepwise mutation model and located within genes (rho = 0.32, P < 0.03). This result can be explained by a background selection hypothesis. The fact that the same correlation is not confirmed for nucleotide diversity suggests that the strength of purifying selection at or near this class of microsatellites is higher than for nucleotide mutations.     

The evolutionary advantage of fitness‐dependent recombination in diploids: A deterministic mutation–selection balance model

Recombination's omnipresence in nature is one of the most intriguing problems in evolutionary biology. The question of why recombination exhibits certain general features is no less interesting than that of why it exists at all. One such feature is recombination's fitness dependence (FD). The so far developed population genetics models have focused on the evolution of FD recombination mainly in haploids, although the empirical evidence for this phenomenon comes mostly from diploids. Using numerical analysis of modifier models for infinite panmictic populations, we show here that FD recombination can be evolutionarily advantageous in diploids subjected to purifying selection. We ascribe this advantage to the differential rate of disruption of lower‐ versus higher‐fitness genotypes, which can be manifested in selected systems with at least three loci. We also show that if the modifier is linked to such selected system, it can additionally benefit from modifying this linkage in a fitness‐dependent manner. The revealed evolutionary advantage of FD recombination appeared robust to crossover interference within the selected system, either positive or negative. Remarkably, FD recombination was often favored in situations where any constant nonzero recombination was evolutionarily disfavored, implying a relaxation of the rather strict constraints on major parameters (e.g., selection intensity and epistasis) required for the evolutionary advantage of nonzero recombination formulated by classical models.     

Comparisons of site- and haplotype-frequency methods for detecting positive selection

In this report, we compare the differences between various site- and haplotype-frequency tests in their power to detect positive selection by doing computer simulations. Our results are the following. 1) Although haplotype-frequency tests that are conditional on the number of haplotypes (K) were developed for nonrecombining haplotypes, these tests are insensitive to recombination. Such tests, including the Ewens-Watterson (EW) test, can therefore be applied to recombining haplotypes. 2) Tests conditional on the number of segregating sites (S) become overly conservative in the presence of recombination. 3) The EW test is usually the most powerful test during the sweep phase, especially when the local recombination rate is high. 4) The "extended haplotype homozygosity" test relies heavily on the prior knowledge of the target of selection. With that knowledge, it is the most powerful test, whereas in the absence of this prior information, the test has little power. We also study the sensitivities of the haplotype-frequency tests to background selection and various demographic forces. We find that these tests are sensitive to some forces other than positive selection. To alleviate the problem of low specificity, compound tests, such as the DH test (Zeng et al. 2006), may be a solution. In the companion paper (Zeng K, Shi S, Wu C-I, in preparation), we use the EW test to devise 2 compound tests, which are more powerful in detecting positive selection than DH, but are also relatively insensitive to demography.     

Linkage Modification with Mixed Random Mating and Selfing: A Numerical Study

Although recombination cannot increase under conditions of random mating or complete selfing in regimes of constant selection, with mixed random mating and selfing, selection for increased recombination can occur. For some fitness regimes there may be selection for reduced recombination with both low and high degrees of selfing but selection for increased recombination with moderate degrees of selfing. With some fitness regimes there is a historical effect: depending on which equilibrium a population starts from, there may be selection for either increased or decreased recombination. In other cases the direction of selection may be determined by the present state of individuals within the population. If recombination is already fairly limited, there may be selection for further reduction. If recombination is already fairly frequent, there may be selection for increased recombination. For certain symmetric viability systems there may be an intermediate value of the recombination fraction between 0 and 0.5 toward which the population will evolve. Although it is not yet possible to classify precisely those fitness matrices that can exhibit selection for increased recombination, it does appear that selection for increased recombination can occur only if at least two of the double homozygotes are less fit than would be expected on the basis of a comparison of the fitnesses of the single and double heterozygotes on an additive scale.     

GC-biased gene conversion and selection affect GC content in the Oryza genus (rice)

Base composition varies among and within eukaryote genomes. Although mutational bias and selection have initially been invoked, more recently GC-biased gene conversion (gBGC) has been proposed to play a central role in shaping nucleotide landscapes, especially in yeast, mammals, and birds. gBGC is a kind of meiotic drive in favor of G and C alleles, associated with recombination. Previous studies have also suggested that gBGC could be at work in grass genomes. However, these studies were carried on third codon positions that can undergo selection on codon usage. As most preferred codons end in G or C in grasses, gBGC and selection can be confounded. Here we investigated further the forces that might drive GC content evolution in the rice genus using both coding and noncoding sequences. We found that recombination rates correlate positively with equilibrium GC content and that selfing species (Oryza sativa and O. glaberrima) have significantly lower equilibrium GC content compared with more outcrossing species. As recombination is less efficient in selfing species, these results suggest that recombination drives GC content. We also detected a positive relationship between expression levels and GC content in third codon positions, suggesting that selection favors codons ending with G or C bases. However, the correlation between GC content and recombination cannot be explained by selection on codon usage alone as it was also observed in noncoding positions. Finally, analyses of polymorphism data ruled out the hypothesis that genomic variation in GC content is due to mutational processes. Our results suggest that both gBGC and selection on codon usage affect GC content in the Oryza genus and likely in other grass species.