Within- and between-species DNA sequence variation and the 'footprint' of natural selection

Extensive DNA data emerging from genome-sequencing projects have revitalized interest in the mechanisms of molecular evolution. Although the contribution of natural selection at the molecular level has been debated for over 30 years, the relevant data and appropriate statistical methods to address this issue have only begun to emerge. This paper will first present the predominant models of neutral, nearly neutral, and adaptive molecular evolution. Then, a method to identify the role of natural selection in molecular evolution by comparing within- and between-species DNA sequence variation will be presented. Computer simulations show that such methods are powerful for detecting even very weak selection. Examination of DNA variation data within and between Drosophila species suggests that 'silent' sites evolve under a balance between weak selection and genetic drift. Simulated data also show that sequence comparisons are a powerful method to detect adaptive protein evolution, even when selection is weak or affects a small fraction of nucleotide sites. In the Drosophila data examined, positive selection appears to be a predominant force in protein evolution.     

Accuracy and power of the likelihood ratio test in detecting adaptive molecular evolution

The selective pressure at the protein level is usually measured by the nonsynonymous/synonymous rate ratio (omega = dN/dS), with omega < 1, omega = 1, and omega > 1 indicating purifying (or negative) selection, neutral evolution, and diversifying (or positive) selection, respectively. The omega ratio is commonly calculated as an average over sites. As every functional protein has some amino acid sites under selective constraints, averaging rates across sites leads to low power to detect positive selection. Recently developed models of codon substitution allow the omega ratio to vary among sites and appear to be powerful in detecting positive selection in empirical data analysis. In this study, we used computer simulation to investigate the accuracy and power of the likelihood ratio test (LRT) in detecting positive selection at amino acid sites. The test compares two nested models: one that allows for sites under positive selection (with omega > 1), and another that does not, with the chi2 distribution used for significance testing. We found that use of the chi(2) distribution makes the test conservative, especially when the data contain very short and highly similar sequences. Nevertheless, the LRT is powerful. Although the power can be low with only 5 or 6 sequences in the data, it was nearly 100% in data sets of 17 sequences. Sequence length, sequence divergence, and the strength of positive selection also were found to affect the power of the LRT. The exact distribution assumed for the omega ratio over sites was found not to affect the effectiveness of the LRT.     

Likelihood-based clustering (LiBaC) for codon models, a method for grouping sites according to similarities in the underlying process of evolution

Models of codon evolution are useful for investigating the strength and direction of natural selection via a parameter for the nonsynonymous/synonymous rate ratio (omega = d(N)/d(S)). Different codon models are available to account for diversity of the evolutionary patterns among sites. Codon models that specify data partitions as fixed effects allow the most evolutionary diversity among sites but require that site partitions are a priori identifiable. Models that use a parametric distribution to express the variability in the omega ratio across site do not require a priori partitioning of sites, but they permit less among-site diversity in the evolutionary process. Simulation studies presented in this paper indicate that differences among sites in estimates of omega under an overly simplistic analytical model can reflect more than just natural selection pressure. We also find that the classic likelihood ratio tests for positive selection have a high false-positive rate in some situations. In this paper, we developed a new method for assigning codon sites into groups where each group has a different model, and the likelihood over all sites is maximized. The method, called likelihood-based clustering (LiBaC), can be viewed as a generalization of the family of model-based clustering approaches to models of codon evolution. We report the performance of several LiBaC-based methods, and selected alternative methods, over a wide variety of scenarios. We find that LiBaC, under an appropriate model, can provide reliable parameter estimates when the process of evolution is very heterogeneous among groups of sites. Certain types of proteins, such as transmembrane proteins, are expected to exhibit such heterogeneity. A survey of genes encoding transmembrane proteins suggests that overly simplistic models could be leading to false signal for positive selection among such genes. In these cases, LiBaC-based methods offer an important addition to a "toolbox" of methods thereby helping to uncover robust evidence for the action of positive selection.     

Widespread positive selection in synonymous sites of mammalian genes

Evolution of protein sequences is largely governed by purifying selection, with a small fraction of proteins evolving under positive selection. The evolution at synonymous positions in protein-coding genes is not nearly as well understood, with the extent and types of selection remaining, largely, unclear. A statistical test to identify purifying and positive selection at synonymous sites in protein-coding genes was developed. The method compares the rate of evolution at synonymous sites (Ks) to that in intron sequences of the same gene after sampling the aligned intron sequences to mimic the statistical properties of coding sequences. We detected purifying selection at synonymous sites in approximately 28% of the 1,562 analyzed orthologous genes from mouse and rat, and positive selection in approximately 12% of the genes. Thus, the fraction of genes with readily detectable positive selection at synonymous sites is much greater than the fraction of genes with comparable positive selection at nonsynonymous sites, i.e., at the level of the protein sequence. Unlike other genes, the genes with positive selection at synonymous sites showed no correlation between Ks and the rate of evolution in nonsynonymous sites (Ka), indicating that evolution of synonymous sites under positive selection is decoupled from protein evolution. The genes with purifying selection at synonymous sites showed significant anticorrelation between Ks and expression level and breadth, indicating that highly expressed genes evolve slowly. The genes with positive selection at synonymous sites showed the opposite trend, i.e., highly expressed genes had, on average, higher Ks. For the genes with positive selection at synonymous sites, a significantly lower mRNA stability is predicted compared to the genes with negative selection. Thus, mRNA destabilization could be an important factor driving positive selection in nonsynonymous sites, probably, through regulation of expression at the level of mRNA degradation and, possibly, also translation rate. So, unexpectedly, we found that positive selection at synonymous sites of mammalian genes is substantially more common than positive selection at the level of protein sequences. Positive selection at synonymous sites might act through mRNA destabilization affecting mRNA levels and translation.     

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.     

Identifying sites under positive selection with uncertain parameter estimates.

Codon-based substitution models are routinely used to measure selective pressures acting on protein-coding genes. To this effect, the nonsynonymous to synonymous rate ratio (dN/dS = omega) is estimated. The proportion of amino-acid sites potentially under positive selection, as indicated by omega > 1, is inferred by fitting a probability distribution where some sites are permitted to have omega > 1. These sites are then inferred by means of an empirical Bayes or by a Bayes empirical Bayes approach that, respectively, ignores or accounts for sampling errors in maximum-likelihood estimates of the distribution used to infer the proportion of sites with omega > 1. Here, we extend a previous full-Bayes approach to include models with high power and low false-positive rates when inferring sites under positive selection. We propose some heuristics to alleviate the computational burden, and show that (i) full Bayes can be superior to empirical Bayes when analyzing a small data set or small simulated data, (ii) full Bayes has only a small advantage over Bayes empirical Bayes with our small test data, and (iii) Bayesian methods appear relatively insensitive to mild misspecifications of the random process generating adaptive evolution in our simulations, but in practice can prove extremely sensitive to model specification. We suggest that the codon model used to detect amino acids under selection should be carefully selected, for instance using Akaike information criterion (AIC).     

Statistical methods for detecting natural selection from genomic data

In the study of molecular and phenotypic evolution, understanding the relative importance of random genetic drift and positive selection as the mechanisms for driving divergences between populations and maintaining polymorphisms within populations has been a central issue. A variety of statistical methods has been developed for detecting natural selection operating at the amino acid and nucleotide sequence levels. These methods may be largely classified into those aimed at detecting recurrent and/or recent/ongoing natural selection by utilizing the divergence and/or polymorphism data. Using these methods, pervasive positive selection has been identified for protein-coding and non-coding sequences in the genomic analysis of some organisms. However, many of these methods have been criticized by using computer simulation and real data analysis to produce excessive false-positives and to be sensitive to various disturbing factors. Importantly, some of these methods have been invalidated experimentally. These facts indicate that many of the statistical methods for detecting natural selection are unreliable. In addition, the signals that have been believed as the evidence for fixations of advantageous mutations due to positive selection may also be interpreted as the evidence for fixations of deleterious mutations due to random genetic drift. The genomic diversity data are rapidly accumulating in various organisms, and detection of natural selection may play a critical role for clarifying the relative role of random genetic drift and positive selection in molecular and phenotypic evolution. It is therefore important to develop reliable statistical methods that are unbiased as well as robust against various disturbing factors, for inferring natural selection.     

Frequent false detection of positive selection by the likelihood method with branch-site models

Positive Darwinian selection promotes fixations of advantageous mutations during gene evolution and is probably responsible for most adaptations. Detecting positive selection at the DNA sequence level is of substantial interest because such information provides significant insights into possible functional alterations during gene evolution as well as important nucleotide substitutions involved in adaptation. Efficient detection of positive selection, however, has been difficult because selection often operates on only a few sites in a short period of evolutionary time. A likelihood-based method with branch-site models was recently introduced to overcome such difficulties. Here I examine the accuracy of the method using computer simulation. I find that the method detects positive selection in 20%-70% of cases when the DNA sequences are generated by computer simulation under no positive selection. Although the frequency of such false detection varies depending on, among other things, the tree topology, branch length, and selection scheme, the branch-site likelihood method generally gives misleading results. Thus, detection of positive selection by this method alone is unreliable. This unreliability may have resulted from its over-sensitivity to violations of assumptions made in the method, such as certain distributions of selective strength among sites and equal transition/transversion ratios for synonymous and nonsynonymous substitutions.     

Genealogical evidence for positive selection in the nef gene of HIV-1.

The pattern and process of evolution in the nef gene of HIV-1 was analyzed within and among patients. Using a maximum likelihood method that allows for variable intensity of selection pressure among codons, strong positive selection was detected in a hemophiliac patient over 30 mo of infection. By reconstructing the process of allele substitution in this patient using parsimony, the synapomorphic amino acid changes separating each time point were found to have high probabilities of being under positive selection, with selective coefficients of at least 3.6%. Positive selection was also detected among 39 nef sequences from HIV-1 subtype B. In contrast, multiple pairwise comparisons of nonsynonymous and synonymous substitution rates provided no good evidence for positive selection and sliding window analyses failed to detect most positively selected sites. These findings demonstrate that positive selection is an important determinant of nef gene evolution and that genealogy-based methods outperform pairwise methods in the detection of adaptive evolution. Mapping the locations of positively selected sites may also be of use in identifying targets of the immune response and hence aid vaccine design.     

Ancestral inference on gene trees under selection

The extent to which natural selection shapes diversity within populations is a key question for population genetics. Thus, there is considerable interest in quantifying the strength of selection. A full likelihood approach for inference about selection at a single site within an otherwise neutral fully linked sequence of sites is described here. A coalescent model of evolution is used to model the ancestry of a sample of DNA sequences which have the selected site segregating. The mutation model, for the selected and neutral sites, is the infinitely many-sites model where there is no back or parallel mutation at sites. A unique perfect phylogeny, a gene tree, can be constructed from the configuration of mutations on the sample sequences under this model of mutation. The approach is general and can be used for any bi-allelic selection scheme. Selection is incorporated through modelling the frequency of the selected and neutral allelic classes stochastically back in time, then using a subdivided population model considering the population frequencies through time as variable population sizes. An importance sampling algorithm is then used to explore over coalescent tree space consistent with the data. The method is applied to a simulated data set and the gene tree presented in Verrelli et al. (2002).     

Potential impact of recombination on sitewise approaches for detecting positive natural selection

Current sitewise methods for detecting positive selection on gene sequences (the de facto standard being the CODEML method (Yang et al., 2000)) assume no recombination. This paper presents simulation results indicating that violation of this assumption can lead to false positive detection of sites undergoing positive selection. Through the use of population-scaled mutation and recombination rates, simulations can be performed that permit the generation of appropriate null distributions corresponding to neutral expectations in the presence of recombination, thereby allowing for a more accurate estimation of positive selection.     

Statistical properties of the branch-site test of positive selection

The branch-site test is a likelihood ratio test to detect positive selection along prespecified lineages on a phylogeny that affects only a subset of codons in a protein-coding gene, with positive selection indicated by accelerated nonsynonymous substitutions (with ω = d(N)/d(S) > 1). This test may have more power than earlier methods, which average nucleotide substitution rates over sites in the protein and/or over branches on the tree. However, a few recent studies questioned the statistical basis of the test and claimed that the test generated too many false positives. In this paper, we examine the null distribution of the test and conduct a computer simulation to examine the false-positive rate and the power of the test. The results suggest that the asymptotic theory is reliable for typical data sets, and indeed in our simulations, the large-sample null distribution was reliable with as few as 20-50 codons in the alignment. We examined the impact of sequence length, the strength of positive selection, and the proportion of sites under positive selection on the power of the branch-site test. We found that the test was far more powerful in detecting episodic positive selection than branch-based tests, which average substitution rates over all codons in the gene and thus miss the signal when most codons are under strong selective constraint. Recent claims of statistical problems with the branch-site test are due to misinterpretations of simulation results. Our results, as well as previous simulation studies that have demonstrated the robustness of the test, suggest that the branch-site test may be a useful tool for detecting episodic positive selection and for generating biological hypotheses for mutation studies and functional analyses. The test is sensitive to sequence and alignment errors and caution should be exercised concerning its use when data quality is in doubt.     

Purifying selection maintains highly conserved noncoding sequences in Drosophila

The majority of metazoan genomes consist of nonprotein-coding regions, although the functional significance of most noncoding DNA sequences remains unknown. Highly conserved noncoding sequences (CNSs) have proven to be reliable indicators of functionally constrained sequences such as cis-regulatory elements and noncoding RNA genes. However, CNSs may arise from nonselective evolutionary processes such as genomic regions with extremely low mutation rates known as mutation "cold spots." Here we combine comparative genomic data from recently completed insect genome projects with population genetic data in Drosophila melanogaster to test predictions of the mutational cold spot model of CNS evolution in the genus Drosophila. We find that point mutations in intronic and intergenic CNSs exhibit a significant reduction in levels of divergence relative to levels of polymorphism, as well as a significant excess of rare derived alleles, compared with either the nonconserved spacer regions between CNSs or with 4-fold silent sites in coding regions. Controlling for the effects of purifying selection, we find no evidence of positive selection acting on Drosophila CNSs, although we do find evidence for the action of recurrent positive selection in the spacer regions between CNSs. We estimate that approximately 85% of sites in Drosophila CNSs are under constraint with selection coefficients (N(e)s) on the order of 10-100, and thus, the estimated strength and number of sites under purifying selection is greater for Drosophila CNSs relative to those in the human genome. These patterns of nonneutral molecular evolution are incompatible with the mutational cold spot hypothesis to explain the existence of CNSs in Drosophila and, coupled with similar findings in mammals, argue against the general likelihood that CNSs are generated by mutational cold spots in any metazoan genome.     

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     

A Bayesian model comparison approach to inferring positive selection

A popular approach to detecting positive selection is to estimate the parameters of a probabilistic model of codon evolution and perform inference based on its maximum likelihood parameter values. This approach has been evaluated intensively in a number of simulation studies and found to be robust when the available data set is large. However, uncertainties in the estimated parameter values can lead to errors in the inference, especially when the data set is small or there is insufficient divergence between the sequences. We introduce a Bayesian model comparison approach to infer whether the sequence as a whole contains sites at which the rate of nonsynonymous substitution is greater than the rate of synonymous substitution. We incorporated this probabilistic model comparison into a Bayesian approach to site-specific inference of positive selection. Using simulated sequences, we compared this approach to the commonly used empirical Bayes approach and investigated the effect of tree length on the performance of both methods. We found that the Bayesian approach outperforms the empirical Bayes method when the amount of sequence divergence is small and is less prone to false-positive inference when the sequences are saturated, while the results are indistinguishable for intermediate levels of sequence divergence.     

Bait-ER: A Bayesian method to detect targets of selection in Evolve-and-Resequence experiments

For over a decade, experimental evolution has been combined with high-throughput sequencing techniques. In so-called Evolve-and-Resequence (E&R) experiments, populations are kept in the laboratory under controlled experimental conditions where their genomes are sampled and allele frequencies monitored. However, identifying signatures of adaptation in E&R datasets is far from trivial, and it is still necessary to develop more efficient and statistically sound methods for detecting selection in genome-wide data. Here, we present Bait-ER – a fully Bayesian approach based on the Moran model of allele evolution to estimate selection coefficients from E&R experiments. The model has overlapping generations, a feature that describes several experimental designs found in the literature. We tested our method under several different demographic and experimental conditions to assess its accuracy and precision, and it performs well in most scenarios. Nevertheless, some care must be taken when analysing trajectories where drift largely dominates and starting frequencies are low. We compare our method with other available software and report that ours has generally high accuracy even for trajectories whose complexity goes beyond a classical sweep model. Furthermore, our approach avoids the computational burden of simulating an empirical null distribution, outperforming available software in terms of computational time and facilitating its use on genome-wide data. We implemented and released our method in a new open-source software package that can be accessed at https://doi.org/10.5281/zenodo.7351736 .     

The comparative method rules! Codon volatility cannot detect positive Darwinian selection using a single genome sequence

All established methods for detecting positive selection at the molecular level rely on comparisons between nucleotide sequences. An exceptional method that purports to detect selection on the basis of a single genomic sequence has recently been proposed. This method uses a measure called "codon volatility," defined for each codon as the ratio between the number of nonsynonymous codons that differ from the codon under study at a single nucleotide position and the number of sense codons that differ from the codon under study at a single nucleotide position. Here, we examine various properties of codon volatility and its derivatives and use simulation of evolutionary processes to determine whether they can be used to detect selective pressures. Codons for only four amino acids (glycine, leucine, arginine, and serine) show any variation in codon volatility. Thus, codon volatility is mainly a proxy for amino acid usage, rather than for codon usage, with 65% of all synonymous changes and 27% of all nonsynonymous changes being undetectable by this measure. Genes identified by the volatility method as being subject to positive selection tend to have idiosyncratic amino acid compositions (e.g., they are glycine rich or arginine poor). An additional property of codon volatility is the near zero variance of its mean expectation, which translates into overestimated statistical significance estimates, especially in the absence of corrections for multiple comparisons. A comparison with measures of selection inferred through comparative methodology reveals no relationship between the results of the two methods. Finally, we show that codon volatility can increase in the absence of positive Darwinian selection; that is, increased codon volatility is not indicative of positive selection.     

False-positive selection identified by ML-based methods: examples from the Sig1 gene of the diatom Thalassiosira weissflogii and the tax gene of a human T-cell lymphotropic virus

Sexually induced gene 1 (Sig1) in the centric diatom Thalassiosira weissflogii is considered to encode a gamete recognition protein. Sorhannus (2003) analyzed nucleotide sequences of Sig1 using parsimony analysis and the maximum-likelihood (ML)-based Bayesian method for inferring positive selection at single amino acid sites and reported that positively selected sites were detected by the latter method but not by the former. He then concluded that for this type of study, the ML-based method is more reliable than parsimony analysis. Here we show that his results apparently represent false-positive cases of the ML-based method and that there is no solid evidence that this gene contains positively selected sites. We further demonstrate that in the tax gene of human T-cell lymphotropic virus type I (HTLV-I), all codon sites, including invariable sites, can be inferred as positively selected sites by the ML-based method. These observations indicate that the ML-based method may produce many false-positive sites. One of the main reasons for the occurrence of false positives is that in the ML-based method, codon sites are grouped into several categories, with different nonsynonymous/synonymous rate ratios (omegas), on a purely statistical basis, and positive selection is inferred indirectly by examining whether the average omega for each category is greater than 1. In parsimony analysis, however, the evolutionary change of nucleotides at each codon site is examined. For this reason, parsimony-based methods rarely produce false positives and are safer than ML-based methods for detecting positive selection at individual codon sites, although a large number of sequences are necessary.     

Patterns of mutation and selection at synonymous sites in Drosophila

That natural selection affects molecular evolution at synonymous sites in protein-coding sequences is well established and is thought to predominantly reflect selection for translational efficiency/accuracy mediated through codon bias. However, a recently developed maximum likelihood framework, when applied to 18 coding sequences in 3 species of Drosophila, confirmed an earlier report that the Notch gene in Drosophila melanogaster was evolving under selection in favor of those codons defined as unpreferred in this species. This finding opened the possibility that synonymous sites may be subject to a variety of selective pressures beyond weak selection for increased frequencies of the codons currently defined as "preferred" in D. melanogaster. To further explore patterns of synonymous site evolution in Drosophila in a lineage-specific manner, we expanded the application of the maximum likelihood framework to 8,452 protein coding sequences with well-defined orthology in D. melanogaster, Drosophila sechellia, and Drosophila yakuba. Our analyses reveal intragenomic and interspecific variation in mutational patterns as well as in patterns and intensity of selection on synonymous sites. In D. melanogaster, our results provide little statistical evidence for recent selection on synonymous sites, and Notch remains an outlier. In contrast, in D. sechellia our findings provide evidence in support of selection predominantly in favor of preferred codons. However, there is a small subset of genes in this species that appear to be evolving under selection in favor of unpreferred codons, which indicates that selection on synonymous sites is not limited to the preferential fixation of mutations that enhance the speed or accuracy of translation in this species.