Estimates of the average strength of natural selection are not inflated by sampling error or publication bias

Kingsolver et al.'s review of phenotypic selection gradients from natural populations provided a glimpse of the form and strength of selection in nature and how selection on different organisms and traits varies. Because this review's underlying database could be a key tool for answering fundamental questions concerning natural selection, it has spawned discussion of potential biases inherent in the review process. Here, we explicitly test for two commonly discussed sources of bias: sampling error and publication bias. We model the relationship between variance among selection gradients and sample size that sampling error produces by subsampling large empirical data sets containing measurements of traits and fitness. We find that this relationship was not mimicked by the review data set and therefore conclude that sampling error does not bias estimations of the average strength of selection. Using graphical tests, we find evidence for bias against publishing weak estimates of selection only among very small studies (N<38). However, this evidence is counteracted by excess weak estimates in larger studies. Thus, estimates of average strength of selection from the review are less biased than is often assumed. Devising and conducting straightforward tests for different biases allows concern to be focused on the most troublesome factors.     

Statistical analysis of pathogenicity of somatic mutations in cancer

Recent large-scale sequencing studies have revealed that cancer genomes contain variable numbers of somatic point mutations distributed across many genes. These somatic mutations most likely include passenger mutations that are not cancer causing and pathogenic driver mutations in cancer genes. Establishing a significant presence of driver mutations in such data sets is of biological interest. Whereas current techniques from phylogeny are applicable to large data sets composed of singly mutated samples, recently exemplified with a p53 mutation database, methods for smaller data sets containing individual samples with multiple mutations need to be developed. By constructing distinct models of both the mutation process and selection pressure upon the cancer samples, exact statistical tests to examine this problem are devised. Tests to examine the significance of selection toward missense, nonsense, and splice site mutations are derived, along with tests assessing variation in selection between functional domains. Maximum-likelihood methods facilitate parameter estimation, including levels of selection pressure and minimum numbers of pathogenic mutations. These methods are illustrated with 25 breast cancers screened across the coding sequences of 518 kinase genes, revealing 90 base substitutions in 71 genes. Significant selection pressure upon truncating mutations was established. Furthermore, an estimated minimum of 29.8 mutations were pathogenic.     

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.     

Recent progress in polymorphism-based population genetic inference

The recent availability of whole-genome sequencing data affords tremendous power for statistical inference. With this, there has been great interest in the development of polymorphism-based approaches for the estimation of population genetic parameters. These approaches seek to estimate, for example, recently fixed or sweeping beneficial mutations, the rate of recurrent positive selection, the distribution of selection coefficients, and the demographic history of the population. Yet despite estimating similar parameters using similar data sets, results between methodologies are far from consistent. We here summarize the current state of the field, compare existing approaches, and attempt to reconcile emerging discrepancies. We also discuss the biases in selection estimators introduced by ignoring the demographic history of the population, discuss the biases in demographic estimators introduced by assuming neutrality, and highlight the important challenge to the field of achieving a true joint estimation procedure to circumvent these confounding effects.     

Multiple hypothesis testing to detect lineages under positive selection that affects only a few sites

Detection of positive Darwinian selection has become ever more important with the rapid growth of genomic data sets. Recent branch-site models of codon substitution account for variation of selective pressure over branches on the tree and across sites in the sequence and provide a means to detect short episodes of molecular adaptation affecting just a few sites. In likelihood ratio tests based on such models, the branches to be tested for positive selection have to be specified a priori. In the absence of a biological hypothesis to designate so-called foreground branches, one may test many branches, but a correction for multiple testing becomes necessary. In this paper, we employ computer simulation to evaluate the performance of 6 multiple test correction procedures when the branch-site models are used to test every branch on the phylogeny for positive selection. Four of the methods control the familywise error rates (FWERs), whereas the other 2 control the false discovery rate (FDR). We found that all correction procedures achieved acceptable FWER except for extremely divergent sequences and serious model violations, when the test may become unreliable. The power of the test to detect positive selection is influenced by the strength of selection and the sequence divergence, with the highest power observed at intermediate divergences. The 4 correction procedures that control the FWER had similar power. We recommend Rom's procedure for its slightly higher power, but the simple Bonferroni correction is useable as well. The 2 correction procedures that control the FDR had slightly more power and also higher FWER. We demonstrate the multiple test procedures by analyzing gene sequences from the extracellular domain of the cluster of differentiation 2 (CD2) gene from 10 mammalian species. Both our simulation and real data analysis suggest that the multiple test procedures are useful when multiple branches have to be tested on the same data set.     

Multidimensional vector space representation for convergent evolution and molecular phylogeny

With growing amounts of genome data and constant improvement of models of molecular evolution, phylogenetic reconstruction became more reliable. However, our knowledge of the real process of molecular evolution is still limited. When enough large-sized data sets are analyzed, any subtle biases in statistical models can support incorrect topologies significantly because of the high signal-to-noise ratio. We propose a procedure to locate sequences in a multidimensional vector space (MVS), in which the geometry of the space is uniquely determined in such a way that the vectors of sequence evolution are orthogonal among different branches. In this paper, the MVS approach is developed to detect and remove biases in models of molecular evolution caused by unrecognized convergent evolution among lineages or unexpected patterns of substitutions. Biases in the estimated pairwise distances are identified as deviations (outliers) of sequence spatial vectors from the expected orthogonality. Modifications to the estimated distances are made by minimizing an index to quantify the deviations. In this way, it becomes possible to reconstruct the phylogenetic tree, taking account of possible biases in the model of molecular evolution. The efficacy of the modification procedure was verified by simulating evolution on various topologies with rate heterogeneity and convergent change. The phylogeny of placental mammals in previous analyses of large data sets has varied according to the genes being analyzed. Systematic deviations caused by convergent evolution were detected by our procedure in all representative data sets and were found to strongly affect the tree structure. However, the bias correction yielded a consistent topology among data sets. The existence of strong biases was validated by examining the sites of convergent evolution between the hedgehog and other species in mitochondrial data set. This convergent evolution explains why it has been difficult to determine the phylogenetic placement of the hedgehog in previous studies.     

Contrasting the efficacy of selection on the X and autosomes in Drosophila

To investigate the relative efficacy of both positive and purifying natural selection on the X chromosome and the autosomes in Drosophila, we compared rates and patterns of molecular evolution between these chromosome sets using the newly available alignments of orthologous genes from 12 species. Parameters that may influence the relative X versus autosomal substitution rates include the relative effective population sizes, the male and female germline mutation rates, the distribution of allelic effects on fitness, and the degree of dominance of novel mutations. Our analysis reveals that codon usage bias is consistently greater for X-linked genes, suggesting that purifying selection consistently has greater efficacy on the X chromosome than on the autosomes across the Drosophila phylogeny. However, our results are less consistent with respect to the efficacy of positive selection, with only some lineages showing a higher substitution rate on the X chromosome. This suggests that either the distribution of selective effects of mutations or other relevant parameters are sufficiently variable across species to tip the balance in different ways in individual lineages. These data suggest that rates of substitution are not solely governed by adaptive evolution. This genome-wide analysis provides a clear picture that the efficacy of selection varies intragenomically and that this effect is markedly more consistent across the phylogeny in the case of purifying selection. Our results also suggest that simple models that predict systematic differences in rates of evolution between the X and the autosomes can only be made to be compatible with these Drosophila data if the relevant population genetic parameters that drive substitution rates differ among species and chromosomal contexts.     

Variable strength of translational selection among 12 Drosophila species

Codon usage bias in Drosophila melanogaster genes has been attributed to negative selection of those codons whose cellular tRNA abundance restricts rates of mRNA translation. Previous studies, which involved limited numbers of genes, can now be compared against analyses of the entire gene complements of 12 Drosophila species whose genome sequences have become available. Using large numbers (6138) of orthologs represented in all 12 species, we establish that the codon preferences of more closely related species are better correlated. Differences between codon usage biases are attributed, in part, to changes in mutational biases. These biases are apparent from the strong correlation (r = 0.92, P < 0.001) among these genomes' intronic G + C contents and exonic G + C contents at degenerate third codon positions. To perform a cross-species comparison of selection on codon usage, while accounting for changes in mutational biases, we calibrated each genome in turn using the codon usage bias indices of highly expressed ribosomal protein genes. The strength of translational selection was predicted to have varied between species largely according to their phylogeny, with the D. melanogaster group species exhibiting the strongest degree of selection.     

Estimating the distribution of selection coefficients from phylogenetic data with applications to mitochondrial and viral DNA

The distribution of selection coefficients of new mutations is of key interest in population genetics. In this paper we explore how codon-based likelihood models can be used to estimate the distribution of selection coefficients of new amino acid replacement mutations from phylogenetic data. To obtain such estimates we assume that all mutations at the same site have the same selection coefficient. We first estimate the distribution of selection coefficients from two large viral data sets under the assumption that the viral population size is the same along all lineages of the phylogeny and that the selection coefficients vary among sites. We then implement several new models in which the lineages of the phylogeny may have different population sizes. We apply the new models to a data set consisting of the coding regions from eight primate mitochondrial genomes. The results suggest that there might be little power to determine the exact shape of the distribution of selection coefficient but that the normal and gamma distributions fit the data significantly better than the exponential distribution.     

Evaluation of an improved branch-site likelihood method for detecting positive selection at the molecular level

Detecting positive Darwinian selection at the DNA sequence level has been a subject of considerable interest. However, positive selection is difficult to detect because it often operates episodically on a few amino acid sites, and the signal may be masked by negative selection. Several methods have been developed to test positive selection that acts on given branches (branch methods) or on a subset of sites (site methods). Recently, Yang, Z., and R. Nielsen (2002. Codon-substitution models for detecting molecular adaptation at individual sites along specific lineages. Mol. Biol. Evol. 19:908-917) developed likelihood ratio tests (LRTs) based on branch-site models to detect positive selection that affects a small number of sites along prespecified lineages. However, computer simulations suggested that the tests were sensitive to the model assumptions and were unable to distinguish between relaxation of selective constraint and positive selection (Zhang, J. 2004. Frequent false detection of positive selection by the likelihood method with branch-site models. Mol. Biol. Evol. 21:1332-1339). Here, we describe a modified branch-site model and use it to construct two LRTs, called branch-site tests 1 and 2. We applied the new tests to reanalyze several real data sets and used computer simulation to examine the performance of the two tests by examining their false-positive rate, power, and robustness. We found that test 1 was unable to distinguish relaxed constraint from positive selection affecting the lineages of interest, while test 2 had acceptable false-positive rates and appeared robust against violations of model assumptions. As test 2 is a direct test of positive selection on the lineages of interest, it is referred to as the branch-site test of positive selection and is recommended for use in real data analysis. The test appeared conservative overall, but exhibited better power in detecting positive selection than the branch-based test. Bayes empirical Bayes identification of amino acid sites under positive selection along the foreground branches was found to be reliable, but lacked power.     

Animal Mitochondria,Positive Selection and Cyto-Nuclear Coevolution: Insights from Pulmonates

Pulmonate snails have remarkably high levels of mtDNA polymorphism within species and divergence between species, making them an interesting group for the study of mutation and selection on mitochondrial genomes. The availability of sequence data from most major lineages – collected largely for studies of phylogeography - provides an opportunity to perform several tests of selection that may provide general insights into the evolutionary forces that have produced this unusual pattern. Several protein coding mtDNA datasets of pulmonates were analyzed towards this direction. Two different methods for the detection of positive selection were used, one based on phylogeny, and the other on the McDonald-Kreitman test. The cyto-nuclear coevolution hypothesis, often implicated to account for the high levels of mtDNA divergence of some organisms, was also addressed by assessing the divergence pattern exhibited by a nuclear gene. The McDonald-Kreitman test indicated multiple signs of positive selection in the mtDNA genes, but was significantly biased when sequence divergence was high. The phylogenetic method identified five mtDNA datasets as affected by positive selection. In the nuclear gene, the McDonald-Kreitman test provided no significant results, whereas the phylogenetic method identified positive selection as likely present. Overall, our findings indicate that: 1) slim support for the cyto-nuclear coevolution hypothesis is present, 2) the elevated rates of mtDNA polymorphims and divergence in pulmonates do not appear to be due to pervasive positive selection, 3) more stringent tests show that spurious positive selection is uncovered when distant taxa are compared and 4) there are significant examples of positive selection acting in some cases, so it appears that mtDNA evolution in pulmonates can escape from strict deleterious evolution suggested by the Muller’s ratchet effect.     

Phylogeny of the Oriental Drosophila melanogaster species group: a multilocus reconstruction

The melanogaster species group of Drosophila (subgenus Sophophora) has long been a favored model for evolutionary studies because of its morphological and ecological diversity and wide geographic distribution. However, phylogenetic relationships among species and subgroups within this lineage are not well understood. We reconstructed the phylogeny of 17 species representing 7 "oriental" species subgroups, which are especially closely related to D. melanogaster. We used DNA sequences of four nuclear and two mitochondrial loci in an attempt to obtain the best possible estimate of species phylogeny and to assess the extent and sources of remaining uncertainties. Comparison of trees derived from single-gene data sets allowed us to identify several strongly supported clades, which were also consistently seen in combined analyses. The relationships among these clades are less certain. The combined data set contains data partitions that are incongruent with each other. Trees reconstructed from the combined data set and from internally homogenous data sets consisting of three or four genes each differ at several deep nodes. The total data set tree is fully resolved and strongly supported at most nodes. Statistical tests indicated that this tree is compatible with all individual and combined data sets. Therefore, we accepted this tree as the most likely model of historical relationships. We compared the new molecular phylogeny to earlier estimates based on morphology and chromosome structure and discuss its taxonomic and evolutionary implications.     

A phylogenomics approach for selecting robust sets of phylogenetic markers

Reconstructing the evolutionary relationships of species is a major goal in biology. Despite the increasing number of completely sequenced genomes, a large number of phylogenetic projects rely on targeted sequencing and analysis of a relatively small sample of marker genes. The selection of these phylogenetic markers should ideally be based on accurate predictions of their combined, rather than individual, potential to accurately resolve the phylogeny of interest. Here we present and validate a new phylogenomics strategy to efficiently select a minimal set of stable markers able to reconstruct the underlying species phylogeny. In contrast to previous approaches, our methodology does not only rely on the ability of individual genes to reconstruct a known phylogeny, but it also explores the combined power of sets of concatenated genes to accurately infer phylogenetic relationships of species not previously analyzed. We applied our approach to two broad sets of cyanobacterial and ascomycetous fungal species, and provide two minimal sets of six and four genes, respectively, necessary to fully resolve the target phylogenies. This approach paves the way for the informed selection of phylogenetic markers in the effort of reconstructing the tree of life.     

A likelihood approach to estimating phylogeny from discrete morphological character data

Evolutionary biologists have adopted simple likelihood models for purposes of estimating ancestral states and evaluating character independence on specified phylogenies; however, for purposes of estimating phylogenies by using discrete morphological data, maximum parsimony remains the only option. This paper explores the possibility of using standard, well-behaved Markov models for estimating morphological phylogenies (including branch lengths) under the likelihood criterion. An important modification of standard Markov models involves making the likelihood conditional on characters being variable, because constant characters are absent in morphological data sets. Without this modification, branch lengths are often overestimated, resulting in potentially serious biases in tree topology selection. Several new avenues of research are opened by an explicitly model-based approach to phylogenetic analysis of discrete morphological data, including combined-data likelihood analyses (morphology + sequence data), likelihood ratio tests, and Bayesian analyses.     

Phylogenetic models and model selection for noncoding DNA

Awareness of the complex structure and evolutionary dynamics of noncoding DNA has improved both noncoding sequence alignment and the use of microstructural changes as characters in phylogenetic analysis. The next step is to consider improvements in the use and selection of phylogenetic models for noncoding sequence data. Models of character evolution are central to phylogeny estimation, but the use of an inadequate model can mislead topology selection and branch length estimations. This is particularly likely when sequence divergence is either limited (nearly invariable, as in population-level or species-level studies) or extreme (nearly saturated, as in deep-level studies that focus on conserved secondary structures). Noncoding data sets are often at these extremes, and they can be particularly awkward for model definition and model selection. This paper introduces the goals of model use in phylogenetics and identifies ten issues that arise from the application of models to noncoding sequence data. It is concluded that most of these issues derive from small data set sizes, very low or very high sequence variability, limitations of current phylogenetic models, and possibly character definition and nonindependence. Recommendations are made that should help to improve alignment, character quality, model selection, and phylogeny estimation based on noncoding sequence data.     

Does choice in model selection affect maximum likelihood analysis?

In order to have confidence in model-based phylogenetic analysis, the model of nucleotide substitution adopted must be selected in a statistically rigorous manner. Several model-selection methods are applicable to maximum likelihood (ML) analysis, including the hierarchical likelihood-ratio test (hLRT), Akaike information criterion (AIC), Bayesian information criterion (BIC), and decision theory (DT), but their performance relative to empirical data has not been investigated thoroughly. In this study, we use 250 phylogenetic data sets obtained from TreeBASE to examine the effects that choice in model selection has on ML estimation of phylogeny, with an emphasis on optimal topology, bootstrap support, and hypothesis testing. We show that the use of different methods leads to the selection of two or more models for approximately 80% of the data sets and that the AIC typically selects more complex models than alternative approaches. Although ML estimation with different best-fit models results in incongruent tree topologies approximately 50% of the time, these differences are primarily attributable to alternative resolutions of poorly supported nodes. Furthermore, topologies and bootstrap values estimated with ML using alternative statistically supported models are more similar to each other than to topologies and bootstrap values estimated with ML under the Kimura two-parameter (K2P) model or maximum parsimony (MP). In addition, Swofford-Olsen-Waddell-Hillis (SOWH) tests indicate that ML trees estimated with alternative best-fit models are usually not significantly different from each other when evaluated with the same model. However, ML trees estimated with statistically supported models are often significantly suboptimal to ML trees made with the K2P model when both are evaluated with K2P, indicating that not all models perform in an equivalent manner. Nevertheless, the use of alternative statistically supported models generally does not affect tests of monophyletic relationships under either the Shimodaira-Hasegawa (S-H) or SOWH methods. Our results suggest that although choice in model selection has a strong impact on optimal tree topology, it rarely affects evolutionary inferences drawn from the data because differences are mainly confined to poorly supported nodes. Moreover, since ML with alternative best-fit models tends to produce more similar estimates of phylogeny than ML under the K2P model or MP, the use of any statistically based model-selection method is vastly preferable to forgoing the model-selection process altogether.     

AffyTrees: facilitating comparative analysis of Affymetrix plant microarray chips

Microarrays measure the expression of large numbers of genes simultaneously and can be used to delve into interaction networks involving many genes at a time. However, it is often difficult to decide to what extent knowledge about the expression of genes gleaned in one model organism can be transferred to other species. This can be examined either by measuring the expression of genes of interest under comparable experimental conditions in other species, or by gathering the necessary data from comparable microarray experiments. However, it is essential to know which genes to compare between the organisms. To facilitate comparison of expression data across different species, we have implemented a Web-based software tool that provides information about sequence orthologs across a range of Affymetrix microarray chips. AffyTrees provides a quick and easy way of assigning which probe sets on different Affymetrix chips measure the expression of orthologous genes. Even in cases where gene or genome duplications have complicated the assignment, groups of comparable probe sets can be identified. The phylogenetic trees provide a resource that can be used to improve sequence annotation and detect biases in the sequence complement of Affymetrix chips. Being able to identify sequence orthologs and recognize biases in the sequence complement of chips is necessary for reliable cross-species microarray comparison. As the amount of work required to generate a single phylogeny in a nonautomated manner is considerable, AffyTrees can greatly reduce the workload for scientists interested in large-scale cross-species comparisons.     

A chloroplast DNA phylogeny of eastern Phlox (Polemoniaceae): implications of congruence and incongruence with the ITS phylogeny

The comparison of independent phylogenies is a valuable approach to the study of evolutionary pattern and process. Available data on eastern North American Phlox, including our recent ITS phylogeny, suggest that relationships are complicated in the group and that hybridization may have been a contributing factor. We used restriction site data from the chloroplast genome to develop a second phylogeny for eastern Phlox. Sampling was the same as that for the ITS study and consisted of 79 samples (including all 22 eastern Phlox species and most eastern subspecies, as well as multiple populations of many taxa). The resulting cpDNA phylogeny agrees with the ITS phylogeny in many respects, strengthening earlier conclusions. Nevertheless, incongruence between the trees is noteworthy: many samples, particularly of members of the P. pilosa and P. glaberrima complexes, are placed in different clades. A variety of tests were carried out to assess congruence in terms of topological patterns, character congruence, and homogeneity of data sets. Significant conflict between the phylogenies is discussed in light of the hypothesis that hybridization has affected relationships in this genus.     

An empirical assessment of long-branch attraction artefacts in deep eukaryotic phylogenomics

In the context of exponential growing molecular databases, it becomes increasingly easy to assemble large multigene data sets for phylogenomic studies. The expected increase of resolution due to the reduction of the sampling (stochastic) error is becoming a reality. However, the impact of systematic biases will also become more apparent or even dominant. We have chosen to study the case of the long-branch attraction artefact (LBA) using real instead of simulated sequences. Two fast-evolving eukaryotic lineages, whose evolutionary positions are well established, microsporidia and the nucleomorph of cryptophytes, were chosen as model species. A large data set was assembled (44 species, 133 genes, and 24,294 amino acid positions) and the resulting rooted eukaryotic phylogeny (using a distant archaeal outgroup) is positively misled by an LBA artefact despite the use of a maximum likelihood-based tree reconstruction method with a complex model of sequence evolution. When the fastest evolving proteins from the fast lineages are progressively removed (up to 90%), the bootstrap support for the apparently artefactual basal placement decreases to virtually 0%, and conversely only the expected placement, among all the possible locations of the fast-evolving species, receives increasing support that eventually converges to 100%. The percentage of removal of the fastest evolving proteins constitutes a reliable estimate of the sensitivity of phylogenetic inference to LBA. This protocol confirms that both a rich species sampling (especially the presence of a species that is closely related to the fast-evolving lineage) and a probabilistic method with a complex model are important to overcome the LBA artefact. Finally, we observed that phylogenetic inference methods perform strikingly better with simulated as opposed to real data, and suggest that testing the reliability of phylogenetic inference methods with simulated data leads to overconfidence in their performance. Although phylogenomic studies can be affected by systematic biases, the possibility of discarding a large amount of data containing most of the nonphylogenetic signal allows recovering a phylogeny that is less affected by systematic biases, while maintaining a high statistical support.     

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.