Correlation Between Ka/Ks and Ks is Related to Substitution Model and Evolutionary Lineage

In 2005, Wyckoff and coworkers described a surprisingly strong correlation between Ka/Ks and Ks in several data sets using the LPB93 algorithm. This finding indicated the possibility of a paradigm shift in the way selection strength can be measured using the Ka/Ks ratio. We carried out a calculation of Ka and Ks using six different algorithms on three cross-species orthologous data sets and found a highly variable correlation among the algorithms and lineages. Algorithms based on the GY-HKY substitution model exhibit a weaker positive correlation or a stronger negative correlation than those based on the K2P and JC69 substitution model. Even if one algorithm shows a positive correlation between Ka/Ks and Ks in a warm-blooded lineage, it may show no correlation in a cold-blooded lineage. This algorithm-related and evolutionary lineage-related correlation indicates the need for great caution in drawing conclusions when using only one Ka and Ks algorithm in a genomewide analysis of selection strength. Our results indicated that currently used algorithms for Ka and Ks calculations are flawed and need improvements.     

Molecular evolution of an imprinted gene: repeatability of patterns of evolution within the mammalian insulin-like growth factor type II receptor.

The repeatability of patterns of variation in Ka/Ks and Ks is expected if such patterns are the result of deterministic forces. We have contrasted the molecular evolution of the mammalian insulin-like growth factor type II receptor (Igf2r) in the mouse-rat comparison with that in the human-cow comparison. In so doing, we investigate explanations for both the evolution of genomic imprinting and for Ks variation (and hence putatively for mutation rate evolution). Previous analysis of Igf2r, in the mouse-rat comparison, found Ka/Ks patterns that were suggested to be contrary to those expected under the conflict theory of imprinting. We find that Ka/Ks variation is repeatable and hence confirm these patterns. However, we also find that the molecular evolution of Igf2r signal sequences suggests that positive selection, and hence conflict, may be affecting this region. The variation in Ks across Igf2r is also repeatable. To the best of our knowledge this is the first demonstration of such repeatability. We consider three explanations for the variation in Ks across the gene: (1) that it is the result of mutational biases, (2) that it is the result of selection on the mutation rate, and (3) that it is the product of selection on codon usage. Explanations 2 and 3 predict a Ka-Ks correlation, which is not found. Explanation 3 also predicts a negative correlation between codon bias and Ks, which is also not found. However, in support of explanation 1 we do find that in rodents the rate of silent C --> T mutations at CpG sites does covary with Ks, suggesting that methylation-induced mutational patterns can explain some of the variation in Ks. We find evidence to suggest that this CpG effect is due to both variation in CpG density, and to variation in the frequency with which CpGs mutate. Interestingly, however, a GC4 analysis shows no covariance with Ks, suggesting that to eliminate methyl-associated effects CpG rates themselves must be analyzed. These results suggest that, in contrast to previous studies of intragenic variation, Ks patterns are not simply caused by the same forces responsible for Ka/Ks correlations.     

Patterns of divergence among conifer ESTs and polymorphism in Pinus sylvestris identify putative selective sweeps

Finding genes that are under positive selection is a difficult task, especially in non-model organisms. Here, we have analyzed expressed sequence tag (EST) data from 4 species (Pinus pinaster, Pinus taeda, Picea glauca, and Pseudotsuga menziesii) to investigate selection patterns during their evolution and to identify genes likely to be under positive selection. To confirm selection, population samples of these genes have been sequenced in Pinus sylvestris, a species that was not included in the EST data set. The estimates of branch-specific Ka/Ks (nonsynonymous/synonymous substitution rates) across all genes in the EST data set were similar or smaller than estimates from other higher plant species. There was no evidence for the traditional indication of positive selection, Ka/Ks above 1. However, several lines of evidence based on polymorphism patterns suggest that genes with high Ka/Ks (0.20-0.52) in the EST data set are in fact more affected by positive selection in P. sylvestris than genes with low Ka/Ks (0.01-0.04). The high Ka/Ks genes have a lower level of polymorphism and more negative Tajima's D than the low Ka/Ks genes. Further, in the high Ka/Ks group, the Hudson-Kreitman-Aguade test is significant. This suggests that the EST data set is a good starting point for finding genes under positive selection in conifers and that even moderate Ka/Ks values could be indicative of selection. A group of 5 genes with high Ka/Ks collectively show evidence for positive selection within P. sylvestris.     

Selective constraints in cold‐region wild boars may defuse the effects of small effective population size on molecular evolution of mitogenomes

Spatial range expansion during population colonization is characterized by demographic events that may have significant effects on the efficiency of natural selection. Population genetics suggests that genetic drift brought by small effective population size (N_e) may undermine the efficiency of selection, leading to a faster accumulation of nonsynonymous mutations. However, it is still unknown whether this effect might be balanced or even reversed by strong selective constraints. Here, we used wild boars and local domestic pigs from tropical (Vietnam) and subarctic region (Siberia) as animal model to evaluate the effects of functional constraints and genetic drift on shaping molecular evolution. The likelihood‐ratio test revealed that Siberian clade evolved significantly different from Vietnamese clades. Different datasets consistently showed that Siberian wild boars had lower Ka/Ks ratios than Vietnamese samples. The potential role of positive selection for branches with higher Ka/Ks was evaluated using branch‐site model comparison. No signal of positive selection was found for the higher Ka/Ks in Vietnamese clades, suggesting the interclade difference was mainly due to the reduction in Ka/Ks for Siberian samples. This conclusion was further confirmed by the result from a larger sample size, among which wild boars from northern Asia (subarctic and nearby region) had lower Ka/Ks than those from southern Asia (temperate and tropical region). The lower Ka/Ks might be due to either stronger functional constraints, which prevent nonsynonymous mutations from accumulating in subarctic wild boars, or larger N_e in Siberian wild boars, which can boost the efficacy of purifying selection to remove functional mutations. The latter possibility was further ruled out by the Bayesian skyline plot analysis, which revealed that historical N_e of Siberian wild boars was smaller than that of Vietnamese wild boars. Altogether, these results suggest stronger functional constraints acting on mitogenomes of subarctic wild boars, which may provide new insights into their local adaptation of cold resistance.     

Expected Relationship Between the Silent Substitution Rate and the GC Content: Implications for the Evolution of Isochores

The relationship between the silent substitution rate (K _s) and the GC content along the genome is a focal point of the debate about the origin of the isochore structure in vertebrates. Recent estimation of the silent substitution rate showed a positive correlation between K _s and GC content, in contradiction with the predictions of both the regional mutation bias model and the selection or biased gene conversion model. The aim of this paper is to help resolve this contradiction between theoretical studies and data. We analyzed the relationship between K _s and GC content under (1) uniform mutation bias, (2) a regional mutation bias, and (3) mutation bias and selection. We report that an increase in K _s with GC content is expected under mutation bias because of either nonequilibrium of the isochore structure or an increasing mutation rate from AT toward GC nucleotides in GC-richer isochores. We show by simulations that CpG deamination tends to increase the mutation rate with GC content in a regional mutation bias model. We also demonstrate that the relationship between K _s and GC under the selectionist or biased gene conversion model is positive under weak selection if the mutation selection equilibrium GC frequency is less than 0.5. Received: 28 March 2001 / Accepted: 16 May 2001     

Average allozyme heterozygosity in vertebrates correlates with Ka/Ks measured in the human-mouse lineage

It is well established that different allozyme proteins vary in heterozygosity in averages made over large numbers of species. For example, the enzyme 6-phosphogluconate dehydrogenase has a much higher average heterozygosity than glutamate dehydrogenase. Allozyme data alone provide insufficient power to determine the evolutionary cause of such a difference. Many studies have now been carried out on the DNA sequences coding for allozymes. These have identified diverse selective and nonselective causes of polymorphisms at individual loci. However the studies are mainly in a small number of model species; thus, it is difficult to identify from these DNA studies specific causes of global average heterozygosity differences among allozyme proteins. Here we demonstrate that estimates of average heterozygosity for 37 allozyme proteins in vertebrates correlate positively with Ka and Ka/Ks but not with Ks, measured in the human-mouse lineage. The values of Ka/Ks are less than 0.25, and Ka/Ks is negatively correlated with subunit number (quaternary structure), a measure of structural constraint. Proteins with lower levels of constraint have higher values of both Ka/Ks and heterozygosity. These results better support the hypothesis that differences in average allozyme diversity between proteins are more closely related to differences in the level of purifying selection than to differences in the underlying mutation rate or level of positive selection.     

Positive selection and the molecular evolution of a gene of male reproduction, Acp26Aa of Drosophila

The gene for a male ejaculatory protein, Acp26Aa, in four sibling species of the Drosophila melanogaster subgroup has previously been shown to have a nonsynonymous rate (Ka) of nucleotide substitution that is indistinguishable from the synonymous rate (Ks). By examining this gene in two other species of this subgroup, we found that Ka is generally large and can sometimes be more than twice as large as Ks. This suggests that positive selection may be operating at this locus of male reproduction.      

SRY基因在人猿超科和旧大陆猴中具有不同的进化规律

通过ＰＣＲ扩增、测序,得到了白臀叶猴和红面猴的ＳＲＹ基因全序列。结合现有的灵长类其他物种序列进行分析,验证了ＨＭＧ盒的保守性。通过构建系统发育树,比较旧大陆猴和人猿超科两个类群内和类群间ＨＭＧ盒侧翼序列Ｋａ／Ｋｓ的比率。有趣的是,人猿超科两物种比较呈现较高的Ｋａ／Ｋｓ比值,但在旧大陆猴中及旧大陆猴与狨猴间的Ｋａ／Ｋｓ比值显著低于人猿超科的,呈现很不同的格局。同时,对于ＨＭＧ盒序列,Ｋａ／Ｋｓ比值在     

Analysis of the phylogenetic distribution of isochores in vertebrates and a test of the thermal stability hypothesis

Warm-blooded vertebrates show large-scale variation in G + C content along their chromosomes, a pattern which appears to be largely absent from cold-blooded vertebrates. However, compositional variation in poikilotherms has generally been studied by ultracentrifugation rather than sequence analysis. In this paper, we investigate the compositional properties of coding sequences from a broad range of vertebrate poikilotherms using DNA sequence analysis. We find that on average poikilotherms have lower third-codon position GC contents (GC3) than homeotherms but that some poikilotherms have higher mean GC3 values. We find that most poikilotherms have lower variation in GC3 than homeotherms but that there is a correlation between GC12 and GC3 for some species, indicating that there is systematic variation in base composition across their genomes. We also demonstrate that the GC3 of genes in the zebrafish, Danio rerio, is correlated with that in humans, suggesting that vertebrates share a basic isochore structure. However, we find no correlation between either the mean GC3 or the standard deviation in GC3 and body temperature.     

Maximum likelihood of evolutionary trees: hardness and approximation

MOTIVATION: Maximum likelihood (ML) is an increasingly popular optimality criterion for selecting evolutionary trees. Yet the computational complexity of ML was open for over 20 years, and only recently resolved by the authors for the Jukes-Cantor model of substitution and its generalizations. It was proved that reconstructing the ML tree is computationally intractable (NP-hard). In this work we explore three directions, which extend that result. RESULTS: (1) We show that ML under the assumption of molecular clock is still computationally intractable (NP-hard). (2) We show that not only is it computationally intractable to find the exact ML tree, even approximating the logarithm of the ML for any multiplicative factor smaller than 1.00175 is computationally intractable. (3) We develop an algorithm for approximating log-likelihood under the condition that the input sequences are sparse. It employs any approximation algorithm for parsimony, and asymptotically achieves the same approximation ratio. We note that ML reconstruction for sparse inputs is still hard under this condition, and furthermore many real datasets satisfy it.     

A new method for estimating nonsynonymous substitutions and its applications to detecting positive selection

The standard methods for computing the number of nonsynonymous substitutions (Ka) lump all amino acid changes into one single class, even though their rates of substitution vary by at least 10-fold (Tang et al., 2004). Classifying these changes by their physicochemical properties has not been suitably effective in isolating the fastest evolving classes of changes. We now propose to use the Universal index U of Tang et al. (2004) to classify the 75 elementary amino acid changes (codons differing by 1 bp) by their evolutionary exchangeability. Let Ki denote the Ka value of each class (i = 1, ..., 75 from the most to the least exchangeable). The cumulative Ki for the top 10 classes, denoted Kh (for high-exchangeability types), has two important properties: (1) Kh usually accounts for 25%-30% of total amino acid changes and (2) when the observed number of amino acid substitutions is large, Kh is predictably twice the value of Ka. This shall be referred to as the twofold approximation. The new method for estimating Kh is applied to the comparisons between human and macaque and between mouse and rat. The twofold approximation holds well in these data sets, and the signature of positive selection can be more easily discerned using the Kh statistic than using Ka. Many genes with Ka/Ks > 0.5 can now be shown to have Kh/Ks > 1 and to have evolved adaptively, at least for the high-exchangeability group of amino acid changes.     

Evaluation of six methods for estimating synonymous and nonsynonymous substitution rates

Methods for estimating synonymous and nonsynonymous substitution rates among protein-coding sequences adopt different mutation （substitution） models with subtle yet significant differences, which lead to different estimates of evolutionary information. Little attention has been devoted to the comparison of methods for obtaining reliable estimates since the amount of sequence variations within targeted datasets is always unpredictable. To our knowledge, there is little information available in literature about evaluation of these different methods. In this study, we compared six widely used methods and provided with evaluation results using simulated sequences. The results indicate that incorporating sequence features （such as transition/transversion bias and nucleotide/codon frequency bias） into methods could yield better performance. We recommend that conclusions related to or derived from Ka and Ks analyses should not be readily drawn only according to results from one method.     

Comparison of three methods for estimating rates of synonymous and nonsynonymous nucleotide substitutions

Three frequently used methods for estimating the synonymous and nonsynonymous substitution rates (Ks and Ka) were evaluated and compared for their accuracies; these methods are denoted by LWL85, LPB93, and GY94, respectively. For this purpose, we used a codon-evolution model to obtain the expected Ka and Ks values for the above three methods and compared the values with those obtained by the three methods. We also proposed some modifications of LWL85 and LPB93 to increase their accuracies. Our computer simulations under the codon-evolution model showed that for sequences < or =300 codons, the performance of GY94 may not be reliable. For longer sequences, GY94 is more accurate for estimating the Ka/Ks ratio than the modified LPB93 and LWL85 in the majority of the cases studied. This is particularly so when k > or = 3, which is the transition/transversion (mutation) rate ratio. However, when k is approximately 2 and when the sequence divergence is relatively large, the modified LWL85 performed better than GY94 and the modified LPB93. The inferiority of LPB93 to LWL85 is surprising because LPB93 was intended to improve LWL85. Also, it has been thought that the codon-based method of GY94 is better than the heuristic method of LWL85, but our simulation results showed that in many cases, the opposite was true, even though our simulation was based on the codon-evolution model.     

Positive selection signatures in the TLR7 family

While adaptive immunity genes evolve rapidly under the influence of positive selection, innate immune system genes are known to evolve slowly due to strong purifying selection. Among the sensors of the innate immune system, Toll-like receptors (TLRs) are particularly important due to their ability to recognize and respond to pathogen-associated molecular patterns (PAMP), such as lipopolysaccharides, peptidoglycans, and nucleic acids from bacteria or viruses. In the present study, we examine the evolutionary process that has operated on the TLR7 family genes TLR7, TLR8, and TLR9. The results demonstrate that the average Ka/Ks (the ratio between nonsynonymous and synonymous substitution rates) of each TLR family gene is far lower than one regardless of estimating methods, supporting previous observations of strong purifying selection in this gene family. Interestingly, however, analysis of Ka/Ks ratios along the coding regions of TLR7 family genes by sliding-window analysis reveals a few narrow high peaks (Ka/Ks > 1). The most prominent peak corresponds to a specific region in the ectodomain, which exists only in the TLR7 family, suggesting that this unique structure of the TLR7 family might have been a target of positive selection in a variety of lineages. Furthermore, maximum likelihood model tests suggest that positive selection is the best explanation for a certain fraction of the amino acid substitutions in the TLR9.     

Reductive genome evolution from the mother of Rickettsia

The Rickettsia genus is a group of obligate intracellular α-proteobacteria representing a paradigm of reductive evolution. Here, we investigate the evolutionary processes that shaped the genomes of the genus. The reconstruction of ancestral genomes indicates that their last common ancestor contained more genes, but already possessed most traits associated with cellular parasitism. The differences in gene repertoires across modern Rickettsia are mainly the result of differential gene losses from the ancestor. We demonstrate using computer simulation that the propensity of loss was variable across genes during this process. We also analyzed the ratio of nonsynonymous to synonymous changes (Ka/Ks) calculated as an average over large sets of genes to assay the strength of selection acting on the genomes of Rickettsia, Anaplasmataceae, and free-living γ-proteobacteria. As a general trend, Ka/Ks were found to decrease with increasing divergence between genomes. The high Ka/Ks for closely related genomes are probably due to a lag in the removal of slightly deleterious nonsynonymous mutations by natural selection. Interestingly, we also observed a decrease of the rate of gene loss with increasing divergence, suggesting a similar lag in the removal of slightly deleterious pseudogene alleles. For larger divergence (Ks > 0.2), Ka/Ks converge toward similar values indicating that the levels of selection are roughly equivalent between intracellular α-proteobacteria and their free-living relatives. This contrasts with the view that obligate endocellular microorganisms tend to evolve faster as a consequence of reduced effectiveness of selection, and suggests a major role of enhanced background mutation rates on the fast protein divergence in the obligate intracellular α-proteobacteria.     

Evolution of the isochore structure in the scale of chromosome: insight from the mutation bias and fixation bias

Following the development of reliable methods for inferring the direction of mutations of the single nucleotide polymorphism (SNP), and the revealing of the human isochore map, it has become possible to investigate the evolution of the isochore structure in a continuous region. In this study, the recent evolution of the isochore structure on human chromosome 18, as inferred from the SNP, was examined. A remarkable mutation bias was found, which was destroying the present isochore structure. However, a fixation bias contributed by the biased gene conversion (BGC) effect and a rising fixation probability of derived alleles with increasing GC content was extending the present isochore structure. Combining the two opposing processes, the old isochore structure was declining and a more homogenous isochore structure with higher GC content was being formed on the chromosome. During this process, both the CpG and genic sites, which were present in the isochore but were paid little attention to before, played an important role. In addition, the recombination was confirmed to promote the GC alleles fixed in the genome because of the BGC effect. For the first time, it was observed that with the occurrence of little recombination, AT alleles had the identical fixation probability with GC alleles in the recombination cold spots.