Estimation of phylogeny and invariant sites under the general Markov model of nucleotide sequence evolution

The models of nucleotide substitution used by most maximum likelihood-based methods assume that the evolutionary process is stationary, reversible, and homogeneous. We present an extension of the Barry and Hartigan model, which can be used to estimate parameters by maximum likelihood (ML) when the data contain invariant sites and there are violations of the assumptions of stationarity, reversibility, and homogeneity. Unlike most ML methods for estimating invariant sites, we estimate the nucleotide composition of invariant sites separately from that of variable sites. We analyze a bacterial data set where problems due to lack of stationarity and homogeneity have been previously well noted and use the parametric bootstrap to show that the data are consistent with our general Markov model. We also show that estimates of invariant sites obtained using our method are fairly accurate when applied to data simulated under the general Markov model.     

Two stationary nonhomogeneous Markov models of nucleotide sequence evolution

The general Markov model (GMM) of nucleotide substitution does not assume the evolutionary process to be stationary, reversible, or homogeneous. The GMM can be simplified by assuming the evolutionary process to be stationary. A stationary GMM is appropriate for analyses of phylogenetic data sets that are compositionally homogeneous; a data set is considered to be compositionally homogeneous if a statistical test does not detect significant differences in the marginal distributions of the sequences. Though the general time-reversible (GTR) model assumes stationarity, it also assumes reversibility and homogeneity. We propose two new stationary and nonhomogeneous models--one constrains the GMM to be reversible, whereas the other does not. The two models, coupled with the GTR model, comprise a set of nested models that can be used to test the assumptions of reversibility and homogeneity for stationary processes. The two models are extended to incorporate invariable sites and used to analyze a seven-taxon hominoid data set that displays compositional homogeneity. We show that within the class of stationary models, a nonhomogeneous model fits the hominoid data better than the GTR model. We note that if one considers a wider set of models that are not constrained to be stationary, then an even better fit can be obtained for the hominoid data. However, the methods for reducing model complexity from an extremely large set of nonstationary models are yet to be developed.     

New substitution models for rooting phylogenetic trees

The root of a phylogenetic tree is fundamental to its biological interpretation, but standard substitution models do not provide any information on its position. Here, we describe two recently developed models that relax the usual assumptions of stationarity and reversibility, thereby facilitating root inference without the need for an outgroup. We compare the performance of these models on a classic test case for phylogenetic methods, before considering two highly topical questions in evolutionary biology: the deep structure of the tree of life and the root of the archaeal radiation. We show that all three alignments contain meaningful rooting information that can be harnessed by these new models, thus complementing and extending previous work based on outgroup rooting. In particular, our analyses exclude the root of the tree of life from the eukaryotes or Archaea, placing it on the bacterial stem or within the Bacteria. They also exclude the root of the archaeal radiation from several major clades, consistent with analyses using other rooting methods. Overall, our results demonstrate the utility of non-reversible and non-stationary models for rooting phylogenetic trees, and identify areas where further progress can be made.     

Tests of applicability of several substitution models for DNA sequence data

Using linear invariants for various models of nucleotide substitution, we developed test statistics for examining the applicability of a specific model to a given dataset in phylogenetic inference. The models examined are those developed by Jukes and Cantor (1969), Kimura (1980), Tajima and Nei (1984), Hasegawa et al. (1985), Tamura (1992), Tamura and Nei (1993), and a new model called the eight-parameter model. The first six models are special cases of the last model. The test statistics developed are independent of evolutionary time and phylogeny, although the variances of the statistics contain phylogenetic information. Therefore, these statistics can be used before a phylogenetic tree is estimated. Our objective is to find the simplest model that is applicable to a given dataset, keeping in mind that a simple model usually gives an estimate of evolutionary distance (number of nucleotide substitutions per site) with a smaller variance than a complicated model when the simple model is correct. We have also developed a statistical test of the homogeneity of nucleotide frequencies of a sample of several sequences that takes into account possible phylogenetic correlations. This test is used to examine the stationarity in time of the base frequencies in the sample. For Hasegawa et al.'s and the eight-parameter models, analytical formulas for estimating evolutionary distances are presented. Application of the above tests to several sets of real data has shown that the assumption of stationarity of base composition is usually acceptable when the sequences studied are closely related but otherwise it is rejected. Similarly, the simple models of nucleotide substitution are almost always rejected when actual genes are distantly related and/or the total number of nucleotides examined is large.      

Hidden patterns of phylogenetic non‐stationarity overwhelm comparative analyses of niche conservatism and divergence

Aim Despite the importance of the niche concept in ecological and evolutionary theory, there are still many discussions about its definition and operational evaluation, especially when dealing with niche divergence and conservatism in an explicit phylogenetic context. Here we evaluate patterns of niche evolution in 67 New World Carnivora species, measured using Hellinger distances based on MAXENT models of species distribution. We show how inferences on niche conservatism or divergence depend on the way phylogenetic patterns are analysed using matrix comparison techniques. Innovation Initially we used the simplest approach of Mantel tests to compare Hellinger distances ( N ) derived from MAXENT and phylogenetic distances ( P ) among species. Then we extended the Mantel test to generate a multivariate correlogram, in which phylogenetic patterns are analysed at multiple levels in the phylogeny and can reveal nonlinearity in the relationship between divergence and time. Finally, we proposed a new approach to generate ‘local’ (or ‘specific’) leverages of components for Mantel correlation, evaluating the non‐stationarity in the relationship between N and P for each species. This new approach was used to show if some lineages are more prone to niche shift or conservatism than others. Main conclusions Standard Mantel tests indicated a poor correspondence between N and P matrices, discarding the idea of niche conservatism for Carnivora, but the correlogram supports that closely related species tend to be more similar than expected by chance. Moreover, the variance among Hellinger distances between pairs of closely phylogenetically related species is much larger than for the entire clade. Phylogenetic non‐stationarity analysis shows that in some Carnivora families the niche tends to divergence (Mustelidae and Canidae), whereas in others it tends to conservatism (Procyonidae and Mustelidae) at short phylogenetic distances. Our analyses clearly show that misleading results may appear if niche divergence is analysed only by simple matrix correlations not taking into account complex patterns of phylogenetic nonlinearity and non‐stationarity.     

Testing for covarion-like evolution in protein sequences

The covarion hypothesis of molecular evolution proposes that selective pressures on an amino acid or nucleotide site change through time, thus causing changes of evolutionary rate along the edges of a phylogenetic tree. Several kinds of Markov models for the covarion process have been proposed. One model, proposed by Huelsenbeck (2002), has 2 substitution rate classes: the substitution process at a site can switch between a single variable rate, drawn from a discrete gamma distribution, and a zero invariable rate. A second model, suggested by Galtier (2001), assumes rate switches among an arbitrary number of rate classes but switching to and from the invariable rate class is not allowed. The latter model allows for some sites that do not participate in the rate-switching process. Here we propose a general covarion model that combines features of both models, allowing evolutionary rates not only to switch between variable and invariable classes but also to switch among different rates when they are in a variable state. We have implemented all 3 covarion models in a maximum likelihood framework for amino acid sequences and tested them on 23 protein data sets. We found significant likelihood increases for all data sets for the 3 models, compared with a model that does not allow site-specific rate switches along the tree. Furthermore, we found that the general model fit the data better than the simpler covarion models in the majority of the cases, highlighting the complexity in modeling the covarion process. The general covarion model can be used for comparing tree topologies, molecular dating studies, and the investigation of protein adaptation.     

Reversibility and the age of an allele II. Two-allele models,with selection and mutation

A Markov process with absorbing boundaries may be made recurrent by returning the process to the interior whenever a boundary is reached. The age of such a process may be defined as the length of time since the last return event. Examples drawn from two-allele genetic models are discussed, in which reversibility of the return process means that the age of an allele, whose present frequency in the population is known, has the same probability distribution as its future extinction time. Some discrete models are not reversible, yet if approximated by diffusion processes, the (approximate) age distribution is the same as the future extinction time distribution. Various results in the literature are unified by this viewpoint.     

DNA进化马尔可夫过程模型的评价与推广

本文对ＤＮＡ序列进化过程中核苷酸替代的随机模型进行了评价,对替代速率在时间和空间上不恒定的情形进行了考察和推广。Ｌａｎａｖｅ等（１９８４）曾提出一个模型,宣称对替代的模式未做任何假定,但事实上我们证明它假定替代过程是可逆的。运用２－ｐ、４－ｐ和６－ｐ模型进行的计算表明替代速度在位点间的差异会造成估计的替代数严重偏低,并且替代数越大,偏差也越大。替代模式在位点间的差异也会造成估计值偏低,但偏差不严重     

On the use of nucleic acid sequences to infer early branchings in the tree of life

Simplifying assumptions made in various tree reconstruction methods-- notably rate constancy among nucleotide sites, homogeneity, and stationarity of the substitutional processes--are clearly violated when nucleotide sequences are used to infer distant relationships. Use of tree reconstruction methods based on such oversimplified assumptions can lead to misleading results, as pointed out by previous authors. In this paper, we made use of a (discretized) gamma distribution to account for variable rates of substitution among sites and built models that allowed for unequal base frequencies in different sequences. The models were nonhomogeneous Markov-process models, assuming different patterns of substitution in different parts of the tree. Data of the small-subunit rRNAs from four species were analyzed, where base frequencies were quite different among sequences and rates of substitution were highly variable at sites. Parameters in the models were estimated by maximum likelihood, and models were compared by the likelihood-ratio test. The nonhomogeneous models provided significantly better fit to the data than homogeneous models despite their involvement of many parameters. They also appeared to produce reasonable estimation of the phylogenetic tree; in particular, they seemed able to identify the root of the tree.      

Substitution Model of Sequence Evolution for the Human Immunodeficiency Virus Type 1 Subtype B gp120 Gene over the C2-V5 Region

Phylogenetic analyses frequently rely on models of sequence evolution that detail nucleotide substitution rates, nucleotide frequencies, and site-to-site rate heterogeneity. These models can influence hypothesis testing and can affect the accuracy of phylogenetic inferences. Maximum likelihood methods of simultaneously constructing phylogenetic tree topologies and estimating model parameters are computationally intensive, and are not feasible for sample sizes of 25 or greater using personal computers. Techniques that initially construct a tree topology and then use this non-maximized topology to estimate ML substitution rates, however, can quickly arrive at a model of sequence evolution. The accuracy of this two-step estimation technique was tested using simulated data sets with known model parameters. The results showed that for a star-like topology, as is often seen in human immunodeficiency virus type 1 (HIV-1) subtype B sequences, a random starting topology could produce nucleotide substitution rates that were not statistically different than the true rates. Samples were isolated from 100 HIV-1 subtype B infected individuals from the United States and a 620 nt region of the env gene was sequenced for each sample. The sequence data were used to obtain a substitution model of sequence evolution specific for HIV-1 subtype B env by estimating nucleotide substitution rates and the site-to-site heterogeneity in 100 individuals from the United States. The method of estimating the model should provide users of large data sets with a way to quickly compute a model of sequence evolution, while the nucleotide substitution model we identified should prove useful in the phylogenetic analysis of HIV-1 subtype B env sequences. Received: 4 October 2000 / Accepted: 1 March 2001     

RecQ-dependent death-by-recombination in cells lacking RecG and UvrD

Maintenance of genomic stability is critical for all cells. Homologous recombination (HR) pathways promote genome stability using evolutionarily conserved proteins such as RecA, SSB, and RecQ, the Escherichia coli homologue of five human proteins at least three of which suppress genome instability and cancer. A previous report indicated that RecQ promotes the net accumulation in cells of intermolecular HR intermediates (IRIs), a net effect opposite that of the yeast and two human RecQ homologues. Here we extend those conclusions. We demonstrate that cells that lack both UvrD, an inhibitor of RecA-mediated strand exchange, and RecG, a DNA helicase implicated in IRI resolution, are inviable. We show that the uvrD recG cells die a “death-by-recombination” in which IRIs accumulate blocking chromosome segregation. First, their death requires RecA HR protein. Second, the death is accompanied by cytogenetically visible failure to segregate chromosomes. Third, FISH analyses show that the unsegregated chromosomes have completed replication, supporting the hypothesis that unresolved IRIs prevented the segregation. Fourth, we show that RecQ and induction of the SOS response are required for the accumulation of replicated, unsegregated chromosomes and death, as are RecF, RecO, and RecJ. ExoI exonuclease and MutL mismatch-repair protein are partially required. This set of genes is similar but not identical to those that promote death-by-recombination of ΔuvrD Δruv cells. The data support models in which RecQ promotes the net accumulation in cells of IRIs and RecG promotes resolution of IRIs that form via pathways not wholly identical to those that produce the IRIs resolved by RuvABC. This implies that RecG resolves intermediates other than or in addition to standard Holliday junctions resolved by RuvABC. The role of RecQ in net accumulation of IRIs may be shared by one or more of its human homologues.     

Phylogenetic distances for neighbour dependent substitution processes

We consider models of nucleotidic substitution processes where the rate of substitution at a given site depends on the state of the neighbours of the site. We first estimate the time elapsed between an ancestral sequence at stationarity and a present sequence. Second, assuming that two sequences are issued from a common ancestral sequence at stationarity, we estimate the time since divergence. In the simplest non-trivial case of a Jukes-Cantor model with CpG influence, we provide and justify mathematically consistent estimators in these two settings. We also provide asymptotic confidence intervals, valid for nucleotidic sequences of finite length, and we compute explicit formulas for the estimators and for their confidence intervals. In the general case of an RN model with YpR influence, we extend these results under a proviso, namely that the equation defining the estimator has a unique solution.     

Pleiotropic effect of disrupting a conserved sequence involved in a long-range compensatory interaction in the Drosophila Adh gene

Recent advances in experimental analyses of the evolution of RNA secondary structures suggest a more complex scenario than that typically considered by Kimura's classical model of compensatory evolution. In this study, we examine one such case in more detail. Previous experimental analysis of long-range compensatory interactions between the two ends of Drosophila Adh mRNA failed to fit the classical model of compensatory evolution. To further investigate and verify long-range pairing in Drosophila Adh with respect to models of compensatory evolution and its potential functional role, we introduced site-directed mutations in the Drosophila melanogaster Adh gene. We explore two alternative hypotheses for why previous analysis of long-range compensatory interactions failed to fit the classical model. Specifically, we investigate whether the disruption of a conserved short-range pairing within Adh exon 2 has an effect on Adh expression or if there is a dual functional role of a conserved sequence in the 3'-UTR in both long-range pairing and the negative regulation of Adh expression. We find that a classical result was not observed due to the pleiotropic effect of changing a nucleotide involved in both long-range base pairing and the negative regulation of gene expression.     

Why is sterility virulence most common in sexually transmitted infections? Examining the role of epidemiology

Sterility virulence, or the reduction in host fecundity due to infection, occurs in many host–pathogen systems. Notably, sterility virulence is more common for sexually transmitted infections (STIs) than for directly transmitted pathogens, while other forms of virulence tend to be limited in STIs. This has led to the suggestion that sterility virulence may have an adaptive explanation. By focusing upon finite population models, we show that the observed patterns of sterility virulence can be explained by consideration of the epidemiological differences between STIs and directly transmitted pathogens. In particular, when pathogen transmission is predominantly density invariant (as for STIs), and mortality is density dependent, sterility virulence can be favored by demographic stochasticity, whereas if pathogen transmission is predominantly density dependent, as is common for most directly transmitted pathogens, sterility virulence is disfavored. We show these conclusions can hold even if there is a weak selective advantage to sterilizing.     

An integrate-and-fire model to generate spike trains with long-range dependence

Long-range dependence (LRD) has been observed in a variety of phenomena in nature, and for several years also in the spiking activity of neurons. Often, this is interpreted as originating from a non-Markovian system. Here we show that a purely Markovian integrate-and-fire (IF) model, with a noisy slow adaptation term, can generate interspike intervals (ISIs) that appear as having LRD. However a proper analysis shows that this is not the case asymptotically. For comparison, we also consider a new model of individual IF neuron with fractional (non-Markovian) noise. The correlations of its spike trains are studied and proven to have LRD, unlike classical IF models. On the other hand, to correctly measure long-range dependence, it is usually necessary to know if the data are stationary. Thus, a methodology to evaluate stationarity of the ISIs is presented and applied to the various IF models. We explain that Markovian IF models may seem to have LRD because of non-stationarities.     

Reversibility and efficiency in coding protein information

Why the genetic code has a fixed length? Protein information is transferred by coding each amino acid using codons whose length equals 3 for all amino acids. Hence the most probable and the least probable amino acid get a codeword with an equal length. Moreover, the distributions of amino acids found in nature are not uniform and therefore the efficiency of such codes is sub-optimal. The origins of these apparently non-efficient codes are yet unclear. In this paper we propose an a priori argument for the energy efficiency of such codes resulting from their reversibility, in contrast to their time inefficiency. Such codes are reversible in the sense that a primitive processor, reading three letters in each step, can always reverse its operation, undoing its process.We examine the codes for the distributions of amino acids that exist in nature and show that they could not be both time efficient and reversible. We investigate a family of Zipf-type distributions and present their efficient (non-fixed length) prefix code, their graphs, and the condition for their reversibility. We prove that for a large family of such distributions, if the code is time efficient, it could not be reversible. In other words, if pre-biotic processes demand reversibility, the protein code could not be time efficient. The benefits of reversibility are clear: reversible processes are adiabatic, namely, they dissipate a very small amount of energy. Such processes must be done slowly enough; therefore time efficiency is non-important. It is reasonable to assume that early biochemical complexes were more prone towards energy efficiency, where forward and backward processes were almost symmetrical.     

Detecting non-Brownian trait evolution in adaptive radiations

Many phylogenetic comparative methods that are currently widely used in the scientific literature assume a Brownian motion model for trait evolution, but the suitability of that model is rarely tested, and a number of important factors might affect whether this model is appropriate or not. For instance, we might expect evolutionary change in adaptive radiations to be driven by the availability of ecological niches. Such evolution has been shown to produce patterns of change that are different from those modelled by the Brownian process. We applied two tests for the assumption of Brownian motion that generally have high power to reject data generated under non-Brownian niche-filling models for the evolution of traits in adaptive radiations. As a case study, we used these tests to explore the evolution of feeding adaptations in two radiations of warblers. In one case, the patterns revealed do not accord with Brownian motion but show characteristics expected under certain niche-filling models.     

可逆性肺动脉高压的治疗在心脏移植围术期的应用

目的：通过早期判断并治疗心脏移植围术期可逆性肺动脉高压,降低移植手术后右心功能衰竭的发生率。方法：20例接受心脏移植手术的病人,术前放置肺动脉导管,测定肺动脉压、肺循环阻力。对肺动脉高压的病人在肺动脉端泵入硝酸甘油、前列腺素E1以确定可逆性。并在术后早期抗排异治疗的基础上应用增强心肌收缩力、降低肺动脉压力、强化氧疗和呼吸管理等综合措施。结果：20例病人中6例出现急性右心功能衰竭,其中4例经治疗后症状改善、出院,2例死亡。结论：术前早期判断并治疗可逆性肺动脉高压,可以有效预防并减少心脏移植术后右心功能衰竭的发生,提高手术成功率。     

Mammalian genes as molecular clocks?

In analyzing the silent nucleotide substitutions in some mammalian mitochondrial mRNA coding genes, we had found that the frequency of each of the four nucleotides in rat, mouse, and cow, but not in humans, is the same in the silent third codon position (Lanave C, Preparata G, Saccone C, Serio G (1984) J Mol Evol 20:86-93). Because our findings for these three species were compatible with a stationary Markov process for the evolution of nucleotide sequences, we applied such a model to calculate the effective evolutionary silent substitution rate (vs) and the divergence times among the species. In this paper we have analyzed the first and second codon positions in the same mammalian mitochondrial genes. We found that in the first and second codon positions the human mitochondrial genes satisfy the stationarity conditions. This has allowed us to use the stochastic model mentioned above to calculate the divergence times among mouse, rat, cow, and human. Furthermore, we have analyzed the silent substitution rate in one nuclear gene for these four mammals. We found that in this gene the effective silent substitution rate is about 3 times lower than in mitochondrial genes, and that humans are in this case stationary with respect to the other three mammals in the third codon position as well. Application of our Markov model to this latter gene yields divergence times consistent with our previous determinations.