蛋白质序列间进化距离的估计

本文考察了目前采用的估计同源蛋白质序列间进化距离的方法缺陷,并提出了几个新的计算公式,它们考虑了氨基酸位点间显然存在的替代速率的差异。另外,提出了一种考虑氨基酸间不同替代概率的最大似然估计方法。文中对这些公式进行了计算比较,并对它在实际中的运用提出了建议。     

多QTL定位的压缩估计方法

本文综述了多标记分析和多QTL定位的压缩估计方法。对于前者,Xu（Genetics,2003,163：789—801）首先提出了Bayesian压缩估计方法。其关键在于让每个效应有一个特定的方差参数,而该方差又服从一定的先验分布,以致能从资料中估计之。由此,能够同时估计大量分子标记基因座的遗传效应,即使大多数标记的效应是可忽略的。然而,对于上位性遗传模型,其运算时间还是过长。为此,笔者将上述思想嵌入极大似然法,提出了惩罚最大似然方法。模拟研究显示：该方法能处理变量个数大于样本容量10倍左右的线性遗传模型。对于后者,本文详细介绍了基于固定区间和可变区间的Bayesian压缩估计方法。固定区间方法可处理中等密度的分子标记资料;可变区间方法则可分析高密度分子标记资料,甚至是上位性遗传模型。对于上位性检测,已介绍的惩罚最大似然方法和可变区间Bayesian压缩估计方法可供利用。应当指出,压缩估计方法在今后的eQTL和QTN定位以及基因互作网络分析等研究中也是有应用价值的。     

突变积累实验中极大似然法和距法的比较

最近,人们突变积累实验（MA）中测定有害基因突变（DGM）的兴趣大增。在MA实验中有两种常见的DGM估计方法（极大似然法ML和距法MM）,依靠计算机模拟和处理真实数据的应用软件来比较这两种方法。结论是：ML法难于得到最大似然估计（MLEs),所以ML法不如MM法估计有效;即使MLEs可得,也因其具严重的微样误差（据偏差和抽样差异）而产生估计偏差;似然函数曲线较平坦而难于区分高峰态和低峰态的分布。     

以雾灵山夜蛾科为材料评估进化模型对DNA条码分类的影响

为了探究进化模型对DNA条形码分类的影响, 本研究以雾灵山夜蛾科44个种的标本为材料, 获得COI基因序列。使用邻接法（neighbor-joining）、 最大简约法（maximum parsimony）、 最大似然法（maximum likelihood）以及贝叶斯法（Bayesian inference）构建系统发育树, 并且对邻接法的12种模型、 最大似然法的7种模型、 贝叶斯法的2种模型进行模型成功率的评估。结果表明, 邻接法的12种模型成功率相差不大, 较稳定; 最大似然法及贝叶斯法的不同模型成功率存在明显差异, 不稳定; 最大简约法不基于模型, 成功率比较稳定。邻接法及最大似然法共有6种相同的模型, 这6种模型在不同的方法中成功率存在差异。此外, 分子数据中存在单个物种仅有一条序列的情况, 显著降低了模型成功率, 表明在DNA条形码研究中, 每个物种需要有多个样本。     

最大似然法及其应用

最大似然法是参数估计的一种重要方法。 在遗传学研究中,广泛地应用于计数资料的总 体成数估计。由于估计值以满足在观察结果中 的出现概率最大为条件,故又称最大似然估计。     

云贵高原银星竹鼠的遗传多样性与遗传结构研究

作为一类营地下生活的啮齿动物,银星竹鼠Rhizomys pruinosus具有较高的食用价值和药用价值,已成为我国南方地区特种经济动物养殖业的重点发展物种。以核内重组蛋白激活基因1(RAG1)的基因片段为分子标记,采用分子生物学方法,本研究对来自12个采样点的173个银星竹鼠个体进行群体遗传分析,探讨该物种群体遗传多样性和遗传结构。序列多态性分析结果显示,银星竹鼠RAG1基因部分序列848 bp,共检测出多态性位点18个,其中单突变位点3个,简约信息位点15个。遗传多样性分析表明,173份样本共统计出RAG1基因单倍型11个,单倍型多样性为0.712±0.025,核苷酸多样性为0.002 64±0.003 71,显著低于其他啮齿动物。最大似然法、邻接法和贝叶斯法构建的系统发育树显示,银星竹鼠群体分化为3个分支,其谱系地理格局出现明显分化。同时,分子变异分析结果证实,银星竹鼠种群间的遗传变异极显著高于种群内的,说明该物种存在显著的遗传结构和遗传分化水平。上述研究结果综合表明,银星竹鼠群体的遗传多样性水平较低,遗传分化结构较为显著,这可能与该物种的地下生活方式、扩散能力弱、山脉河流阻隔作用、地质气候事件等因素有关。本研究结果将为云贵高原地区物种多样性、生物多样性保护提供科学的参考依据。     

远交群体动态性状基因定位的似然分析Ⅰ.理论方法

受动物遗传育种中用来估计动态性状育种值的随机回归测定日模型思想的启发 ,将关于时间 (测定日期 )的Legendre多项式镶嵌在遗传模型的每个遗传效应中 ,以刻画QTL对动态性状变化过程的作用 ,从而建立起动态性状基因定位的数学模型。利用远交设计群体 ,阐述了动态性状基因定位的似然分析原理 ,推导了定位参数似然估计的EM法两步求解过程。结合动态性状遗传分析的特点和普通数量性状基因定位研究进展 ,还提出了有关动态性状基因定位进一步研究的设想     

评估一种在最大似然系统发育估计中用于参数优化的连续近似计算方法的可行性

选择理由：最大似然法是一种重要的进化树构建方法。但由于运算量大,使它的应用受到限制。近似的算法可以减少最大似然法的运算量,从而加快运算速度。文章对这种近似方法的可靠性进行了评估。对于最大似然法的运用有重大影响。     

H广义线性模型中的参数估计的比较

本文研究H广义线性模型中未知参数的两种估计方法,一种是边际似然函数法,另一种是Lee和Nelder提出来的L-N法．对于一类具有两个随机效应的典型的Poisson-Gamma类模型,在一些正则性条件之下,我们已经证明了其中固定效应卢的L-N估计的强相合性及渐近正态性,并得到了其收敛于真值的速度．针对这类模型,本文进一步给出了其边际似然函数的解析表达式,并且通过Monte Carlo模拟,对模型中固定效应β的边际似然估计和L—N估计进行了比较,模拟表明L—N估计比边际似然估计在拟Poisson-Gamma模型中有着更加优良的表现,具有更高的精度。     

山羊BMPR-IB基因密码子偏好性及聚类分析

[目的]利用生物信息学分析山羊BMPR-IB基因密码子使用特征,对不同物种BMPR-IB基因通过不同的聚类方法进行分析。[方法]利用Usage Codon在线程序和Codon W软件分析山羊和其他物种BMPR-IB基因对密码子偏好性的使用情况,通过欧式平方距离和最小进化法分别进行聚类分析。[结果]山羊BMPR-IB基因无G/C碱基的使用倾向,GCC、CTG、CAG、CCC、AGA、AGT、GTG和TGA为山羊BMPR-IB基因的偏好密码子,其余53种密码子的使用较为均衡。通过最小进化法建立起来的不同物种间的系统发育分析结果与动物学分类一致,且不同物种BMPR-IB基因编码蛋白表达水平存在种属差异。[结论]BMPR-IB基因偏爱使用以A或T结尾的密码子,基于欧式距离系数建立起来的聚类和最大似然法构建的聚类不一致,造成这种差异的原因可能是在进化过程中单基因突变所引起的。     

Comparison of likelihood and Bayesian methods for estimating divergence times using multiple gene Loci and calibration points, with application to a radiation of cute-looking mouse lemur species

Divergence time and substitution rate are seriously confounded in phylogenetic analysis, making it difficult to estimate divergence times when the molecular clock (rate constancy among lineages) is violated. This problem can be alleviated to some extent by analyzing multiple gene loci simultaneously and by using multiple calibration points. While different genes may have different patterns of evolutionary rate change, they share the same divergence times. Indeed, the fact that each gene may violate the molecular clock differently leads to the advantage of simultaneous analysis of multiple loci. Multiple calibration points provide the means for characterizing the local evolutionary rates on the phylogeny. In this paper, we extend previous likelihood models of local molecular clock for estimating species divergence times to accommodate multiple calibration points and multiple genes. Heterogeneity among different genes in evolutionary rate and in substitution process is accounted for by the models. We apply the likelihood models to analyze two mitochondrial protein-coding genes, cytochrome oxidase II and cytochrome b, to estimate divergence times of Malagasy mouse lemurs and related outgroups. The likelihood method is compared with the Bayes method of Thorne et al. (1998, Mol. Biol. Evol. 15:1647-1657), which uses a probabilistic model to describe the change in evolutionary rate over time and uses the Markov chain Monte Carlo procedure to derive the posterior distribution of rates and times. Our likelihood implementation has the drawbacks of failing to accommodate uncertainties in fossil calibrations and of requiring the researcher to classify branches on the tree into different rate groups. Both problems are avoided in the Bayes method. Despite the differences in the two methods, however, data partitions and model assumptions had the greatest impact on date estimation. The three codon positions have very different substitution rates and evolutionary dynamics, and assumptions in the substitution model affect date estimation in both likelihood and Bayes analyses. The results demonstrate that the separate analysis is unreliable, with dates variable among codon positions and between methods, and that the combined analysis is much more reliable. When the three codon positions were analyzed simultaneously under the most realistic models using all available calibration information, the two methods produced similar results. The divergence of the mouse lemurs is dated to be around 7-10 million years ago, indicating a surprisingly early species radiation for such a morphologically uniform group of primates.     

Inferring speciation times under an episodic molecular clock

We extend our recently developed Markov chain Monte Carlo algorithm for Bayesian estimation of species divergence times to allow variable evolutionary rates among lineages. The method can use heterogeneous data from multiple gene loci and accommodate multiple fossil calibrations. Uncertainties in fossil calibrations are described using flexible statistical distributions. The prior for divergence times for nodes lacking fossil calibrations is specified by use of a birth-death process with species sampling. The prior for lineage-specific substitution rates is specified using either a model with autocorrelated rates among adjacent lineages (based on a geometric Brownian motion model of rate drift) or a model with independent rates among lineages specified by a log-normal probability distribution. We develop an infinite-sites theory, which predicts that when the amount of sequence data approaches infinity, the width of the posterior credibility interval and the posterior mean of divergence times form a perfect linear relationship, with the slope indicating uncertainties in time estimates that cannot be reduced by sequence data alone. Simulations are used to study the influence of among-lineage rate variation and the number of loci sampled on the uncertainty of divergence time estimates. The analysis suggests that posterior time estimates typically involve considerable uncertainties even with an infinite amount of sequence data, and that the reliability and precision of fossil calibrations are critically important to divergence time estimation. We apply our new algorithms to two empirical data sets and compare the results with those obtained in previous Bayesian and likelihood analyses. The results demonstrate the utility of our new algorithms.     

Approximate likelihood calculation on a phylogeny for Bayesian estimation of divergence times

The molecular clock provides a powerful way to estimate species divergence times. If information on some species divergence times is available from the fossil or geological record, it can be used to calibrate a phylogeny and estimate divergence times for all nodes in the tree. The Bayesian method provides a natural framework to incorporate different sources of information concerning divergence times, such as information in the fossil and molecular data. Current models of sequence evolution are intractable in a Bayesian setting, and Markov chain Monte Carlo (MCMC) is used to generate the posterior distribution of divergence times and evolutionary rates. This method is computationally expensive, as it involves the repeated calculation of the likelihood function. Here, we explore the use of Taylor expansion to approximate the likelihood during MCMC iteration. The approximation is much faster than conventional likelihood calculation. However, the approximation is expected to be poor when the proposed parameters are far from the likelihood peak. We explore the use of parameter transforms (square root, logarithm, and arcsine) to improve the approximation to the likelihood curve. We found that the new methods, particularly the arcsine-based transform, provided very good approximations under relaxed clock models and also under the global clock model when the global clock is not seriously violated. The approximation is poorer for analysis under the global clock when the global clock is seriously wrong and should thus not be used. The results suggest that the approximate method may be useful for Bayesian dating analysis using large data sets.     

Bayesian relaxed clock estimation of divergence times in foraminifera

Accurate and precise estimation of divergence times during the Neo-Proterozoic is necessary to understand the speciation dynamic of early Eukaryotes. However such deep divergences are difficult to date, as the molecular clock is seriously violated. Recent improvements in Bayesian molecular dating techniques allow the relaxation of the molecular clock hypothesis as well as incorporation of multiple and flexible fossil calibrations. Divergence times can then be estimated even when the evolutionary rate varies among lineages and even when the fossil calibrations involve substantial uncertainties. In this paper, we used a Bayesian method to estimate divergence times in Foraminifera, a group of unicellular eukaryotes, known for their excellent fossil record but also for the high evolutionary rates of their genomes. Based on multigene data we reconstructed the phylogeny of Foraminifera and dated their origin and the major radiation events. Our estimates suggest that Foraminifera emerged during the Cryogenian (650-920 Ma, Neo-Proterozoic), with a mean time around 770 Ma, about 220 Myr before the first appearance of reliable foraminiferal fossils in sediments (545 Ma). Most dates are in agreement with the fossil record, but in general our results suggest earlier origins of foraminiferal orders. We found that the posterior time estimates were robust to specifications of the prior. Our results highlight inter-species variations of evolutionary rates in Foraminifera. Their effect was partially overcome by using the partitioned Bayesian analysis to accommodate rate heterogeneity among data partitions and using the relaxed molecular clock to account for changing evolutionary rates. However, more coding genes appear necessary to obtain more precise estimates of divergence times and to resolve the conflicts between fossil and molecular date estimates.     

Dating the Dipsacales: comparing models, genes, and evolutionary implications

Dipsacales is an asterid angiosperm clade of ca. 1100 species, with most of its lineages occupying temperate regions of the Northern Hemisphere. A recent phylogenetic analysis based on 7593 nucleotides of chloroplast DNA recovered a well-resolved and strongly supported phylogenetic hypothesis, which we use here to estimate divergence times within the group. A molecular clock is strongly rejected, regardless of data partition. We used recently proposed methods that relax the assumption of rate constancy among lineages (local clocks, nonparametric rate smoothing, penalized likelihood, and Bayesian relaxed clock) to estimate the ages of major lineages. Age estimates for Dipsacales varied widely among markers and codon positions, and depended on the fossils used for calibration and method of analysis. Some methods yielded dates for the Dipsacales diversification that appear to be too old (prior to the presumed 125 my [million years] age of eudicots), and others suggested ages that are too young based on well-documented Dipsacales fossils. Concordant penalized likelihood and Bayesian studies imply that Dipsacales originated in the Cretaceous, as did its two major lineages, Adoxaceae and Caprifoliaceae. However, diversification of crown Adoxaceae and Caprifoliaceae mainly occurred in the Tertiary, with the origin of major lineages within these clades mainly occurring during the Eocene. Another round of diversification appears to have occurred in the Miocene. Several radiations, such as Valerianaceae in South America and Dipsacaceae around the Mediterranean, are even more recent. This study demonstrates the wide range of divergence times that can be obtained using different methods and data sets, and cautions against reliance on age estimates based on only a single gene or methodology. Despite this variance, significant conclusions can be made about the timing of Dipsacales evolution.     

Time scale of eutherian evolution estimated without assuming a constant rate of molecular evolution

Controversies over the molecular clock hypothesis were reviewed. Since it is evident that the molecular clock does not hold in an exact sense, accounting for evolution of the rate of molecular evolution is a prerequisite when estimating divergence times with molecular sequences. Recently proposed statistical methods that account for this rate variation are overviewed and one of these procedures is applied to the mitochondrial protein sequences and to the nuclear gene sequences from many mammalian species in order to estimate the time scale of eutherian evolution. This Bayesian method not only takes account of the variation of molecular evolutionary rate among lineages and among genes, but it also incorporates fossil evidence via constraints on node times. With denser taxonomic sampling and a more realistic model of molecular evolution, this Bayesian approach is expected to increase the accuracy of divergence time estimates.     

Molecular evidence on plant divergence times

Estimation of divergence times from sequence data has become increasingly feasible in recent years. Conflicts between fossil evidence and molecular dates have sparked the development of new methods for inferring divergence times, further encouraging these efforts. In this paper, available methods for estimating divergence times are reviewed, especially those geared toward handling the widespread variation in rates of molecular evolution observed among lineages. The assumptions, strengths, and weaknesses of local clock, Bayesian, and rate smoothing methods are described. The rapidly growing literature applying these methods to key divergence times in plant evolutionary history is also reviewed. These include the crown group ages of green plants, land plants, seed plants, angiosperms, and major subclades of angiosperms. Finally, attempts to infer divergence times are described in the context of two very different temporal settings: recent adaptive radiations and much more ancient biogeographic patterns.     

Taxon sampling effects in molecular clock dating: an example from the African Restionaceae

Three commonly used molecular dating methods for correction of variable rates (non-parametric rate smoothing, penalized likelihood, and Bayesian rate correction) as well as the assumption of a global molecular clock were tested for sensitivity to taxon sampling. The test dataset of 6854 basepairs for 300 terminals includes a nearly complete sample of the Restio-clade of the African Restionaceae (272 of the 288 species), as well as 26 outgroup species. Of this, nested subsets of 35, 51, 80, 120, 150, and the full 300 species were used. Molecular dating experiments with these datasets showed that all methods are sensitive to undersampling, but that this effect is more severe in analyses that use more extreme rate smoothing. Additionally, the undersampling effect is positively related to distance from the calibration node. The combined effect of undersampling and distance from the calibration node resulted in up to threefold differences in the age estimation of nodes from the same dataset with the same calibration point. We suggest that the most suitable methods are penalized likelihood and Bayesian when a global clock assumption has been rejected, as these methods are more successful at finding optimal levels of smoothing to correct for rate heterogeneity, and are less sensitive to undersampling.     

Molecular dating for phylogenies containing a mix of populations and species by using Bayesian and RelTime approaches

Simultaneous molecular dating of population and species divergences is essential in many biological investigations, including phylogeography, phylodynamics and species delimitation studies. In these investigations, multiple sequence alignments consist of both intra‐ and interspecies samples (mixed samples). As a result, the phylogenetic trees contain interspecies, interpopulation and within‐population divergences. Bayesian relaxed clock methods are often employed in these analyses, but they assume the same tree prior for both inter‐ and intraspecies branching processes and require specification of a clock model for branch rates (independent vs. autocorrelated rates models). We evaluated the impact of a single tree prior on Bayesian divergence time estimates by analysing computer‐simulated data sets. We also examined the effect of the assumption of independence of evolutionary rate variation among branches when the branch rates are autocorrelated. Bayesian approach with coalescent tree priors generally produced excellent molecular dates and highest posterior densities with high coverage probabilities. We also evaluated the performance of a non‐Bayesian method, RelTime, which does not require the specification of a tree prior or a clock model. RelTime's performance was similar to that of the Bayesian approach, suggesting that it is also suitable to analyse data sets containing both populations and species variation when its computational efficiency is needed.     

A distance-based least-square method for dating speciation events

Distance-based phylogenetic methods are widely used in biomedical research. However, there has been little development of rigorous statistical methods and software for dating speciation and gene duplication events by using evolutionary distances. Here we present a simple, fast and accurate dating method based on the least-squares (LS) method that has already been widely used in molecular phylogenetic reconstruction. Dating methods with a global clock or two different local clocks are presented. Single or multiple fossil calibration points can be used, and multiple data sets can be integrated in a combined analysis. Variation of the estimated divergence time is estimated by resampling methods such as bootstrapping or jackknifing. Application of the method to dating the divergence time among seven ape species or among 35 mammalian species including major mammalian orders shows that the estimated divergence time with the LS criterion is nearly identical to those obtained by the likelihood method or Bayesian inference.