Relative efficiencies of the maximum parsimony and distance-matrix methods in obtaining the correct phylogenetic tree

The relative efficiencies of the maximum parsimony (MP) and distance-matrix methods in obtaining the correct tree (topology) were studied by using computer simulation. The distance-matrix methods examined are the neighbor-joining, distance-Wagner, Tateno et al. modified Farris, Faith, and Li methods. In the computer simulation, six or eight DNA sequences were assumed to evolve following a given model tree, and the evolutionary changes of the sequences were followed. Both constant and varying rates of nucleotide substitution were considered. From the sequences thus obtained, phylogenetic trees were constructed using the six tree-making methods and compared with the model (true) tree. This process was repeated 300 times for each different set of parameters. The results obtained indicate that when the number of nucleotide substitutions per site is small and a relatively small number of nucleotides are used, the probability of obtaining the correct topology (P1) is generally lower in the MP method than in the distance-matrix methods. The P1 value for the MP method increases with increasing number of nucleotides but is still generally lower than the value for the NJ or DW method. Essentially the same conclusion was obtained whether or not the rate of nucleotide substitution was constant or whether or not a transition bias in nucleotide substitution existed. The relatively poor performance of the MP method for these cases is due to the fact that information from singular sites is not used in this method. The MP method also showed a relatively low P1 value when the model of varying rate of nucleotide substitution was used and the number of substitutions per site was large. However, the MP method often produced cases in which the correct tree was one of several equally parsimonious trees. When these cases were included in the class of "success," the MP method performed better than the other methods, provided that the number of nucleotide substitutions per site was small.     

Relative efficiencies of the maximum-parsimony and distance-matrix methods of phylogeny construction for restriction data.

The relative efficiencies of the maximum-parsimony (MP), UPGMA, and neighbor-joining (NJ) methods in obtaining the correct tree (topology) for restriction-site and restriction-fragment data were studied by computer simulation. In this simulation, six DNA sequences of 16,000 nucleotides were assumed to evolve following a given model tree. The recognition sequences of 20 different six-base restriction enzymes were used to identify the restriction sites of the DNA sequences generated. The restriction-site data and restriction-fragment data thus obtained were used to reconstruct a phylogenetic tree, and the tree obtained was compared with the model tree. This process was repeated 300 times. The results obtained indicate that when the rate of nucleotide substitution is constant the probability of obtaining the correct tree (Pc) is generally higher in the NJ method than in the MP method. However, if we use the average topological deviation from the model tree (dT) as the criterion of comparison, the NJ and MP methods are nearly equally efficient. When the rate of nucleotide substitution varies with evolutionary lineage, the NJ method is better than the MP method, whether Pc or dT is used as the criterion of comparison. With 500 nucleotides and when the number of nucleotide substitutions per site was very small, restriction-site data were, contrary to our expectation, more useful than sequence data. Restriction-fragment data were less useful than restriction-site data, except when the sequence divergence was very small. UPGMA seems to be useful only when the rate of nucleotide substitution is constant and sequence divergence is high.     

Relative efficiencies of the maximum-likelihood, neighbor-joining, and maximum-parsimony methods when substitution rate varies with site

The relative efficiencies of the maximum-likelihood (ML), neighbor- joining (NJ), and maximum-parsimony (MP) methods in obtaining the correct topology and in estimating the branch lengths for the case of four DNA sequences were studied by computer simulation, under the assumption either that there is variation in substitution rate among different nucleotide sites or that there is no variation. For the NJ method, several different distance measures (Jukes-Cantor, Kimura two- parameter, and gamma distances) were used, whereas for the ML method three different transition/transversion ratios (R) were used. For the MP method, both the standard unweighted parsimony and the dynamically weighted parsimony methods were used. The results obtained are as follows: (1) When the R value is high, dynamically weighted parsimony is more efficient than unweighted parsimony in obtaining the correct topology. (2) However, both weighted and unweighted parsimony methods are generally less efficient than the NJ and ML methods even in the case where the MP method gives a consistent tree. (3) When all the assumptions of the ML method are satisfied, this method is slightly more efficient than the NJ method. However, when the assumptions are not satisfied, the NJ method with gamma distances is slightly better in obtaining the correct topology than is the ML method. In general, the two methods show more or less the same performance. The NJ method may give a correct topology even when the distance measures used are not unbiased estimators of nucleotide substitutions. (4) Branch length estimates of a tree with the correct topology are affected more easily than topology by violation of the assumptions of the mathematical model used, for both the ML and the NJ methods. Under certain conditions, branch lengths are seriously overestimated or underestimated. The MP method often gives serious underestimates for certain branches. (5) Distance measures that generate the correct topology, with high probability, do not necessarily give good estimates of branch lengths. (6) The likelihood-ratio test and the confidence-limit test, in Felsenstein's DNAML, for examining the statistical of branch length estimates are quite sensitive to violation of the assumptions and are generally too liberal to be used for actual data. Rzhetsky and Nei's branch length test is less sensitive to violation of the assumptions than is Felsenstein's test. (7) When the extent of sequence divergence is < or = 5% and when > or = 1,000 nucleotides are used, all three methods show essentially the same efficiency in obtaining the correct topology and in estimating branch lengths.(ABSTRACT TRUNCATED AT 400 WORDS)      

Efficiencies of fast algorithms of phylogenetic inference under the criteria of maximum parsimony, minimum evolution, and maximum likelihood when a large number of sequences are used

In phylogenetic inference by maximum-parsimony (MP), minimum-evolution (ME), and maximum-likelihood (ML) methods, it is customary to conduct extensive heuristic searches of MP, ME, and ML trees, examining a large number of different topologies. However, these extensive searches tend to give incorrect tree topologies. Here we show by extensive computer simulation that when the number of nucleotide sequences (m) is large and the number of nucleotides used (n) is relatively small, the simple MP or ML tree search algorithms such as the stepwise addition (SA) plus nearest neighbor interchange (NNI) search and the SA plus subtree pruning regrafting (SPR) search are as efficient as the extensive search algorithms such as the SA plus tree bisection-reconnection (TBR) search in inferring the true tree. In the case of ME methods, the simple neighbor-joining (NJ) algorithm is as efficient as or more efficient than the extensive NJ+TBR search. We show that when ME methods are used, the simple p distance generally gives better results in phylogenetic inference than more complicated distance measures such as the Hasegawa-Kishino-Yano (HKY) distance, even when nucleotide substitution follows the HKY model. When ML methods are used, the simple Jukes-Cantor (JC) model of phylogenetic inference generally shows a better performance than the HKY model even if the likelihood value for the HKY model is much higher than that for the JC model. This indicates that at least in the present case, selecting of a substitution model by using the likelihood ratio test or the AIC index is not appropriate. When n is small relative to m and the extent of sequence divergence is high, the NJ method with p distance often shows a better performance than ML methods with the JC model. However, when the level of sequence divergence is low, this is not the case.     

Efficiencies of different genes and different tree-building methods in recovering a known vertebrate phylogeny

The relative efficiencies of different protein-coding genes of the mitochondrial genome and different tree-building methods in recovering a known vertebrate phylogeny (two whale species, cow, rat, mouse, opossum, chicken, frog, and three bony fish species) was evaluated. The tree-building methods examined were the neighbor joining (NJ), minimum evolution (ME), maximum parsimony (MP), and maximum likelihood (ML), and both nucleotide sequences and deduced amino acid sequences were analyzed. Generally speaking, amino acid sequences were better than nucleotide sequences in obtaining the true tree (topology) or trees close to the true tree. However, when only first and second codon positions data were used, nucleotide sequences produced reasonably good trees. Among the 13 genes examined, Nd5 produced the true tree in all tree-building methods or algorithms for both amino acid and nucleotide sequence data. Genes Cytb and Nd4 also produced the correct tree in most tree-building algorithms when amino acid sequence data were used. By contrast, Co2, Nd1, and Nd41 showed a poor performance. In general, large genes produced better results, and when the entire set of genes was used, all tree-building methods generated the true tree. In each tree-building method, several distance measures or algorithms were used, but all these distance measures or algorithms produced essentially the same results. The ME method, in which many different topologies are examined, was no better than the NJ method, which generates a single final tree. Similarly, an ML method, in which many topologies are examined, was no better than the ML star decomposition algorithm that generates a single final tree. In ML the best substitution model chosen by using the Akaike information criterion produced no better results than simpler substitution models. These results question the utility of the currently used optimization principles in phylogenetic construction. Relatively simple methods such as the NJ and ML star decomposition algorithms seem to produce as good results as those obtained by more sophisticated methods. The efficiencies of the NJ, ME, MP, and ML methods in obtaining the correct tree were nearly the same when amino acid sequence data were used. The most important factor in constructing reliable phylogenetic trees seems to be the number of amino acids or nucleotides used.      

九种绢丝昆虫线粒体12S rRNA基因的序列特征和系统发育分析

为探讨鳞翅目中绢丝昆虫之间的系统发育关系和分子进化特征,本研究测定了中国柞蚕Antheraea pernyi野生型和放养型的线粒体12S rRNA基因的部分序列,结合来自GenBank数据库的17条序列,对总共9种绢丝昆虫（2科3属）的12S rRNA基因序列进行了分析。利用软件MEGA 3.1进行碱基组成、变异位点的统计和分子进化分析,分别用类平均聚类法（UPGMA）、邻接法（NJ）、最小进化法（ME）、最大简约法（MP）重建系统发生树。测定的中国柞蚕野生型的12S rRNA基因序列（427 bp）与放养型“豫早1号”的序列完全一致。序列对齐后共鉴定80个变异位点,50个简约信息位点。碱基组成分析显示在科属间具有明显差异,AT含量蚕蛾科高于大蚕蛾科;在A和T碱基的使用上,大蚕蛾科偏好使用T,而蚕蛾科则偏好使用A。与动物中常见的以转换为主的碱基替换模式不同,所分析的9种昆虫中除桑蚕属内部为转换与颠换基本一致外,其余物种间均是颠换多于转换。进化分析支持柞蚕属、樗蚕属和桑蚕属的单系。基于UPGMA法的进化树支持琥珀蚕是柞蚕属的较原始类型,而NJ、ME和MP法则支持印度柞蚕是较原始的类型,因此,柞蚕属种间的进化关系尚需进一步研究。     

Phylogenetic analysis using parsimony and likelihood methods

The assumptions underlying the maximum-parsimony (MP) method of phylogenetic tree reconstruction were intuitively examined by studying the way the method works. Computer simulations were performed to corroborate the intuitive examination. Parsimony appears to involve very stringent assumptions concerning the process of sequence evolution, such as constancy of substitution rates between nucleotides, constancy of rates across nucleotide sites, and equal branch lengths in the tree. For practical data analysis, the requirement of equal branch lengths means similar substitution rates among lineages (the existence of an approximate molecular clock), relatively long interior branches, and also few species in the data. However, a small amount of evolution is neither a necessary nor a sufficient requirement of the method. The difficulties involved in the application of current statistical estimation theory to tree reconstruction were discussed, and it was suggested that the approach proposed by Felsenstein (1981,J. Mol. Evol. 17: 368–376) for topology estimation, as well as its many variations and extensions, differs fundamentally from the maximum likelihood estimation of a conventional statistical parameter. Evidence was presented showing that the Felsenstein approach does not share the asymptotic efficiency of the maximum likelihood estimator of a statistical parameter. Computer simulations were performed to study the probability that MP recovers the true tree under a hierarchy of models of nucleotide substitution; its performance relative to the likelihood method was especially noted. The results appeared to support the intuitive examination of the assumptions underlying MP. When a simple model of nucleotide substitution was assumed to generate data, the probability that MP recovers the true topology could be as high as, or even higher than, that for the likelihood method. When the assumed model became more complex and realistic, e.g., when substitution rates were allowed to differ between nucleotides or across sites, the probability that MP recovers the true topology, and especially its performance relative to that of the likelihood method, generally deteriorates. As the complexity of the process of nucleotide substitution in real sequences is well recognized, the likelihood method appears preferable to parsimony. However, the development of a statistical methodology for the efficient estimation of the tree topology remains a difficult open problem.     

Reanalysis of Murphy et al.'s data gives various mammalian phylogenies and suggests overcredibility of Bayesian trees

Murphy and colleagues reported that the mammalian phylogeny was resolved by Bayesian phylogenetics. However, the DNA sequences they used had many alignment gaps and undetermined nucleotide sites. We therefore reanalyzed their data by minimizing unshared nucleotide sites and retaining as many species as possible (13 species). In constructing phylogenetic trees, we used the Bayesian, maximum likelihood (ML), maximum parsimony (MP), and neighbor-joining (NJ) methods with different substitution models. These trees were constructed by using both protein and DNA sequences. The results showed that the posterior probabilities for Bayesian trees were generally much higher than the bootstrap values for ML, MP, and NJ trees. Two different Bayesian topologies for the same set of species were sometimes supported by high posterior probabilities, implying that two different topologies can be judged to be correct by Bayesian phylogenetics. This suggests that the posterior probability in Bayesian analysis can be excessively high as an indication of statistical confidence and therefore Murphy et al.'s tree, which largely depends on Bayesian posterior probability, may not be correct.     

Statistical properties of bootstrap estimation of phylogenetic variability from nucleotide sequences: II. Four taxa without a molecular clock

Summary The statistical properties of sample estimation and bootstrap estimation of phylogenetic variability from a sample of nucleotide sequences were studied by considering model trees of three taxa with an outgroup. The cases of constant and varying rates of nucleotide substitution were compared. From sequences obtained by simulation, phylogenetic trees were constructed by using the maximum parsimony (MP) and neighbor joining (NJ) methods. The effectiveness and consistency of the MP method were studied in terms of proportions of informative sites. The results of simulation showed that bootstrap estimation of the confidence level for an inferred phylogeny can be used even under unequal rates of evolution if the rate differences are not large so that the MP method is not misleading. The condition under which the MP method becomes misleading (inconsistent) is more stringent for slowly evolving sequences than for rapidly evolving ones, and it also depends on the length of the internal branch. If the rate differences are large so that the MP method becomes consistently misleading, then bootstrap estimation will reinforce an erroneous conclusion on topology. Similar conclusions apply to the NJ method with uncorrected distances. The NJ method with corrected distances performs poorly when the sequence length is short but can avoid the inconsistency problem if the sequence length is long and if the distances can be estimated accurately.Offprint requests to: W.-H. Li     

探讨两栖纲三个目之间的系统发生关系

现存两栖纲分为3个目,然而它们的系统发生关系仍存在较大的争议.选择Genbank上25种两栖动物线粒体全序列,结合已测定的福建大头蛙(Lim nonectes fujianensis)线粒体基因组全序列,以天鹅和眼镜凯门鳄为外群,用线粒体tRNA基因的合并数据重建系统树.采用P AU P(version 4.0b10)软件构建MP和NJ树,tree-puzzle5.2构建ML树.结果显示,NJ树和ML树以较高的自引导值支持有尾目和蚓螈目为姐妹群,而MP树则支持无尾目和有尾目为姐妹群.     

从细胞色素b基因序列探讨笛鲷属的分子系统发生关系

测定了9种中国南海的笛鲷属鱼类的细胞色素b基因的部分序列,结合来自GenBank中1种分布于菲律宾和9种分布于美国大西洋的笛鲷属鱼类的相应同源序列,用邻接法和最大简约法构建分子系统树。结果显示:红鳍笛鲷(Lutjanuserythropterus)与红笛鲷(L.sanguineus)之间的同源序列碱基差异百分率只有0.32%,支持二者是同种异名的观点;中国南海的笛鲷属鱼类间的平均碱基差异要高于美国大西洋笛鲷属鱼类。在MP和NJ树中,美国大西洋笛鲷表现为亲缘关系较近,来源于中国南海的笛鲷鱼类相对集中在树的基部,分歧较大。这与所研究的笛鲷地理分布和地理隔离基本相一致,同时也说明中国南海笛鲷分化较早并且分歧较大。     

基于12S rRNA基因序列探讨崇安地蜥的分类地位

为探讨崇安地蜥Platyplacous sylvaticus的分类地位,测定了崇安地蜥线粒体12S rRNA基因全序列,并从GenBank中下载了东亚产10种草蜥、3种地蜥的同源序列进行分析,采用Mega V2.1软件的NJ法和ME法、PAUP4.0软件的MP法构建分子系统树.结果表明:崇安地蜥线粒体12S rRNA基因全序列(952 bp)中T、C、A、G碱基含量分别为23.1%、22.9%、35.9%、18.1%;与其它同源序列比对后有978 bp,发现321个位点出现变异,占总位点数32.8%,其中199个简约信息位点,为总变异位点的62%;转换/颠换之比平均为2.16.构建的分子系统树中,NJ树和ME树完全一致,与MP树略有差异.3种构树法中崇安地蜥与南台草蜥Takydromus sauteri、峨眉地蜥P.intermedius、先岛地蜥P.dorsalis均聚为一支,崇安地蜥与先岛地蜥亲缘关系最近.本实验结果支持将地蜥属并入草蜥属和取消地蜥亚属的观点.     

重建系统演化树的一种新方法--试错法

重建系统演化树是进化研究的一个极为重要的方面。系统树的构建依赖于一定的方法和数据。在分子系统演化研究中,所使用的数据大多是ＤＮＡ序列、氨基酸序列和分子标记。而就构树方法来说,ＮＪ法、ＭＬ法和ＭＰ法是三种最为普遍使用的方法。本文给出了一种新的建树方法,即试错法。该方法不但具有与ＮＪ法一样好的建树效果,而且不存在难以解释的负枝长问题。     

Nucleotide substitution models and estimation of phylogeny

The nucleotide substitution matrix inferred from avian data sets using cytochrome b differs considerably from the models commonly used in phylogenetic analyses. To analyze the possible effects of this particular pattern of change in phylogeny estimation we performed a computer simulation in which we started with a real sequence and used the inferred model of change to produce a tree of 10 species. Maximum parsimony (MP), maximum likelihood (ML), and various distance methods were then used to recover the topology and the branch lengths. We used two kinds of data with varying levels of variation. In addition, we tested with the removal of third positions and different weighting schemes. At low levels of variation, MP was outstanding in recovering the topology (90% correct), while unweighted pair-group method, arithmetic average (UPGMA), regardless of distances used, was poor (40%). At the higher level, most methods had a chance of around 40%-58% of finding the true tree. However, in most cases, the trees found were only slightly wrong, with only one or a few branches misplaced. On the other hand, the use of a "wrong" model had serious effects on the estimation of branch lengths (distances). Although precision was high, accuracy was poor with most methods, giving branch lengths that were biased downward. When seeded with the true distance matrix, Fitch and NJ always found the true tree, while UPGMA frequently failed to do so. The effect of removing third positions was dramatic at low levels of variation, because only one MP program was able to find a true tree at all, albeit rarely, while none of the others ever did so. At higher levels, the situation was better, but still much worse than with the whole data set.     

分子系统进化关系分析的一种新方法--贝叶斯法在硬蜱属中的应用

距离矩阵邻接法、最大简约法和最大似然法是重建生物系统关系的3种主要方法。普遍认为最大似然法在原理上优于前二种方法，但其计算复杂费时。由于现行计算机的能力尚达不到其要求而实用性差，特别是在处理大数据集样本(即大于25个分类单元)时，用此方法几乎不可能。新近提出的贝叶斯法(Bayesianmethod)既保留了最大似然法的基本原理，又引进了马尔科夫链的蒙特卡洛方法，并使计算时间大大缩短。本文用贝叶斯法对硬蜱属(Ixodes)19个种的线粒体16S rDNA片段进行了系统进化分析。从总体上看，分析结果与现有的基于形态学的分类体系基本吻合。但与现存的假说相反，莱姆病的主要宿主蓖籽硬蜱复合种组并非单系。通过比较贝叶斯法与其它三种方法的结果，我们认为贝叶斯法是一种系统进化分析的好方法，它既能根据分子进化的现有理论和各种模型用概率重建系统进化关系，又克服了最大似然法计算速度慢、不适用于大数据集样本的缺陷。贝叶斯法根据后验概率直观地表示系统进化关系的分析结果，不需要用自引导法进行检验。可以预料，贝叶斯法将会被广泛地应用到系统进化分析上[动物学报49(3)：380—388，2003]。     

线蛱蝶亚科蝶类部分类群线粒体COI基因的分子系统发生分析

以线粒体细胞色素氧化酶I（COI）基因作分子标记,对线蛱蝶亚科蝴蝶进行序列测定．序列分析的结果表明．经比对和处理后的序列总长度是645bp,其中有199个变异位点,147个简约信息位点;所编码的氨基酸序列中有18个变异位点,7个信息位点．A＋T平均含量为69．6％,G＋C平均含量为30．4％,碱基组成出现AT偏斜．以蛱蝶亚科及秀蛱蝶亚科物种为外类群,用NJ、MP及贝叶斯法重建了该亚科的系统发生树,探讨了它们主要类群间的系统发生关系．分子系统树显示,线蛱蝶亚科由以下3大支系：环蛱蝶族＋翠蛱蝶族、线蛱蝶族、丽蛱蝶族构成;其中,环蛱蝶族为单系群（NJ树也支持线蛱蝶族的单系性）;翠蛱蝶族与环蛱蝶族亲缘关系较近：丽蛱蝶族可能是该亚科较早分化出的一支．     

Molecular phylogeny of oribatid mites (Oribatida, Acari): evidence for multiple radiations of parthenogenetic lineages

Nucleotide sequences of the D3 expansion segment and its flanking regions of the 28S rDNA gene were used to evaluate phylogenetic relationships among representative sexual and asexual oribatid mites (Oribatida, Acariformes). The aim of this study was to investigate the hypothesis that oribatid mites consist of species-rich clusters of asexual species that may have radiated while being parthenogenetic. Furthermore, the systematic position of the astigmate mites (Astigmata, Acariformes) which have been hypothesised to represent a paedomorphic lineage within the oribatid mites, is investigated. This is the first phylogenetic tree for oribatid mites s.l. (incl. Astigmata) based on nucleotide sequences. Intraspecific genetic variation in the D3 region was very low, confirming the hypothesis that this region is a good species marker. Results from neighbour joining (NJ) and maximum parsimony (MP) algorithms indicate that several species-rich parthenogenetic groups like Camisiidae, Nanhermanniidae and Malaconothridae are monophyletic, consistent with the hypothesis that some oribatid mite groups diversified despite being parthenogenetic. The MP and maximum likelihood (ML) method indicated that the D3 region is a good tool for elucidating the relationship of oribatid mite species on a small scale(genera, families) but is not reliable for large-scale taxonomy, because branches from the NJ algorithm collapsed in the MP and ML tree. In all trees calculated by different algorithms the Astigmata clustered within the oribatid mites, as proposed earlier.     

芍药属牡丹组基于形态学证据的系统发育关系分析

对芍药属牡丹组Paeonia L.sect.Moutan DC.（全部野生种）40个居群进行了基于形态学证据的系统学分析,试图建立组内种间的系统发育关系。利用PAUP （4.0）计算机程序分别构建了建立在25个形态学性状基础上的所有研究类群的距离树（UPGMA、NJ）和最大简约树（MP）。所得树的拓扑结构基本一致,差异只发生在距离树和简约树之间,在由形态和细胞学关系都很近的5个种（牡丹P.suffruticosa、矮牡丹P.jishanensis、卵叶牡丹P.qiui、紫斑牡丹P.rockii和凤丹P.o     

PHYLOGENETIC RELATIONSHIPS WITHIN THE COLONIAL VOLVOCALES (CHLOROPHYTA) INFERRED FROM rbcL GENE SEQUENCE DATA

The chloroplast-encoded large subunit of the ribulose-1, 5-bisphosphate carboxylase / oxygenase (rbcL) gene was sequenced from 20 species of the colonial Volvocales (the Volvacaceae, Goniaceae, and Tetrabaenaceae) in order to elucidate phylogenetic relationships within the colonial Volvocales. Eleven hundred twenty-eight base pairs in the coding regions of the (rbcL) gene were analyzed by the neighbor-joining (NJ) method using three kinds of distance estimations, as well as by the maximum parsimony (MP) method. A large group comprising all the anisogamous and oogamous volvocacean species was resolved in the MP tree as well as in the NJ trees based on overall and synonymous substitutions. In all the trees constructed, Basichlamys and Tetrabaena (Tetrabaenaceae) constituted a very robust phylogenetic group. Although not supported by high bootstrap values, the MP tree and the NJ tree based on nonsynonymous substitutions indicated that the Tetrabaenaceae is the sister group to the large group comprising the Volvocaceae and the Goniaceae. In addition, the present analysis strongly suggested that Pandorina and Astrephomene are monophyletic genera whereas Eudorina is nonmonophyletic. These results are essentially consistent with the results of the recent cladistic analyses of morphological data. However, the monophyly of the Volvocaceae previously supported by four morphological synapomorphies is found only in the NJ tree based on nonsynonymous substitutions (with very low bootstrap values). The genus Volvox was clearly resolved as a polyphyletic group with V. rousseletii Pocock separated from other species of Volvox in the rbcL gene comparisons, although this genus represents a monophyletic group in the previous morphological analyses. Furthermore, none of the rbcL gene trees supported the monophyly of the Goniaceae; Astrephomene was placed in various phylogenetic positions .     

拓扑树间的通经拓扑距离

给出了一种新的系统树间的拓扑距离,使用NJ,MP,UPGMA等3种方法对13种动物的线粒体中14个基因（含组合的）DNA序列数据进行系统树的构建,利用分割拓扑距离和本文给出的通经拓扑距离对这14种系统树这间及其与真树进行比较。结果显示,NJ法对获得已知树的有效率最高,MP法次之,UPGMA法最低。这14种DNA序列所构建的系统树与已知树的拓扑距离基本上是随其DNA序列长度增加而减小,但两者的相关系数并未达到显著水平,分割拓扑距离在总体上可反映树间的拓扑结构差异,但其测度精确度比通经拓扑距离要低。