Phylogenetic test of the molecular clock and linearized trees

To estimate approximate divergence times of species or species groups with molecular data, we have developed a method of constructing a linearized tree under the assumption of a molecular clock. We present two tests of the molecular clock for a given topology: two-cluster test and branch-length test. The two-cluster test examines the hypothesis of the molecular clock for the two lineages created by an interior node of the tree, whereas the branch-length test examines the deviation of the branch length between the tree root and a tip from the average length. Sequences evolving excessively fast or slow at a high significance level may be eliminated. A linearized tree will then be constructed for a given topology for the remaining sequences under the assumption of rate constancy. We have used these methods to analyze hominoid mitochondrial DNA and drosophilid Adh gene sequences.

Molecular phylogeny and divergence times of drosophilid species

The phylogenetic relationships and divergence times of 39 drosophilid species were studied by using the coding region of the Adh gene. Four genera--Scaptodrosophila, Zaprionus, Drosophila, and Scaptomyza (from Hawaii)--and three Drosophila subgenera--Drosophila, Engiscaptomyza, and Sophophora--were included. After conducting statistical analyses of the nucleotide sequences of the Adh, Adhr (Adh-related gene), and nuclear rRNA genes and a 905-bp segment of mitochondrial DNA, we used Scaptodrosophila as the outgroup. The phylogenetic tree obtained showed that the first major division of drosophilid species occurs between subgenus Sophophora (genus Drosophila) and the group including subgenera Drosophila and Engiscaptomyza plus the genera Zaprionus and Scaptomyza. Subgenus Sophophora is then divided into D. willistoni and the clade of D. obscura and D. melanogaster species groups. In the other major drosophilid group, Zaprionus first separates from the other species, and then D. immigrans leaves the remaining group of species. This remaining group then splits into the D. repleta group and the Hawaiian drosophilid cluster (Hawaiian Drosophila, Engiscaptomyza, and Scaptomyza). Engiscaptomyza and Scaptomyza are tightly clustered. Each of the D. repleta, D. obscura, and D. melanogaster groups is monophyletic. The splitting of subgenera Drosophila and Sophophora apparently occurred about 40 Mya, whereas the D. repleta group and the Hawaiian drosophilid cluster separated about 32 Mya. By contrast, the splitting of Engiscaptomyza and Scaptomyza occurred only about 11 Mya, suggesting that Scaptomyza experienced a rapid morphological evolution. The D. obscura and D. melanogaster groups apparently diverged about 25 Mya. Many of the D. repleta group species studied here have two functional Adh genes (Adh-1 and Adh-2), and these duplicated genes can be explained by two duplication events.

Interior-branch and bootstrap tests of phylogenetic trees

We have compared statistical properties of the interior-branch and bootstrap tests of phylogenetic trees when the neighbor-joining tree-building method is used. For each interior branch of a predetermined topology, the interior-branch and bootstrap tests provide the confidence values, PC and PB, respectively, that indicate the extent of statistical support of the sequence cluster generated by the branch. In phylogenetic analysis these two values are often interpreted in the same way, and if PC and PB are high (say, > or = 0.95), the sequence cluster is regarded as reliable. We have shown that PC is in fact the complement of the P-value used in the standard statistical test, but PB is not. Actually, the bootstrap test usually underestimates the extent of statistical support of species clusters. The relationship between the confidence values obtained by the two tests varies with both the topology and expected branch lengths of the true (model) tree. The most conspicuous difference between PC and PB is observed when the true tree is starlike, and there is a tendency for the difference to increase as the number of sequences in the tree increases. The reason for this is that the bootstrap test tends to become progressively more conservative as the number of sequences in the tree increases. Unlike the bootstrap, the interior-branch test has the same statistical properties irrespective of the number of sequences used when a predetermined tree is considered. Therefore, the interior-branch test appears to be preferable to the bootstrap test as long as unbiased estimators of evolutionary distances are used. However, when the interior-branch is applied to a tree estimated from a given data set, PC may give an overestimate of statistical confidence. For this case, we developed a method for computing a modified version (P'C) of the PC value and showed that this P'C tends to give a conservative estimate of statistical confidence, though it is not as conservative as PB. In this paper we have introduced a model in which evolutionary distances between sequences follow a multivariate normal distribution. This model allowed us to study the relationships between the two tests analytically.

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.

Evolution of immunoglobulin VH pseudogenes in chickens

In chickens, there is a single functional gene (VH1) coding for the heavy chain variable region of immunoglobulins, and immunoglobulin diversity is generated by gene conversion of the VH1 gene by many variable region pseudogenes (psi VH's) that exist on the 5' side of the VH1 gene. To understand the evolution of this unique genetic system, we conducted statistical analyses of VH1 and psi VH genes together with functional VH genes from other higher vertebrate species. The results indicate, first, that chicken VH genes are all closely related to one another and were derived relatively recently from an ancestral gene belonging to one of the three major groups of VH genes in higher vertebrates. Second, the rate of nonsynonymous substitution is slightly higher than that of synonymous substitution in the complementarity-determining regions (CDRs), which suggests that diversity-enhancing selection has operated in the CDRs even for pseudogenes. However, both the rates of synonymous and nonsynonymous substitution are higher in the CDRs than in the framework regions (FRs), apparently because of an interaction between positive selection and meiotic gene conversion in the CDRs. Third, a dot matrix analysis of the psi VH genes and genomic diversity (D) genes has indicated that the 3' end of psi VH genes is attached by D-gene-like sequences, and this region of psi VH genes has high similarity with D gene sequences. This suggests that V and D genes were fused at some point of evolutionary time and this fused element multiplied by gene duplication. Finally, two alternative hypotheses of explaining the evolution of the chicken VH gene system are presented.

Four-cluster analysis: a simple method to test phylogenetic hypotheses

A simple statistical test for comparing three alternative phylogenetic hypotheses for four monophyletic groups is presented. This test is based on the minimum-evolution principle, and it does not require any information regarding the branching order within each monophyletic group. It is computationally efficient and can be easily extended to five or more monophyletic groups.

Natural selection at the class II major histocompatibility complex loci of mammals

The role of natural selection at major histocompatibility complex (MHC) loci was studied by analysis of molecular sequence data from mammalian class II MHC loci. As found previously for the class I MHC molecule and a hypothetical model of the class II molecule, the rate of non-synonymous nucleotide substitution exceeded that of synonymous substitution in the codons encoding the antigen recognition site of polymorphic class II molecules. This pattern is evidence that the polymorphism at these loci is maintained by a form of balancing selection, such as overdominant selection. By contrast, in the case of monomorphic class II loci, no such enhancement of the rate of non-synonymous substitution was observed. Phylogenetic analysis indicates that, in contrast to monomorphic ('non-classical') class I MHC loci, some monomorphic class II loci of mammals are quite ancient. The DMA and DMB loci, for example, diverged before all other known mammalian class II loci, possibly before the divergence of tetrapods from bony fishes. Analysis of the patterns of sharing of polymorphic residues at class II MHC loci by mammals of different species revealed that extensive convergent evolution has occurred at these loci; but no support was found for the hypothesis that MHC polymorphisms have been maintained since before the divergence of orders of eutherian mammals.

Inconsistency of the maximum parsimony method when the rate of nucleotide substitution is constant

The inconsistency of the maximum parsimony method is known to occur even when the rate of nucleotide substitution is constant. To understand why this inconsistency occurs, a mathematical study was conducted for the cases of five, six, and seven sequences. The results obtained indicate that this inconsistency occurs because the probability of occurrence of nucleotide configurations generated by one substitution on a short interior branch is often lower than that of configurations generated by more substitutions on other longer branches. The chance of occurrence of this event--or, the inconsistency of the maximum parsimony method--apparently increases as the number of sequences increases. The inconsistency may occur even when the extent of sequence divergence is relatively small.

Variance and covariances of the numbers of synonymous and nonsynonymous substitutions per site

Nei and Gojobori (1986) developed a simple method to estimate the numbers of synonymous (ds) and nonsynonymous (dN) substitutions per site. In the present paper, we have developed a method for computing variances and covariances of ds's and dN's and of the proportions of synonymous (ps) and nonsynonymous (pN) differences. We also have developed a method for computing the variances of mean dS, dN, pS, pN, without constructing a phylogenetic tree of the genes. We have conducted computer simulations based on simple evolutionary models and have shown that the new method gives good estimates of variances and covariances.

METREE: a program package for inferring and testing minimum-evolution trees

The METREE program package for estimating phylogenetic trees with the minimum evolution method is written in Turbo C 2.0 and is intended to be used on any IBM-compatible personal computers that have a mathematical coprocessor. The package is simple to use and is menu driven. A program for visualizing and printing out the final tree is also included.

Divergent evolution and evolution by the birth-and-death process in the immunoglobulin VH gene family

Immunoglobulin diversity is generated primarily by the heavy- and light-chain variable-region gene families. To understand the pattern of long-term evolution of the heavy-chain variable-region (VH) gene family, which is composed of a large number of member genes, the evolutionary relationships of representative VH genes from diverse organisms of vertebrates were studied by constructing a phylogenetic tree. This tree indicates that the vertebrate VH genes can be classified into group A, B, C, D, and E genes. All VH genes from cartilaginous fishes such as sharks and skates from a monophyletic group and belong to group E, whereas group D consists of bony-fish VH genes. By contrast, group C includes not only some fish genes but also amphibian, reptile, bird, and mammalian genes. Group A and B genes were composed of the genes from mammals and amphibians. The phylogenetic analysis also suggests that mammalian VH genes are classified into three clusters--i.e., mammalian clans I, II, and III-and that these clans have coexisted in the genome for >400 Myr. To study the short-term evolution of VH genes, the phylogenetic analysis of human group A (clan I) and C (clan III) genes was also conducted. The results obtained show that VH pseudogenes have evolved much faster than functional genes and that they have branched off from various functional VH genes. There is little indication that the VH gene family has been subject to concerted evolution that homogenizes member genes. These observations indicate that the VH genes are subject to divergent evolution due to diversifying selection and evolution by the birth-and-death process caused by gene duplication and dysfunctioning mutation. Thus, the evolutionary pattern of this monofunctional multigene family is quite different from that of such gene families as the ribosomal RNA and histone gene families.

MEGA: Molecular Evolutionary Genetics Analysis software for microcomputers

A computer program package called MEGA has been developed for estimating evolutionary distances, reconstructing phylogenetic trees and computing basic statistical quantities from molecular data. It is written in C++ and is intended to be used on IBM and IBM-compatible personal computers. In this program, various methods for estimating evolutionary distances from nucleotide and amino acid sequence data, three different methods of phylogenetic inference (UPGMA, neighbor-joining and maximum parsimony) and two statistical tests of topological differences are included. For the maximum parsimony method, new algorithms of branch-and-bound and heuristic searches are implemented. In addition, MEGA computes statistical quantities such as nucleotide and amino acid frequencies, transition/transversion biases, codon frequencies (codon usage tables), and the number of variable sites in specified segments in nucleotide and amino acid sequences. Advanced on-screen sequence data and phylogenetic-tree editors facilitate publication-quality outputs with a wide range of printers. Integrated and interactive designs, on-line context-sensitive helps, and a text-file editor make MEGA easy to use.

Unbiased estimates of the number of nucleotide substitutions when substitution rate varies among different sites

When the number of nucleotides examined is relatively small, the estimators of nucleotide substitutions between DNA sequences often introduce systematic error even if the data used fit the mathematical model underlying the estimation formula. The systematic error of this kind is especially large for models that allow variation in substitution rate among different sites. In the present paper we present a number of formulas that produce virtually bias-free estimates of evolutionary distances for these models.

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)

Effective population size, genetic diversity, and coalescence time in subdivided populations

A formula for the effective population size for the finite island model of subdivided populations is derived. The formula indicates that the effective size can be substantially greater than the actual number of individuals in the entire population when the migration rate among subpopulations is small. It is shown that the mean nucleotide diversity, coalescence time, and heterozygosity for genes sampled from the entire population can be predicted fairly well from the theory for randomly mating populations if the effective population size for the finite island model is used.

Theoretical foundation of the minimum-evolution method of phylogenetic inference

The minimum-evolution (ME) method of phylogenetic inference is based on the assumption that the tree with the smallest sum of branch length estimates is most likely to be the true one. In the past this assumption has been used without mathematical proof. Here we present the theoretical basis of this method by showing that the expectation of the sum of branch length estimates for the true tree is smallest among all possible trees, provided that the evolutionary distances used are statistically unbiased and that the branch lengths are estimated by the ordinary least-squares method. We also present simple mathematical formulas for computing branch length estimates and their standard errors for any unrooted bifurcating tree, with the least-squares approach. As a numerical example, we have analyzed mtDNA sequence data obtained by Vigilant et al. and have found the ME tree for 95 human and 1 chimpanzee (outgroup) sequences. The tree was somewhat different from the neighbor-joining tree constructed by Tamura and Nei, but there was no statistically significant difference between them.

Evolutionary relationships of human populations on a global scale

Using gene frequency data for 29 polymorphic loci (121 alleles), we conducted a phylogenetic analysis of 26 representative populations from around the world by using the neighbor-joining (NJ) method. We also conducted a separate analysis of 15 populations by using data for 33 polymorphic loci. These analyses have shown that the first major split of the phylogenetic tree separates Africans from non-Africans and that this split occurs with a 100% bootstrap probability. The second split separates Caucasian populations from all other non-African populations, and this split is also supported by bootstrap tests. The third major split occurs between Native American populations and the Greater Asians that include East Asians (mongoloids), Pacific Islanders, and Australopapuans (native Australians and Papua New Guineans), but Australopapuans are genetically quite different from the rest of the Greater Asians. The second and third levels of population splitting are quite different from those of the phylogenetic tree obtained by Cavalli-Sforza et al. (1988), where Caucasians, Northeast Asians, and Ameridians from the Northeurasian supercluster and the rest of non-Africans form the Southeast Asian supercluster. One of the major factors that caused the difference between the two trees is that Cavalli-Sforza et al. used unweighted pair-group method with arithmetic mean (UPGMA) in phylogenetic inference, whereas we used the NJ method in which evolutionary rate is allowed to vary among different populations. Bootstrap tests have shown that the UPGMA tree receives poor statistical support whereas the NJ tree is well supported. Implications that the phylogenetic tree obtained has on the current controversy over the out-of-Africa and the multiregional theories of human origins are discussed.

Estimation of the number of nucleotide substitutions in the control region of mitochondrial DNA in humans and chimpanzees

Examining the pattern of nucleotide substitution for the control region of mitochondrial DNA (mtDNA) in humans and chimpanzees, we developed a new mathematical method for estimating the number of transitional and transversional substitutions per site, as well as the total number of nucleotide substitutions. In this method, excess transitions, unequal nucleotide frequencies, and variation of substitution rate among different sites are all taken into account. Application of this method to human and chimpanzee data suggested that the transition/transversion ratio for the entire control region was approximately 15 and nearly the same for the two species. The 95% confidence interval of the age of the common ancestral mtDNA was estimated to be 80,000-480,000 years in humans and 0.57-2.72 Myr in common chimpanzees.

Evolutionary relationships of the classes of major histocompatibility complex genes

A number of hypotheses have been proposed to account for the evolutionary origin of the classes of major histocompatibility complex (MHC) genes of vertebrates. According to one hypothesis the class II MHC evolved first, whereas another hypothesis holds that the class I MHC originated first as a result of a recombination between an immunoglobulin-like C-domain and the peptide-binding domain of an HSP70 heat-shock protein. A phylogenetic tree of C-domains from MHC and related molecules supports a relationship between the class II MHC alpha chain and beta 2-microglobulin and between the class II MHC beta-chain and the class I alpha chain. If this phylogeny is correct, the hypothesis that the class I MHC evolved by recombination with HSP70 is less parsimonious than the hypothesis that class II evolved first. Furthermore, when MHC peptide-binding domains are simultaneously aligned with HSP70 domains and with V-domains from members of the immunoglobulin superfamily, they are slightly more similar to the latter than to the former; and the class II alpha 1 and beta 1 domains show much greater similarity to each other than would be expected if they evolved from separate HSP70 domains. Thus, most evidence supports the hypothesis that the ancestral MHC molecule had a class II-like structure.