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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.

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.

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)

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.

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.

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.

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.

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.

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.

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.

Lake's evolutionary parsimony (EP) method of constructing a phylogenetic tree is primarily applied to four DNA sequences. In this method, three quantities--X, Y, and Z--that correspond to three possible unrooted trees are computed, and an invariance property of these quantities is used for choosing the best tree. However, Lake's method depends on a number of unrealistic assumptions. We therefore examined the theoretical basis of his method and reached the following conclusions: (1) When the rates of two transversional changes from a nucleotide are unequal, his invariance property breaks down. (2) Even if the rates of two transversional changes are equal, the invariance property requires some additional conditions. (3) When Kimura's two-parameter model of nucleotide substitution applies and the rate of nucleotide substitution varies greatly with branch, the EP method is generally better than the standard maximum-parsimony (MP) method in recovering the correct tree but is inferior to the neighbor-joining (NJ) and a few other distance matrix methods. (4) When the rate of nucleotide substitution is the same or nearly the same for all branches, the EP method is inferior to the MP method even if the proportion of transitional changes is high. (5) When Lake's assumptions fail, his chi2 test may identify an erroneous tree as the correct tree. This happens because the test is not for comparing different trees. (6) As long as a proper distance measure is used, the NJ method is better than the EP and MP methods whether there is a transition/transversion bias or whether there is variation in substitution rate among different nucleotide sites.

The major histocompatibility complex (MHC) class II molecule consists of noncovalently associated alpha and beta chains. In mammals studied so far, the class II MHC can be divided into a number of regions, each containing one or more alpha-chain genes (A genes) and beta-chain genes (B genes), and it has been known for some time that orthologous relationships exist between genes in corresponding regions from different mammalian species. A phylogenetic analysis of DNA sequences of class II A and B genes confirmed these relationships; but no such orthologous relationship was observed between the B genes of mammals and those of birds. Thus, the class II regions have diverged since the separation of birds and mammals (approximately 300 Mya) but before the radiation of the placental mammalian orders (60-80 Mya). Comparison of the phylogenetic trees for A and B genes revealed an unexpected characteristic of DP-region genes: DPB genes are most closely related to DQB genes, whereas DPA chain genes are most closely related to DRA-chain genes. Thus, the DP region seems to have originated through a recombinational event which brought together a DQB gene and a DRA gene (perhaps approximately 120 Mya). The 5' untranslated region of all class II genes includes sequences which are believed to be important in regulating class II gene expression but which are not conserved in known pseudogenes. These sequences are conserved to an extraordinary degree in the human DQB1 gene and its mouse homologue A beta 1, suggesting that regulation of expression of this locus may play a key role in expression of the entire class II MHC.

Certain major-histocompatibility-complex (MHC) loci are highly polymorphic, and the mechanism of maintenance of this polymorphism remains controversial. Recent studies of the pattern of nucleotide substitution at MHC loci have produced strong evidence that this polymorphism is maintained mainly by positive Darwinian selection that operates on the antigen recognition site (ARS) of the MHC molecule. The ARS of the class I MHC consists of three subregions: (1) the binding cleft, (2) T-cell-receptor-directed residues, and (3) outward-directed residues. Here we report that the rate of nonsynonymous nucleotide substitution is much higher in the binding cleft than in the other ARS subregions. Furthermore, nonsynonymous nucleotide substitutions that result in a change of residue side-chain charge occur significantly more frequently than expected by chance. We conclude that the main target of positive selection on the class I MHC molecules is the binding cleft of the ARS and that this selection acts primarily to promote diversity among alleles with respect to the pattern of residue side-chain charges (charge profile) in the binding cleft. These results provide additional support for the hypothesis that MHC polymorphism is maintained by overdominant selection relating to antigen-binding capacity and thus to disease resistance.

Statistical methods for computing the variances of nucleotide diversity within populations and of nucleotide divergence between populations are developed. Both variances are computed by finding the phylogenetic relationships of the DNA sequences studied through the unweighted pair-group method or some other tree-making method. The methods developed are applicable to both DNA sequence and restriction-site map data.

To examine Gojobori and Nei's hypothesis that the immunoglobulin heavy-chain variable-region (VH) genes in mammals are subject to diversity-enhancing selection, we studied the rates of synonymous and nonsynonymous nucleotide substitution in the complementarity-determining regions (CDRs) and in the framework regions (FRs) of mouse and human VH genes. The results obtained indicate that the non-synonymous rate is higher than the synonymous rate in CDRs, whereas the reverse is true in FRs. This observation supports Gojobori and Nei's hypothesis and suggests that diversity-enhancing selection (similar to overdominant selection) operates mainly in CDRs and that this is one of the evolutionary factors that increase antibody diversity.

The class I major histocompatibility complex genes are composed of classical and nonclassical genes, the latter being largely nonfunctional. To understand the evolutionary relationships of the two groups of class I genes, a phylogenetic analysis of DNA sequences was conducted using 45 genes from six mammalian and one avian species. The results indicate that nonclassical genes in one species are more closely related to classical genes from the same species than to nonclassical genes from a species belonging to a different order or family. This indicates that the differentiation of classical and nonclassical genes occurs rather rapidly in the genome. Classical genes are apparently duplicated with a high frequency in the evolutionary process, and many of the duplicated genes seem to degenerate into nonclassical genes as a result of deleterious mutation. The nonclassical Qa genes in the mouse have sequences homologous to regulatory sequences involved in the universal expression of classical class I genes, but they have accumulated numerous nucleotide substitutions in these sequences. The pattern of nucleotide substitution in nonclassical genes is different from that in classical genes. In nonclassical genes, the rate of nonsynonymous substitution is higher in the antigen recognition site than in other gene regions, as is true of classical genes. However, unlike the case of classical genes, the nonsynonymous rate does not always exceed the synonymous rate in the antigen recognition site. Nonclassical proteins further differ from classical proteins in having amino acid replacements in conserved antigen recognition site positions. These observations are consistent with the hypothesis that nonclassical genes have originated from classical genes but have lost classical class I function because of deleterious mutation.

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.

It is well known that a phylogenetic tree (gene tree) constructed from DNA sequences for a genetic locus does not necessarily agree with the tree that represents the actual evolutionary pathway of the species involved (species tree). One of the important factors that cause this difference is genetic polymorphism in the ancestral species. Under the assumption of neutral mutations, this problem can be studied by evaluating the probability (P) that a gene tree has the same topology as that of the species tree. When one gene (allele) is used from each of the species involved, the probability can be expressed as a simple function of Ti = ti/(2N), where ti is the evolutionary time measured in generations for the ith internodal branch of the species tree and N is the effective population size. When any of the Ti's is less than 1, the probability P becomes considerably less than 1.0. This probability cannot be substantially increased by increasing the number of alleles sampled from a locus. To increase the probability, one has to use DNA sequences from many different loci that have evolved independently of each other.

A new method called the neighbor-joining method is proposed for reconstructing phylogenetic trees from evolutionary distance data. The principle of this method is to find pairs of operational taxonomic units (OTUs [= neighbors]) that minimize the total branch length at each stage of clustering of OTUs starting with a starlike tree. The branch lengths as well as the topology of a parsimonious tree can quickly be obtained by using this method. Using computer simulation, we studied the efficiency of this method in obtaining the correct unrooted tree in comparison with that of five other tree-making methods: the unweighted pair group method of analysis, Farris's method, Sattath and Tversky's method, Li's method, and Tateno et al.'s modified Farris method. The new, neighbor-joining method and Sattath and Tversky's method are shown to be generally better than the other methods.

The nucleotide sequences of four genes of the influenza A virus (nonstructural protein, matrix protein, and a few subtypes of hemagglutinin and neuraminidase) are compiled for a large number of strains isolated from various locations and years, and the evolutionary relationship of the sequences is investigated. It is shown that all of these genes or subtypes are highly polymorphic and that the polymorphic sequences (alleles) are subject to rapid turnover in the population, their average age being much less than that of higher organisms. Phylogenetic analysis suggests that most polymorphic sequences within a subtype or a gene appeared during the last 80 years and that the divergence among the subtypes of hemagglutinin genes might have occurred during the last 300 years. The high degree of polymorphism in this RNA virus is caused by an extremely high rate of mutation, estimated to be 0.01/nucleotide site/year. Despite the high rate of mutation, most influenza virus genes are apparently subject to purifying selection, and the rate of nucleotide substitution is substantially lower than the mutation rate. There is considerable variation in the substitution rate among different genes, and the rate seems to be lower in nonhuman viral strains than in human strains. The difference might be responsible for the so-called freezing effect in some viral strains.

The relative contributions of germline gene variation and somatic mutation to immunoglobulin diversity were studied by comparing germline gene sequences with their rearranged counterparts for the mouse VH, V kappa, and V lambda genes. The mutation rate at the amino acid level was estimated to be 7.0% in the first and second complementarity-determining regions (CDRs) and 2.0% in the framework regions (FRs). The difference in the mutation rate at the nucleotide level between the CDRs and FRs was of the same order of magnitude as that for the amino acid level. Analysis of amino acid diversity or nucleotide diversity indicated that the contribution of somatic mutation to immunoglobulin diversity is approximately 5%. However, the contribution of somatic mutation to the number of different amino acid sequences of immunoglobulins is much larger than that estimated by the analysis of amino acid diversity, and more than 90% of the different immunoglobulins seem to be generated by somatic mutation. Examination of the pattern of nucleotide substitution has suggested that clonal selection after somatic mutation may not be as strong as generally believed.

Two simple methods for estimating the numbers of synonymous and nonsynonymous nucleotide substitutions are presented. Although they give no weights to different types of codon substitutions, these methods give essentially the same results as those obtained by Miyata and Yasunaga's and by Li et al.'s methods. Computer simulation indicates that estimates of synonymous substitutions obtained by the two methods are quite accurate unless the number of nucleotide substitutions per site is very large. It is shown that all available methods tend to give an underestimate of the number of nonsynonymous substitutions when the number is large.

A mathematical theory for the evolutionary change of restriction endonuclease cleavage sites is developed, and the probabilities of various types of restriction-site changes are evaluated. A computer simulation is also conducted to study properties of the evolutionary change of restriction sites. These studies indicate that parsimony methods of constructing phylogenetic trees often make erroneous inferences about evolutionary changes of restriction sites unless the number of nucleotide substitutions per site is less than 0.01 for all branches of the tree. This introduces a systematic error in estimating the number of mutational changes for each branch and, consequently, in constructing phylogenetic trees. Therefore, parsimony methods should be used only in cases where nucleotide sequences are closely related. Reexamination of Ferris et al.'s data on restriction-site differences of mitochondrial DNAs does not support Templeton's conclusions regarding the phylogenetic tree for man and apes and the molecular clock hypothesis. Templeton's claim that Nei and Li's method of estimating the number of nucleotide substitutions per site is seriously affected by parallel losses and loss-gains of restriction sites is also unsupported.

A mathematical formula for estimating the average number of nucleotide substitutions per site (delta) between two homologous DNA sequences is developed by taking into account unequal rates of substitution among different nucleotide pairs. Although this formula is obtained for the equal-input model of nucleotide substitution, computer simulations have shown that it gives a reasonably good estimate for a wide range of nucleotide substitution patterns as long as delta is equal to or smaller than 1. Furthermore, the frequency of cases to which the formula is inapplicable is much lower than that for other similar methods recently proposed. This point is illustrated using insulin genes. A statistical method for estimating the number of nucleotide changes due to deletion and insertion is also developed. Application of this method to globin gene data indicates that the number of nucleotide changes per site increases with evolutionary time but the pattern of the increase is quite irregular.

With the aim of understanding the concerted evolution of the immunoglobulin VH multigene family, a phylogenetic tree for the DNA sequences of 16 mouse and five human germ line genes was constructed. This tree indicates that all genes in this family have undergone substantial evolutionary divergence. The most closely related genes so far identified in the mouse genome seem to have diverged about 6 million years (MY) ago, whereas the most distantly related genes diverged about 300 MY ago. This suggests that gene duplication caused by unequal crossing-over or gene conversion occurs very slowly in this gene family. The rate of occurrence of gene duplication in the VH gene family has been estimated to be 5 x 10(-7) per gene per year, which seems to be at least about 100 times lower than that for the rRNA gene family. This low rate of concerted evolution in the VH gene family helps retain intergenic genetic variability that in turn contributes to antibody diversity. Because of accumulation of destructive mutations, however, about one-third of the mouse and human VH genes seem to have become nonfunctional. Many of these pseudogenes have apparently originated recently, but some of them seem to have existed in the genome for more than 10 MY. The rate of nucleotide substitution for the complementarity-determining regions (CDRs) is as high as that of pseudogenes. This suggests that there is virtually no purifying selection operating in the CDRs and that germ line mutations are effectively used for generating antibody diversity.

Statistical methods for computing the standard errors of the branching points of an evolutionary tree are developed. These methods are for the unweighted pair-group method-determined (UPGMA) trees reconstructed from molecular data such as amino acid sequences, nucleotide sequences, restriction-sites data, and electrophoretic distances. They were applied to data for the human, chimpanzee, gorilla, orangutan, and gibbon species. Among the four different sets of data used, DNA sequences for an 895-nucleotide segment of mitochondrial DNA (Brown et al. 1982) gave the most reliable tree, whereas electrophoretic data (Bruce and Ayala 1979) gave the least reliable one. The DNA sequence data suggested that the chimpanzee is the closest and that the gorilla is the next closest to the human species. The orangutan and gibbon are more distantly related to man than is the gorilla. This topology of the tree is in agreement with that for the tree obtained from chromosomal studies and DNA-hybridization experiments. However, the difference between the branching point for the human and the chimpanzee species and that for the gorilla species and the human-chimpanzee group is not statistically significant. In addition to this analysis, various factors that affect the accuracy of an estimated tree are discussed.