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Chemosensory receptors are essential for the survival of organisms that range from bacteria to mammals. Recent studies have shown that the numbers of functional chemosensory receptor genes and pseudogenes vary enormously among the genomes of different animal species. Although much of the variation can be explained by the adaptation of organisms to different environments, it has become clear that a substantial portion is generated by genomic drift, a random process of gene duplication and deletion. Genomic drift also generates a substantial amount of copy-number variation in chemosensory receptor genes within species. It seems that mutation by gene duplication and inactivation has important roles in both the adaptive and non-adaptive evolution of chemosensation.

Odor perception in mammals is mediated by a large multigene family of olfactory receptor (OR) genes. The number of OR genes varies extensively among different species of mammals, and most species have a substantial number of pseudogenes. To gain some insight into the evolutionary dynamics of mammalian OR genes, we identified the entire set of OR genes in platypuses, opossums, cows, dogs, rats, and macaques and studied the evolutionary change of the genes together with those of humans and mice. We found that platypuses and primates have <400 functional OR genes while the other species have 800-1,200 functional OR genes. We then estimated the numbers of gains and losses of OR genes for each branch of the phylogenetic tree of mammals. This analysis showed that (i) gene expansion occurred in the placental lineage each time after it diverged from monotremes and from marsupials and (ii) hundreds of gains and losses of OR genes have occurred in an order-specific manner, making the gene repertoires highly variable among different orders. It appears that the number of OR genes is determined primarily by the functional requirement for each species, but once the number reaches the required level, it fluctuates by random duplication and deletion of genes. This fluctuation seems to have been aided by the stochastic nature of OR gene expression.

Recent studies of developmental biology have shown that the genes controlling phenotypic characters expressed in the early stage of development are highly conserved and that recent evolutionary changes have occurred primarily in the characters expressed in later stages of development. Even the genes controlling the latter characters are generally conserved, but there is a large component of neutral or nearly neutral genetic variation within and between closely related species. Phenotypic evolution occurs primarily by mutation of genes that interact with one another in the developmental process. The enormous amount of phenotypic diversity among different phyla or classes of organisms is a product of accumulation of novel mutations and their conservation that have facilitated adaptation to different environments. Novel mutations may be incorporated into the genome by natural selection (elimination of preexisting genotypes) or by random processes such as genetic and genomic drift. However, once the mutations are incorporated into the genome, they may generate developmental constraints that will affect the future direction of phenotypic evolution. It appears that the driving force of phenotypic evolution is mutation, and natural selection is of secondary importance.

Olfaction, which is an important physiological function for the survival of mammals, is controlled by a large multigene family of olfactory receptor (OR) genes. Fishes also have this gene family, but the number of genes is known to be substantially smaller than in mammals. To understand the evolutionary dynamics of OR genes, we conducted a phylogenetic analysis of all functional genes identified from the genome sequences of zebrafish, pufferfish, frogs, chickens, humans, and mice. The results suggested that the most recent common ancestor between fishes and tetrapods had at least nine ancestral OR genes, and all OR genes identified were classified into nine groups, each of which originated from one ancestral gene. Eight of the nine group genes are still observed in current fish species, whereas only two group genes were found from mammalian genomes, showing that the OR gene family in fishes is much more diverse than in mammals. In mammals, however, one group of genes, gamma, expanded enormously, containing approximately 90% of the entire gene family. Interestingly, the gene groups observed in mammals or birds are nearly absent in fishes. The OR gene repertoire in frogs is as diverse as that in fishes, but the expansion of group gamma genes also occurred, indicating that the frog OR gene family has both mammal- and fish-like characters. All of these observations can be explained by the environmental change that organisms have experienced from the time of the common ancestor of all vertebrates to the present.

Olfactory receptor (OR) genes form the largest known multigene family in the human genome. To obtain some insight into their evolutionary history, we have identified the complete set of OR genes and their chromosomal locations from the latest human genome sequences. We detected 388 potentially functional genes that have intact ORFs and 414 apparent pseudogenes. The number and the fraction (48%) of functional genes are considerably larger than the ones previously reported. The human OR genes can clearly be divided into class I and class II genes, as was previously noted. Our phylogenetic analysis has shown that the class II OR genes can further be classified into 19 phylogenetic clades supported by high bootstrap values. We have also found that there are many tandem arrays of OR genes that are phylogenetically closely related. These genes appear to have been generated by tandem gene duplication. However, the relationships between genomic clusters and phylogenetic clades are very complicated. There are a substantial number of cases in which the genes in the same phylogenetic clade are located on different chromosomal regions. In addition, OR genes belonging to distantly related phylogenetic clades are sometimes located very closely in a chromosomal region and form a tight genomic cluster. These observations can be explained by the assumption that several chromosomal rearrangements have occurred at the regions of OR gene clusters and the OR genes contained in different genomic clusters are shuffled.

Antennapedia (Antp)-class homeobox genes are involved in the determination of pattern formation along the anterior-posterior axis of the animal embryo. A phylogenetic analysis of Antp-class homeodomains of the nematode, Drosophila, amphioxus, mouse, and human indicates that the 13 cognate group genes of this gene family can be divided into two major groups, i.e., groups I and II. Group I genes can further be divided into subgroups A (cognate groups 1-2), B (cognate group 3), and C (cognate groups 4-8), and group II genes can be divided into subgroups D (cognate groups 9-10) and E (cognate groups 11-13), though this classification is somewhat ambiguous. Evolutionary distances among different amino acid sequences suggest that the divergence between group I and group II genes occurred approximately 1000 million years (MY) ago, and the five different subgroups were formed by approximately 600 MY ago, probably before the divergence of Pseudocoelomates (e.g., nematodes) and Coelomates (e.g., insects and chordates). Our results show that the genes that are phylogenetically close are also closely located in the chromosome, suggesting that the colinearity between the gene expression and gene arrangement was generated by successive tandem gene duplications and that the gene arrangement has been maintained by some sort of selection.

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.

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.

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.

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.

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.

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.

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.

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.

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 formal mathematical analysis of Kimura's (1981) six-parameter model of nucleotide substitution for the case of unequal substitution rates among different pairs of nucleotides is conducted, a new formulae for estimating the number of nucleotide substitutions and its standard error are obtained. By using computer simulation, the validities and utilities of Jukes and Cantor's (1969) one-parameter formula, Takahata and Kimura's (1981) four-parameter formula, and our six-parameter formula for estimating the number of nucleotide substitutions are examined under three different schemes of nucleotide substitution. It is shown that the one-parameter and four-parameter formulae often give underestimates when the number of nucleotide substitutions is large, whereas the six-parameter formula generally gives a good estimate for all the three substitution schemes examined. However, when the number of nucleotide substitutions is large, the six-parameter and four-parameter formulae are often inapplicable unless the number of nucleotides compared is extremely large. It is also shown that as long as the mean number of nucleotide substitutions is smaller than one per nucleotide site the three formulae give more or less the same estimate regardless of the substitution scheme used.

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.

On the neutral mutation hypothesis, the rate of nucleotide substitution is expected to be higher for functionally less important genes or parts of genes than for functionally more important genes, as the latter would be subject to stronger purifying (negative) selectio. On the other hand, selectionists believe that most nucleotide substitutions are caused by positive darwinian selection, in which case the rate of nucleotide substitution in functionally unimportant genes or parts of genes is expected to be relatively lower because the mutations in these regions of DNA would not produce any significant selective advantages. Kimura and Jukes have argued that the higher substitution rate observed at the third positions of codons than at the first two positions supports the neutral mutation hypothesis, as most third-position substitutions are synonymous and do not change the amino acids encoded, although others have discussed the possibility that third-position substitutions are subject to positive darwinian selection. Recently, Kimura noted that the mouse globin pseudogene, psi alpha 3, evolved faster than the normal mouse alpha 1 gene, although he did not compute the substitution rate. Here, we present a method of computing the rate of nucleotide substitution for pseudogenes, and report that the three recently discovered pseudogenes show an extremely high rate of nucleotide substitution. As these pseudogenes apparently have no function, this finding strongly supports the neutral mutation hypothesis.

Using gene frequency data for 62 protein loci and 23 blood group loci, we studied the genetic relationship of the three major races of man, Caucasoid, Negroid, and Mongoloid. Genetic distance data indicate that Caucasoid and Mongoloid are somewhat closer to each other than to Negroid. Analysis of restriction site data for mitochondrial DNA also shows the same genetic relationship. It seems that the Negroid and the Caucasoid-Mongoloid groups diverged about 110,000 +/- 34,000 years ago, whereas Caucasoid and Mongoloid diverged about 41,000 +/- 15,000 years ago. The genetic relationships of various races in each group of Caucasoid, Negroid, and Mongoloid were also studied. All European populations are genetically close to one another except the Lapps, whereas many African, Oceanian, and Amer-indian tribes show large extents of genetic differentiation. The major cause for this differentiation seems to be the bottleneck effect. The Polynesians, Micronesians, and Indonesians are more closely related to the Asian Mongoloids than to the Australoids in Australia and New Guinea. There are also indications that migration played an important role in forming the current genetic relationships among human races. The extent of genetic differentiation between human races is not always correlated with the degree of morphologic differentiation. The genetic differentiation at protein loci seems to occur largely by mutation, genetic drift, and isolation, whereas morphologic characters are apparently subject to stronger natural selection than "average protein loci."

A method of estimating the number of nucleotide substitutions from amino acid sequence data is developed by using Dayhoff's mutation probability matrix. This method takes into account the effect of nonrandom amino acid substitutions and gives an estimate which is similar to the value obtained by Fitch's counting method, but larger than the estimate obtained under the assumption of random substitutions (Jukes and Cantor's formula). Computer simulations based on Dayhoff's mutation probability matrix have suggested that Jukes and Holmquist's method of estimating the number of nucleotide substitutions gives an overestimate when amino acid substitution is not random and the variance of the estimate is generally very large. It is also shown that when the number of nucleotide substitutions is small, this method tends to give an overestimate even when amino acid substitution is purely at random.

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.

In order to explain difference and similarity in producing antibody diversity between immunoglobulin (Ig) and T cell receptor (TCR), authors compared both codon substitution and concerted evolution rate between the variable segment of Ig heavy (Ig VH) and that of TCR (TCR V). The protein sequences of TCR V alpha (including 8 gene segments from mouse and 3 from human), TCR V beta (including 11 from mouse and one from human) and T cell V gamma (including 2 from mouse and 4 from human) were compiled, as well as the protein sequences of Ig VH (3 from human, 11 from mouse, 3 from caiman and one from shark) were collected. It is shown that: (1) the nucleotide substitution of TCR V segment is 2.4 times as large as that of Ig VH in coding region; (2) as for concerted evolution, gene duplicate rates in TCR V and Ig VH are 1.7 X 10(-8) and 1.6 X 10(-8)/gene/year, respectively. The number of TCR V(V alpha equals to 100 and V beta equals to 30) is less than the one of Ig VH (VH equals to 300), for TCR V is subject to negative selection of major histocompatibility complex according to the neutral theory. We discussed that is somatic mutation or DNA rearrangement the main force in producing antibody diversity and are there pseudogenes in TCR V or not.

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.

There are three different methods of estimating the number of nucleotide substitutions between a pair of species from amino acid sequence data, i.e. the Poisson correction method, random evolutionary hit method, and counting the actual but minimum number of nucleotide substitutions. In this paper the relationships among the estimates obtained by these methods are studied empirically. The results obtained indicate that there is a high correlation among these estimates and in practice any of the three methods may be used for constructing evolutionary trees or relating nucleotide substitutions to evolutionary time. The effects of varying rates of nucleotide substition among different sites on the Poisson correction and random evolutionary hit methods are also studied mathematically. It is shown that these two methods are quite insensitive to the variation of the rate of nucleotide substitution.

Mathematical models are presented for the evolution of postmating and premating reproductive isolation. In the case of postmating isolation it is assumed that hybrid sterility or inviability is caused by incompatibility of alleles at one or two loci, and evolution of reproductive isolation occurs by random fixation of different incompatibility alleles in different populations. Mutations are assumed to occur following either the stepwise mutation model or the infinite-allele model. Computer simulations by using Itô's stochastic differential equations have shown that in the model used the reproductive isolation mechanism evolves faster in small populations than in large populations when the mutation rate remains the same. In populations of a given size it evolves faster when the number of loci involved is large than when this is small. In general, however, evolution of isolation mechanisms is a very slow process, and it would take thousands to millions of generations if the mutation rate is of the order of 10(-5) per generation. Since gene substitution occurs as a stochastic process, the time required for the establishment of reproductive isolation has a large variance. Although the average time of evolution of isolation mechanisms is very long, substitution of incompatibility genes in a population occurs rather quickly once it starts. The intrapopulational fertility or viability is always very high. In the model of premating isolation it is assumed that mating preference or compatibility is determined by male- and female-limited characters, each of which is controlled by a single locus with multiple alleles, and mating occurs only when the male and female characters are compatible with each other. Computer simulations have shown that the dynamics of evolution of premating isolation mechanism is very similar to that of postmating isolation mechanism, and the mean and variance of the time required for establishment of premating isolation are very large. Theoretical predictions obtained from the present study about the speed of evolution of reproductive isolation are consistent with empirical data available from vertebrate organisms.

Conducting computer simulations, Nei and Tateno (1978) have shown that Jukes and Holmquist's (1972) method of estimating the number of nucleotide substitutions tends to give an overestimate and the estimate obtained has a large variance. Holmquist and Conroy (1980) repeated some parts of our simulation and claim that the overestimation of nucleotide substitutions in our paper occurred mainly because we used selected data. Examination of Holmquist and Conroy's simulation indicates that their results are essentially the same as ours when the Jukes-Holmquist method is used, but since they used a different method of computation their estimates of nucleotide substitutions differed substantially from ours. Another problem in Holmquist and Conroy's Letter is that they confused the expected number of nucleotide substitution with the number in a sample. This confusion has resulted in a number of unnecessary arguments. They also criticized our X2 measure, but this criticism is apparently due to a misunderstanding of the assumptions of our method and a failure to use our method in the way we described. We believe that our earlier conclusions remain unchanged.

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.

The major histocompatibility complex (MHC) in humans and chimpanzees includes three classical class I loci, A, B and C, which encode glycoproteins expressed on the surface of all nucleated cells. There are also several nonclassical class I loci including E, which have more limited expression. By analyzing published sequences, we have shown that in exons 4 and 5, A locus alleles from both humans and chimpanzees are much more similar to E than to B or C alleles, whereas in exons 2 and 3 alleles from all three classical class I loci are much more similar to each other than any one is to E. We propose that some 20 million years ago, interlocus recombination led to the formation of a hybrid gene in which exons 2 and 3 were derived from the original A locus and exons 4 and 5 were derived from the E locus. The fact that such an ancient event can still be detected suggests that interlocus recombination is rare in the MHC and does not significantly contribute to MHC polymorphism, which is known to be extremely high. The present finding, however, supports Gilbert's idea that exons in a gene may occasionally be replaced by those from another gene in the evolutionary process.

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.

The accuracies and efficiencies of four different methods for constructing phylogenetic trees from molecular data were examined by using computer simulation. The methods examined are UPGMA, Fitch and Margoliash's (1967) (F/M) method, Farris' (1972) method, and the modified Farris method (Tateno, Nei, and Tajima, this paper). In the computer simulation, eight OTUs (32 OTUs in one case) were assumed to evolve according to a given model tree, and the evolutionary change of a sequence of 300 nucleotides was followed. The nucleotide substitution in this sequence was assumed to occur following the Poisson distribution, negative binomial distribution or a model of temporally varying rate. Estimates of nucleotide substitutions (genetic distances) were then computed for all pairs of the nucleotide sequences that were generated at the end of the evolution considered, and from these estimates a phylogenetic tree was reconstructed and compared with the true model tree. The results of this comparison indicate that when the coefficient of variation of branch length is large the Farris and modified Farris methods tend to be better than UPGMA and the F/M method for obtaining a good topology. For estimating the number of nucleotide substitutions for each branch of the tree, however, the modified Farris method shows a better performance than the Farris method. When the coefficient of variation of branch length is small, however, UPGMA shows the best performance among the four methods examined. Nevertheless, any tree-making method is likely to make errors in obtaining the correct topology with a high probability, unless all branch lengths of the true tree are sufficiently long. It is also shown that the agreement between patristic and observed genetic distances is not a good indicator of the goodness of the tree obtained.

Statistical properties of Goodman et al.'s (1974) method of compensating for undetected nucleotide substitutions in evolution are investigated by using computer simulation. It is found that the method tends to overcompensate when the stochastic error of the number of nucleotide substitutions is large. Furthermore, the estimate of the number of nucleotide substitutions obtained by this method has a large variance. However, in order to see whether this method gives overcompensation when applied together with the maximum parsimony method, a much larger scale of simulation seems to be necessary.

To study the evolutionary relationships of the three major groups of humans, Europeans, Asians and Africans, the genetic distances between them were computed by using 4 different sets of genetic loci (84 protein loci, 33 blood group loci, 8 HLA and immunoglobulin loci, and 61 DNA markers). The results obtained indicate that the overall genetic distance between Europeans and Asians is significantly lower than that between Europeans and Africans of that between Asians and Africans and support the hypothesis of an African origin of modern humans. This seems to be the first study to establish the evolutionary relationships of the three major groups of humans at a statistically significant level.

The empirical variance of the immunological distance as measured by microcomplement fixation with albumin is determined. The variance obtained is at least two times larger than the mean when the mean is small and the ratio of the variance to the mean increases with increasing mean. Thus, the immunological dating of evolutionary time has a large standard error. It is shown that in bird lysozymes the relationship between immunological distance (y) and the number of amino acid substitutions per 100 sites (x) is given by y = 4.2 x approximately.

Mathematical studies are conducted on three problems that arise in molecular population genetics. (1) The time required for a particular allele to become extinct in a population under the effects of mutation, selection, and random genetic drift is studied. In the absence of selection, the mean extinction time of an allele with an initial frequency close to 1 is of the order of the reciprocal of the mutation rate when 4Nv less than 1, where N is the effective population size and v is the mutation rate per generation. Advantageous mutations reduce the extinction time considerably, whereas deleterious mutations increase it tremendously even if the effect on fitness is very slight. (2) Mathematical formulae are derived for the distribution and the moments of extinction time of a particular allele from one or both of two related populations or species under the assumption of no selection. When 4Nv less than 1, the mean extinction time is about half that for a single population, if the two populations are descended from a common original stock. (3) The expected number as well as the proportion of common neutral alleles shared by two related species at the tth generation after their separation are studied. It is shown that if 4Nv is small, the two species are expected to share a high proportion of common alleles even 4N generations after separation. In addition to the above mathematical studies, the implications of our results for the common alleles at protein loci in related Drosophila species and for the degeneration of unused characters in cave animals are discussed.

A mathematical theory for computing the probabilities of various nucleotide configurations among related species is developed, and the probability of obtaining the correct tree (topology) from nucleotide sequence data is evaluated using models of evolutionary trees that are close to the tree of mitochondrial DNAs from human, chimpanzee, gorilla, orangutan, and gibbon. Special attention is given to the number of nucleotides required to resolve the branching order among the three most closely related organisms (human, chimpanzee, and gorilla). If the extent of DNA divergence is close to that obtained by Brown et al. for mitochondrial DNA and if sequence data are available only for the three most closely related organisms, the number of nucleotides (m*) required to obtain the correct tree with a probability of 95% is about 4700. If sequence data for two outgroup species (orangutan and gibbon) are available, m* becomes about 2600-2700 when the transformed distance, distance-Wagner, maximum parsimony, or compatibility method is used. In the unweighted pair-group method, m* is not affected by the availability of data from outgroup species. When these five different tree-making methods, as well as Fitch and Margoliash's method, are applied to the mitochondrial DNA data (1834 bp) obtained by Brown et al. and by Hixson and Brown, they all give the same phylogenetic tree, in which human and chimpanzee are most closely related. However, the trees considered here are "gene trees," and to obtain the correct "species tree," sequence data for several independent loci must be used.