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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. [ABSTRACT FROM AUTHOR]

It is well known that the selection coefficient of a mutant allele varies from generation to generation, and the effect of this factor on genetic variation has been studied by many theoreticians. However, no consensus has been reached. One group of investigators believes that fluctuating selection has an effect of enhancing genetic variation, whereas the other group contends that it has a diversity-reducing effect. In recent years, it has become possible to study this problem by using single nucleotide polymorphisms (SNPs) as well as exome sequence data. In this article we present the theoretical distributions of mutant nucleotide frequencies for the two models of fluctuating selection and then compare the distributions with the empirical distributions obtained from SNP and exome sequence data in human populations. Interestingly, both SNP and exome sequence data showed that the neutral mutation model fits the empirical distribution quite well. Furthermore, the mathematical models with diversity-enhancing and diversity-reducing effects also fit the empirical distribution reasonably well. This result implies that there is no need of distinguishing between the diversity-enhancing and diversity-reducing models of fluctuating selection and the nucleotide polymorphism in human populations can be explained largely by neutral mutations when long-term evolution is considered.

Natural selection operating in protein-coding genes is often studied by examining the ratio (omega) of the rates of nonsynonymous to synonymous nucleotide substitution. The branch-site method (BSM) based on a likelihood ratio test is one of such tests to detect positive selection for a predetermined branch of a phylogenetic tree. However, because the number of nucleotide substitutions involved is often very small, we conducted a computer simulation to examine the reliability of BSM in comparison with the small-sample method (SSM) based on Fisher's exact test. The results indicate that BSM often generates false positives compared with SSM when the number of nucleotide substitutions is approximately 80 or smaller. Because the omega value is also used for predicting positively selected sites, we examined the reliabilities of the site-prediction methods, using nucleotide sequence data for the dim-light and color vision genes in vertebrates. The results showed that the site-prediction methods have a low probability of identifying functional changes of amino acids experimentally determined and often falsely identify other sites where amino acid substitutions are unlikely to be important. This low rate of predictability occurs because most of the current statistical methods are designed to identify codon sites with high omega values, which may not have anything to do with functional changes. The codon sites showing functional changes generally do not show a high omega value. To understand adaptive evolution, some form of experimental confirmation is necessary.

F-box proteins are substrate-recognition components of the Skp1-Rbx1-Cul1-F-box protein (SCF) ubiquitin ligases. In plants, F-box genes form one of the largest multigene superfamilies and control many important biological functions. However, it is unclear how and why plants have acquired a large number of F-box genes. Here we identified 692, 337, and 779 F-box genes in Arabidopsis, poplar and rice, respectively, and studied their phylogenetic relationships and evolutionary patterns. We found that the plant F-box superfamily can be divided into 42 families, each of which has a distinct domain organization. We also estimated the number of ancestral genes for each family and identified highly conservative versus divergent families. In conservative families, there has been little or no change in the number of genes since the divergence between eudicots and monocots approximately 145 million years ago. In divergent families, however, the numbers have increased dramatically during the same period. In two cases, the numbers of genes in extant species are >100 times greater than that in the most recent common ancestor (MRCA) of the three species. Proteins encoded by highly conservative genes always have the same domain organization, suggesting that they interact with the same or similar substrates. In contrast, proteins of rapidly duplicating genes sometimes have quite different domain structures, mainly caused by unusually frequent shifts of exon-intron boundaries and/or frameshift mutations. Our results indicate that different F-box families, or different clusters of the same family, have experienced dramatically different modes of sequence divergence, apparently having resulted in adaptive changes in function.

The phylogenetic relationships of Ig light chain (IGL) genes are difficult to resolve, because these genes are short and evolve relatively fast. Here, we classify the IGL sequences from 12 tetrapod species into three distinct groups (kappa, lambda, and sigma isotypes) using conserved amino acid residues, recombination signal sequences, and genomic organization of IGL genes as cladistic markers. From the distribution of the markers we conclude that the earliest extant tetrapods, the amphibians, possess three IGL isotypes: kappa, lambda, and sigma. Of these, two (kappa and lambda) are also found in reptiles and some mammals. The lambda isotype is found in all tetrapods tested to date, whereas the kappa isotype seems to have been lost at least in some birds and in the microbat. Conservation of the cladistic molecular markers suggests that they are associated with functional specialization of the three IGL isotypes. The genomic maps of IGL loci reveal multiple gene rearrangements that occurred in the evolution of tetrapod species. These rearrangements have resulted in interspecific variation of the genomic lengths of the IGL loci and the number and order of IGL constituent genes, but the overall organization of the IGL loci has not changed.

The number of sensory receptor genes varies extensively among different mammalian species. This variation is believed to be caused partly by physiological requirements of animals and partly by genomic drift due to random duplication and deletion of genes. If the contribution of genomic drift is substantial, each species should contain a significant amount of copy number variation (CNV). We therefore investigated CNVs in sensory receptor genes among 270 healthy humans by using published CNV data. The results indicated that olfactory receptor (OR), taste receptor type 2, and vomeronasal receptor type 1 genes show a high level of intraspecific CNVs. In particular, >30% of the approximately 800 OR gene loci in humans were polymorphic with respect to copy number, and two randomly chosen individuals showed a copy number difference of approximately 11 in functional OR genes on average. There was no significant difference in the amount of CNVs between functional and nonfunctional OR genes. Because pseudogenes are expected to evolve in a neutral fashion, this observation suggests that functional OR genes also have evolved in a similar manner with respect to copy number change. In addition, we found that the evolutionary change of copy number of OR genes approximately follows the Gaussian process in probability theory, and the copy number divergence between populations has increased with evolutionary time. We therefore conclude that genomic drift plays an important role for generating intra- and interspecific CNVs of sensory receptor genes. Similar results were obtained when all annotated genes were analyzed.

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.

Olfactory receptor (OR) genes are of vital importance for animals to find food, identify mates, and avoid dangers. In mammals, the number of OR genes is large and varies extensively among different orders, whereas, in insects, the extent of interspecific variation appears to be small, although only a few species have been studied. To understand the evolutionary changes of OR genes, we identified all OR genes from 12 Drosophila species, of which the evolutionary time is roughly equivalent to that of eutherian mammals. The results showed that all species examined have similar numbers ( approximately 60) of functional OR genes. Phylogenetic analysis indicated that the ancestral species also had similar numbers of genes, but there were frequent gains and losses of genes that occurred in each evolutionary lineage. It appears that tandem duplication and random inactivation of duplicate genes are the major factors of gene number change. However, chromosomal rearrangements have contributed to the establishment of genome-wide distribution of OR genes. These results suggest that the repertoire of OR genes in Drosophila has been quite stable compared with the mammalian genes. The difference in evolutionary pattern between Drosophila and mammals can be explained partly by the differences of gene expression mechanisms and partly by the environmental and behavioral differences.

The bacterial recA gene and its eukaryotic homolog RAD51 are important for DNA repair, homologous recombination, and genome stability. Members of the recA/RAD51 family have functions that have differentiated during evolution. However, the evolutionary history and relationships of these members remains unclear. Homolog searches in prokaryotes and eukaryotes indicated that most eubacteria contain only one recA. However, many archaeal species have two recA/RAD51 homologs (RADA and RADB), and eukaryotes possess multiple members (RAD51, RAD51B, RAD51C, RAD51D, DMC1, XRCC2, XRCC3, and recA). Phylogenetic analyses indicated that the recA/RAD51 family can be divided into three subfamilies: (i) RADalpha, with highly conserved functions; (ii) RADbeta, with relatively divergent functions; and (iii) recA, functioning in eubacteria and eukaryotic organelles. The RADalpha and RADbeta subfamilies each contain archaeal and eukaryotic members, suggesting that a gene duplication occurred before the archaea/eukaryote split. In the RADalpha subfamily, eukaryotic RAD51 and DMC1 genes formed two separate monophyletic groups when archaeal RADA genes were used as an outgroup. This result suggests that another duplication event occurred in the early stage of eukaryotic evolution, producing the DMC1 clade with meiosis-specific genes. The RADbeta subfamily has a basal archaeal clade and five eukaryotic clades, suggesting that four eukaryotic duplication events occurred before animals and plants diverged. The eukaryotic recA genes were detected in plants and protists and showed strikingly high levels of sequence similarity to recA genes from proteobacteria or cyanobacteria. These results suggest that endosymbiotic transfer of recA genes occurred from mitochondria and chloroplasts to nuclear genomes of ancestral eukaryotes.

The natural killer (NK) receptor gene complex (NKC) encodes a large number of C-type lectin-like receptors, which are expressed on NK and other immune-related cells. These receptors play an important role in regulating NK-cell cytolytic activity, protecting cells against virus infection and tumorigenesis. To understand the evolutionary history of the NKC, we characterized the C-type lectin-like NKC genes and their organization from four major orders of placental mammals, primates (human), rodents (mouse and rat), carnivores (dog), and artiodactyls (cattle) and then conducted phylogenetic analysis of these genes. The results indicate that the NKC of placental mammals is highly heterogeneous in terms of the gene content and rates of birth and death of different gene lineages, but the NKC is also remarkably conserved in its gene organization and persistence of orthologous gene lineages. Among the 28 identified NKC gene lineages, 4, KLRA1, KLRB1, CLEC2D, and CLEC4A/B/C, have expanded rapidly in rodents only. The high birth and death rate of these 4 gene families might be due to functional differentiation driven by positive selection. Identification of putative NKC sequences in opossum and chicken genomes implies that the expansion of the NKC gene families might have occurred before the radiation of placental mammals but after the divergence of birds from mammals.

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.

In mammals, the cell surface receptors encoded by the leukocyte receptor complex (LRC) regulate the activity of T lymphocytes and B lymphocytes, as well as that of natural killer cells, and thus provide protection against pathogens and parasites. The chicken genome encodes many Ig-like receptors that are homologous to the LRC receptors. The chicken Ig-like receptor (CHIR) genes are members of a large monophyletic gene family and are organized into genomic clusters, which are in conserved synteny with the mammalian LRC. One-third of CHIR genes encode polypeptide molecules that contain both activating and inhibitory motifs. These genes are present in different phylogenetic groups, suggesting that the primordial CHIR gene could have encoded both types of motifs in a single molecule. In contrast to the mammalian LRC genes, the CHIR genes with similar function (inhibition or activation) are evolutionarily closely related. We propose that, in addition to recombination, single nucleotide substitutions played an important role in the generation of receptors with different functions. Structural models and amino acid analyses of the CHIR proteins reveal the presence of different types of Ig-like domains in the same phylogenetic groups, as well as sharing of conserved residues and conserved changes of residues between different CHIR groups and between CHIRs and LRCs. Our data support the notion that the CHIR gene clusters are regions homologous to the mammalian LRC gene cluster and favor a model of evolution by repeated processes of birth and death (expansion-contraction) of the Ig-like receptor genes.

Current efforts to reconstruct the tree of life and histories of multigene families demand the inference of phylogenies consisting of thousands of gene sequences. However, for such large data sets even a moderate exploration of the tree space needed to identify the optimal tree is virtually impossible. For these cases the neighbor-joining (NJ) method is frequently used because of its demonstrated accuracy for smaller data sets and its computational speed. As data sets grow, however, the fraction of the tree space examined by the NJ algorithm becomes minuscule. Here, we report the results of our computer simulation for examining the accuracy of NJ trees for inferring very large phylogenies. First we present a likelihood method for the simultaneous estimation of all pairwise distances by using biologically realistic models of nucleotide substitution. Use of this method corrects up to 60% of NJ tree errors. Our simulation results show that the accuracy of NJ trees decline only by approximately 5% when the number of sequences used increases from 32 to 4,096 (128 times) even in the presence of extensive variation in the evolutionary rate among lineages or significant biases in the nucleotide composition and transition/transversion ratio. Our results encourage the use of complex models of nucleotide substitution for estimating evolutionary distances and hint at bright prospects for the application of the NJ and related methods in inferring large phylogenies.

Plant MADS-box genes form a large gene family for transcription factors and are involved in various aspects of developmental processes, including flower development. They are known to be subject to birth-and-death evolution, but the detailed features of this mode of evolution remain unclear. To have a deeper insight into the evolutionary pattern of this gene family, we enumerated all available functional and nonfunctional (pseudogene) MADS-box genes from the Arabidopsis and rice genomes. Plant MADS-box genes can be classified into types I and II genes on the basis of phylogenetic analysis. Conducting extensive homology search and phylogenetic analysis, we found 64 presumed functional and 37 nonfunctional type I genes and 43 presumed functional and 4 nonfunctional type II genes in Arabidopsis. We also found 24 presumed functional and 6 nonfunctional type I genes and 47 presumed functional and 1 nonfunctional type II genes in rice. Our phylogenetic analysis indicated there were at least about four to eight type I genes and approximately 15-20 type II genes in the most recent common ancestor of Arabidopsis and rice. It has also been suggested that type I genes have experienced a higher rate of birth-and-death evolution than type II genes in angiosperms. Furthermore, the higher rate of birth-and-death evolution in type I genes appeared partly due to a higher frequency of segmental gene duplication and weaker purifying selection in type I than in type II genes.

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.

Bayesian phylogenetics has recently been proposed as a powerful method for inferring molecular phylogenies, and it has been reported that the mammalian and some plant phylogenies were resolved by using this method. The statistical confidence of interior branches as judged by posterior probabilities in Bayesian analysis is generally higher than that as judged by bootstrap probabilities in maximum likelihood analysis, and this difference has been interpreted as an indication that bootstrap support may be too conservative. However, it is possible that the posterior probabilities are too high or too liberal instead. Here, we show by computer simulation that posterior probabilities in Bayesian analysis can be excessively liberal when concatenated gene sequences are used, whereas bootstrap probabilities in neighbor-joining and maximum likelihood analyses are generally slightly conservative. These results indicate that bootstrap probabilities are more suitable for assessing the reliability of phylogenetic trees than posterior probabilities and that the mammalian and plant phylogenies may not have been fully resolved.

Endosymbionts, which are widely observed in nature, have undergone reductive genome evolution because of their long-term intracellular lifestyle. Here we compared the complete genome sequences of two different endosymbionts, Buchnera and a protist mitochondrion, with their close relatives to study the evolutionary rates of functional genes in endosymbionts. The results indicate that the rate of amino acid substitution is two times higher in symbionts than in their relatives. This rate increase was observed uniformly among different functional classes of genes, although strong purifying selection may have counterbalanced the rate increase in a few cases. Our data suggest that, contrary to current views, neither the Muller's ratchet effect nor the slightly deleterious mutation theory sufficiently accounts for the elevated evolutionary rate. Rather, the elevated evolutionary rate appears to be mainly due to enhanced mutation rate, although the possibility of relaxation of purifying selection cannot be ruled out.

When many protein sequences are available for estimating the time of divergence between two species, it is customary to estimate the time for each protein separately and then use the average for all proteins as the final estimate. However, it can be shown that this estimate generally has an upward bias, and that an unbiased estimate is obtained by using distances based on concatenated sequences. We have shown that two concatenation-based distances, i.e., average gamma distance weighted with sequence length (d(2)) and multiprotein gamma distance (d(3)), generally give more satisfactory results than other concatenation-based distances. Using these two distance measures for 104 protein sequences, we estimated the time of divergence between mice and rats to be approximately 33 million years ago. Similarly, the time of divergence between humans and rodents was estimated to be approximately 96 million years ago. We also investigated the dependency of time estimates on statistical methods and various assumptions made by using sequence data from eubacteria, protists, plants, fungi, and animals. Our best estimates of the times of divergence between eubacteria and eukaryotes, between protists and other eukaryotes, and between plants, fungi, and animals were 3, 1.7, and 1.3 billion years ago, respectively. However, estimates of ancient divergence times are subject to a substantial amount of error caused by uncertainty of the molecular clock, horizontal gene transfer, errors in sequence alignments, etc.

Ubiquitin is a highly conserved protein that is encoded by a multigene family. It is generally believed that this gene family is subject to concerted evolution, which homogenizes the member genes of the family. However, protein homogeneity can be attained also by strong purifying selection. We therefore studied the proportion (p(S)) of synonymous nucleotide differences between members of the ubiquitin gene family from 28 species of fungi, plants, and animals. The results have shown that p(S) is generally very high and is often close to the saturation level, although the protein sequence is virtually identical for all ubiquitins from fungi, plants, and animals. A small proportion of species showed a low level of p(S) values, but these values appeared to be caused by recent gene duplication. It was also found that the number of repeat copies of the gene family varies considerably with species, and some species harbor pseudogenes. These observations suggest that the members of this gene family evolve almost independently by silent nucleotide substitution and are subjected to birth-and-death evolution at the DNA level.

The Ig heavy chain variable region (V(H)) genes encode the antigen-binding regions of antibodies. The rabbit genome contains more than 100 V(H) genes, but only one (V(H)1) is preferentially used in the VDJ gene rearrangement. Three highly divergent alleles occur at this V(H)1 locus in most rabbit populations. These three V(H) alleles are also present in snowshoe hare populations, indicating that the polymorphism of the V(H)1 alleles is trans-specific. Here we report the results of a phylogenetic analysis of rabbit Ig germ-line V(H) genes (alleles) together with V(H) genes from humans and mice. We have found that all rabbit V(H) genes belong to one mammalian V(H) group (group C), which also includes various human and mouse V(H) genes. Using the rate of nucleotide substitution obtained from human and mouse V(H) sequences, we have estimated that the V(H)1 polymorphism in the rabbit lineage has been maintained for about 50 million years. This extremely long persistence of V(H)1 polymorphism is apparently caused by overdominant selection, though the real mechanism is unclear.

In the maximum parsimony (MP) and minimum evolution (ME) methods of phylogenetic inference, evolutionary trees are constructed by searching for the topology that shows the minimum number of mutational changes required (M) and the smallest sum of branch lengths (S), respectively, whereas in the maximum likelihood (ML) method the topology showing the highest maximum likelihood (A) of observing a given data set is chosen. However, the theoretical basis of the optimization principle remains unclear. We therefore examined the relationships of M, S, and A for the MP, ME, and ML trees with those for the true tree by using computer simulation. The results show that M and S are generally greater for the true tree than for the MP and ME trees when the number of nucleotides examined (n) is relatively small, whereas A is generally lower for the true tree than for the ML tree. This finding indicates that the optimization principle tends to give incorrect topologies when n is small. To deal with this disturbing property of the optimization principle, we suggest that more attention should be given to testing the statistical reliability of an estimated tree rather than to finding the optimal tree with excessive efforts. When a reliability test is conducted, simplified MP, ME, and ML algorithms such as the neighbor-joining method generally give conclusions about phylogenetic inference very similar to those obtained by the more extensive tree search algorithms.

Evolutionary mechanisms of origins of new gene function have been a subject of long-standing debate. Here we report a convincing case in which positive Darwinian selection operated at the molecular level during the evolution of novel function by gene duplication. The genes for eosinophil cationic protein (ECP) and eosinophil-derived neurotoxin (EDN) in primates belong to the ribonuclease gene family, and the ECP gene, whose product has an anti-pathogen function not displayed by EDN, was generated by duplication of the EDN gene about 31 million years ago. Using inferred nucleotide sequences of ancestral organisms, we showed that the rate of nonsynonymous nucleotide substitution was significantly higher than that of synonymous substitution for the ECP gene. This strongly suggests that positive Darwinian selection operated in the early stage of evolution of the ECP gene. It was also found that the number of arginine residues increased substantially in a short period of evolutionary time after gene duplication, and these amino acid changes probably produced the novel anti-pathogen function of ECP.

Concerted evolution is often invoked to explain the diversity and evolution of the multigene families of major histocompatibility complex (MHC) genes and immunoglobulin (Ig) genes. However, this hypothesis has been controversial because the member genes of these families from the same species are not necessarily more closely related to one another than to the genes from different species. To resolve this controversy, we conducted phylogenetic analyses of several multigene families of the MHC and Ig systems. The results show that the evolutionary pattern of these families is quite different from that of concerted evolution but is in agreement with the birth-and-death model of evolution in which new genes are created by repeated gene duplication and some duplicate genes are maintained in the genome for a long time but others are deleted or become nonfunctional by deleterious mutations. We found little evidence that interlocus gene conversion plays an important role in the evolution of MHC and Ig multigene families.

The relationship between subunit molecular weight and heterozygosity was studied in six different groups of organisms, i.e., 9 species of primates, 32 species of rodents, 56 species of reptiles, 12 species of salamanders, 64 species of teleost fishes, and 29 species of Drosophila. The correlation coefficient between them was positive in all groups, and the magnitude of correlation was roughly in agreement with the theoretical expectation under the mutation-drift hypothesis when the incomplete correlation between molecular weight and mutation rate was taken into account. Furthermore, the correlation was higher when the average heterozygosity was high than when this was low, as theoretically expected.

Theoretical distributions of genetic distance between reproductively isolated taxa are derived by means of computer simulation, taking into account mutation and random genetic drift. The distributions obtained are in good agreement with the observed distributions of interracial and interspecific genetic distances for enzymes loci in Drosophila. This indicates that the gene substitution at enzyme loci can be explained by the neutral mutation theory.

To study the mechanism of maintenance of polymorphism at major histocompatibility complex (MHC) loci, synonymous and nonsynonymous (amino acid-altering) nucleotide substitutions in the putative antigen-recognition site (included in the first domain of the MHC molecule) and other regions of human and mouse class II genes were examined. In the putative antigen-recognition site, the rate of nonsynonymous substitution was found to exceed that of synonymous substitution, whereas in the second domain the former was significantly lower than the latter. In light of a previous theoretical study and parallel findings in class I MHC loci, we conclude that the unusually high degree of polymorphism at class II MHC loci is caused mainly by overdominant selection (heterozygote advantage) operating in the antigen-recognition site.

A mathematical model for the evolutionary change of restriction sites in mitochondrial DNA is developed. Formulas based on this model are presented for estimating the number of nucleotide substitutions between two populations or species. To express the degree of polymorphism in a population at the nucleotide level, a measure called "nucleotide diversity" is proposed.

Available data suggest that the variation in mutation rate among protein loci follows the gamma distribution. Thus, taking into account this variation, formulae are developed for the distribution of allele frequencies, mean and variance of heterozygosity, expected number of alleles, proportion of polymorphic loci, and genetic distance. These formulae should be more appropriate for the analysis of gene frequency data for protein loci than equivalent formulae with constant mutation rate.

A method is presented by which the gene diversity (heterozygosity) of a subdivided population can be analyzed into its components, i.e., the gene diversities within and between subpopulations. This method is applicable to any population without regard to the number of alleles per locus, the pattern of evolutionary forces such as mutation, selection, and migration, and the reproductive method of the organism used. Measures of the absolute and relative magnitudes of gene differentiation among subpopulations are also proposed.