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Although African populations have been shown to be most divergent from any other human populations, it has been difficult to establish the root of the phylogenetic tree of human populations since the rate of evolutionary change may vary from population to population owing to the fluctuation of population size and other factors. However, the root can be determined by using the chimpanzee as an outgroup and by employing proper statistical methods. Using this strategy, we constructed phylogenetic trees of human populations for five different sets of gene frequency data. The data sets used were two sets of microsatellite loci data (25 and 8 loci, respectively), restriction fragment length polymorphism (RFLP) data (79 loci), protein polymorphism data (15 loci), and Alu insertion frequency data (4 loci). All these data sets showed that the root is located in the branch connecting African and non-African populations, and in the four data sets the root was established at a significant level. These results indicate that Africans are the first group of people that split from the rest of the human populations.

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.

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 mathematical theory is developed for computing the probability that m genes sampled from one population (species) and n genes sampled from another are derived from l genes that existed at the time of population splitting. The expected time of divergence between the two most closely related genes sampled from two different populations and the time of divergence (coalescence) of all genes sampled are studied by using this theory. It is shown that the time of divergence between the two most closely related genes can be used as an approximate estimate of the time of population splitting (T) only when T identical to t/(2N) is small, where t and N are the number of generations and the effective population size, respectively. The variance of Nei and Li's estimate (d) of the number of net nucleotide differences between two populations is also studied. It is shown that the standard error (Sd) of d is larger than the mean when T is small (T much less than 1). In this case, Sd is reduced considerably by increasing sample size. When T is large (T greater than 1), however, a large proportion of the variance of d is caused by stochastic factors, and increase in the sample size does not help to reduce Sd. To reduce the stochastic variance of d, one must use data from many independent unlinked gene loci.

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.

Mathematical formulae for the sampling variances of average heterozygosity and Nei's genetic distance are developed. These sampling variances are decomposed into their two components, i.e. the inter-locus and intra-locus variances. The relationship between the number of loci and the number of individuals per locus to be examined for estimating average heterozygosity and genetic distance is also discussed. The utility of the inter-locus variance of heterozygosity for studying the mechanism of maintenance of genetic variability in populations is indicated.

The linkage disequilibrium in a subdivided populaton is shown to be equal to the sum of the average linkage disequilibrium for all subpopulations and the covariance between gene frequencies of the loci concerned. Thus, in a subdivided population the linkage disequilibrium may not be 0 even if the linkage disequilibrium in each subpopulation is 0. If a population is divided into two subpopulations between which migration occurs, the asymptotic rate of approach to linkage equilibrium is equal to either r or 2(m(1) + m(2)) - (m(1) + m(2))(2), whichever is smaller, where r is the recombination value and m(1) and m(2) are the proportions of immigrants in subpopulations 1 and 2, respectively. Thus, if migration rate is high compared with recombination value, the change of linkage disequilibrium in subdivided populations is similar to that of a single random mating population. On the other hand, if migration rate is low, the approach to lnkage equilibrium may be retarded in subdivided populations. If isolated populations begin to exchange genes by migration, linkage disequilibrium may increase temporarily even for neutral loci. If overdominant selection operates and the equilibrium gene frequencies are different in the two subpopulations, a permanent linkage disequilibrium may be produced without epistasis in each subpopulation.

The numbers of gene (codon) differences per locus between two randomly chosen genomes within and between Caucasian, Negro, and Japanese populations have been estimated from gene frequency data for protein loci. The estimated number of gene differences between individuals from different populations is only slightly greater than the number between individuals from the same population.

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.

The probability of fixation of an overdominant mutation in a finite population depends on the equilibrium gene frequency in an infinite population (m) and the product (A) of population size and selection intensity. If m < 0.5 (disadvantageous overdominant genes), the probability is generally much lower than that of neutral genes; but if m is close to 0.5 and A is relatively small, it becomes higher. If m > 0.5 (advantageous overdominant genes), the probability is largely determined by the fitness of heterozygotes rather than that of mutant homozygotes. Thus, overdominance enhances the probability of fixation of advantageous mutations. The average number of generations until fixation of an overdominant mutation also depends on m and A. This average time is long when m is close to 0.5 but short when m is close to 0 or 1. This dependence on m and A is similar to that of Robertson's retardation factor.