The number of nucleotides required to determine the branching order of three species,with special reference to the human-chimpanzee-gorilla divergence

Summary 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.     

Methods for computing the standard errors of branching points in an evolutionary tree and their application to molecular data from humans and apes

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.      

Models of Evolution of Reproductive Isolation

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 It?'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.     

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

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

Statistical Studies on Protein Polymorphism in Natural Populations. III. Distribution of Allele Frequencies and the Number of Alleles per Locus

With the aim of understanding the mechanism of maintenance of protein polymorphism, we have studied the properties of allele frequency distribution and the number of alleles per locus, using gene-frequency data from a wide range of organisms (mammals, birds, reptiles, amphibians, Drosophila and non-Drosophila invertebrates) in which 20 or more loci with at least 100 genes were sampled. The observed distribution of allele frequencies was U-shaped in all of the 138 populations (mostly species or subspecies) examined and generally agreed with the theoretical distribution expected under the mutation-drift hypothesis, though there was a significant excess of rare alleles (gene frequency, 0 ~ 0.05) in about a quarter of the populations. The agreement between the mutation-drift theory and observed data was quite satisfactory for the numbers of polymorphic (gene frequency, 0.05 ~ 0.95) and monomorphic (0.95 ~ 1.0) alleles.—The observed pattern of allele-frequency distribution was incompatible with the prediction from the overdominance hypothesis. The observed correlations of the numbers of rare alleles, polymorphic alleles and monomorphic alleles with heterozygosity were of the order of magnitude that was expected under the mutation-drift hypothesis. Our results did not support the view that intracistronic recombination is an important source of genetic variation. The total number of alleles per locus was positively correlated with molecular weight in most of the species examined, and the magnitude of the correlation was consistent with the theoretical prediction from mutation-drift hypothesis. The correlation between molecular weight and the number of alleles was generally higher than the correlation between molecular weight and heterozygosity, as expected.     

Mean and variance of FST in a finite number of incompletely isolated populations

In the presence of migration F_ST in a finite number of incompletely isolated populations first increases, but after reaching a certain maximum value, it starts to decline and eventually becomes 0. The mean and variance of F_ST in this process are studied by using the recurrence formulas for the moments of gene frequencies in the island model of finite size as well as by using Monte Carlo simulation. The mean and variance in the early generations can be predicted by the approximate formulas developed. On the other hand, if we exclude the cases of an allele being fixed in all subpopulations, the mean of F_ST eventually reaches a steady-state value. This value is given by 1 − 2N_T(1 − λ) approximately, where N_T is the total population size and λ is the rate of decay of heterozygosity at steady state. It is shown that the mean and variance of F_ST depend on the initial gene frequency and when this is close to 0 or 1, Lewontin and Krakauer's test of the neutrality of polymorphic genes is not valid.     

Utility and efficiency of linked marker genes for genetic counseling. II. Identification of linkage phase by offspring phenotypes

For a linked marker locus to be useful for genetic counseling, the counselee must be heterozygous for both disease and marker loci and his or her linkage phase must be known. It is shown that when the phenotypes of the counselee's previous children for the disease and marker loci are known, the linkage phase can often be inferred with a high probability, and thus it is possible to conduct genetic counseling. To evaluate the utility of linked marker genes for genetic counseling, the accuracy of prediction of the risk for a prospective child with a given marker gene to develop the genetic disease and the proportion of families in which a particular marker locus can be used for genetic counseling are studied for X-linked recessive, autosomal dominant, and autosomal recessive diseases. In the case of X-linked genetic diseases, information from children is very useful for determining the linkage phase of the counselee and predicting the genetic disease. In the case of autosomal dominant diseases, not all children are informative, but if the number of children is large, the phenotypes of children are often more informative than the information from grandparents. In the case of autosomal recessive diseases, information from grandparents is usually useless, since they show a normal phenotype for the disease locus. If we use information on the phenotypes of children, however, the linkage phase of the counselee and the risk of a prospective child can be inferred with a high probability. The proportion of informative families depends on the dominance relationship and frequencies of marker alleles, and the number of children. In general, codominant markers are more useful than are dominant markers, and a locus with high heterozygosity is more useful than is a locus with low heterozygosity.