Population genetics of VNTR loci and their applications in evolutionary studies

Variable number of tandem repeats (VNTR) are genetic loci at which short sequence motifs are found repeated different numbers of times among chromosomes. To explore the potential utility of VNTR loci in evolutionary studies, I have conducted a series of studies to address the following questions: (1) What are the population genetic properties of these loci? (2) What are the mutational mechanisms of repeat number change at these loci? (3) Can DNA profiles be used to measure the relatedness between a pair of individuals? (4) Can DNA fingerprint be used to measure the relatedness between populations in evolutionary studies? (5) Can microsatellite and short tandem repeat (STR) loci which mutate stepwisely be used in evolutionary analyses?^ A large number of VNTR loci typed in many populations were studied by means of statistical methods developed recently. The results of this work indicate that there is no significant departure from Hardy-Weinberg expectation (HWE) at VNTR loci in most of the human populations examined, and the departure from HWE in some VNTR loci are not solely caused by the presence of population sub-structure.^ A statistical procedure is developed to investigate the mutational mechanisms of VNTR loci by studying the allele frequency distributions of these loci. Comparisons of frequency distribution data on several hundreds VNTR loci with the predictions of two mutation models demonstrated that there are differences among VNTR loci grouped by repeat unit sizes.^ By extending the ITO method, I derived the distribution of the number of shared bands between individuals with any kinship relationship. A maximum likelihood estimation procedure is proposed to estimate the relatedness between individuals from the observed number of shared bands between them.^ It was believed that classical measures of genetic distance are not applicable to analysis of DNA fingerprints which reveal many minisatellite loci simultaneously in the genome, because the information regarding underlying alleles and loci is not available. I proposed a new measure of genetic distance based on band sharing between individuals that is applicable to DNA fingerprint data.^ To address the concern that microsatellite and STR loci may not be useful for evolutionary studies because of the convergent nature of their mutation mechanisms, by a theoretical study as well as by computer simulation, I conclude that the possible bias caused by the convergent mutations can be corrected, and a novel measure of genetic distance that makes the correction is suggested. In summary, I conclude that hypervariable VNTR loci are useful in evolutionary studies of closely related populations or species, especially in the study of human evolution and the history of geographic dispersal of Homo sapiens. (Abstract shortened by UMI.) ^

Models of DNA sequence evolution

Models of DNA sequence evolution and methods for estimating evolutionary distances are needed for studying the rate and pattern of molecular evolution and for inferring the evolutionary relationships of organisms or genes. In this dissertation, several new models and methods are developed.^ The rate variation among nucleotide sites: To obtain unbiased estimates of evolutionary distances, the rate heterogeneity among nucleotide sites of a gene should be considered. Commonly, it is assumed that the substitution rate varies among sites according to a gamma distribution (gamma model) or, more generally, an invariant+gamma model which includes some invariable sites. A maximum likelihood (ML) approach was developed for estimating the shape parameter of the gamma distribution $(\alpha)$ and/or the proportion of invariable sites $(\theta).$ Computer simulation showed that (1) under the gamma model, $\alpha$ can be well estimated from 3 or 4 sequences if the sequence length is long; and (2) the distance estimate is unbiased and robust against violations of the assumptions of the invariant+gamma model.^ However, this ML method requires a huge amount of computational time and is useful only for less than 6 sequences. Therefore, I developed a fast method for estimating $\alpha,$ which is easy to implement and requires no knowledge of tree. A computer program was developed for estimating $\alpha$ and evolutionary distances, which can handle the number of sequences as large as 30.^ Evolutionary distances under the stationary, time-reversible (SR) model: The SR model is a general model of nucleotide substitution, which assumes (i) stationary nucleotide frequencies and (ii) time-reversibility. It can be extended to SRV model which allows rate variation among sites. I developed a method for estimating the distance under the SR or SRV model, as well as the variance-covariance matrix of distances. Computer simulation showed that the SR method is better than a simpler method when the sequence length $L>1,000$ bp and is robust against deviations from time-reversibility. As expected, when the rate varies among sites, the SRV method is much better than the SR method.^ The evolutionary distances under nonstationary nucleotide frequencies: The statistical properties of the paralinear and LogDet distances under nonstationary nucleotide frequencies were studied. First, I developed formulas for correcting the estimation biases of the paralinear and LogDet distances. The performances of these formulas and the formulas for sampling variances were examined by computer simulation. Second, I developed a method for estimating the variance-covariance matrix of the paralinear distance, so that statistical tests of phylogenies can be conducted when the nucleotide frequencies are nonstationary. Third, a new method for testing the molecular clock hypothesis was developed in the nonstationary case. ^

THEORETICAL STUDIES ON THE METHODS OF RECONSTRUCTING PHYLOGENETIC TREES FROM DNA SEQUENCE DATA (MOLECULAR EVOLUTION, HOMINOID EVOLUTION, COMPUTER SIMULATION)

(1) A mathematical theory for computing the probabilities of various nucleotide configurations is developed, and the probability of obtaining the correct phylogenetic tree (model tree) from sequence data is evaluated for six phylogenetic tree-making methods (UPGMA, distance Wagner method, transformed distance method, Fitch-Margoliash's method, maximum parsimony method, and compatibility method). The number of nucleotides (m*) necessary to obtain the correct tree with a probability of 95% is estimated with special reference to the human, chimpanzee, and gorilla divergence. m* is at least 4,200, but the availability of outgroup species greatly reduces m* for all methods except UPGMA. m* increases if transitions occur more frequently than transversions as in the case of mitochondrial DNA. (2) A new tree-making method called the neighbor-joining method is proposed. This method is applicable either for distance data or character state data. Computer simulation has shown that the neighbor-joining method is generally better than UPGMA, Farris' method, Li's method, and modified Farris method on recovering the true topology when distance data are used. A related method, the simultaneous partitioning method, is also discussed. (3) The maximum likelihood (ML) method for phylogeny reconstruction under the assumption of both constant and varying evolutionary rates is studied, and a new algorithm for obtaining the ML tree is presented. This method gives a tree similar to that obtained by UPGMA when constant evolutionary rate is assumed, whereas it gives a tree similar to that obtained by the maximum parsimony tree and the neighbor-joining method when varying evolutionary rate is assumed. ^

New algorithms for automated phylogenetic reconstruction using artificial intelligence and data mining techniques

Academic and industrial research in the late 90s have brought about an exponential explosion of DNA sequence data. Automated expert systems are being created to help biologists to extract patterns, trends and links from this ever-deepening ocean of information. Two such systems aimed on retrieving and subsequently utilizing phylogenetically relevant information have been developed in this dissertation, the major objective of which was to automate the often difficult and confusing phylogenetic reconstruction process. ^ Popular phylogenetic reconstruction methods, such as distance-based methods, attempt to find an optimal tree topology (that reflects the relationships among related sequences and their evolutionary history) by searching through the topology space. Various compromises between the fast (but incomplete) and exhaustive (but computationally prohibitive) search heuristics have been suggested. An intelligent compromise algorithm that relies on a flexible “beam” search principle from the Artificial Intelligence domain and uses the pre-computed local topology reliability information to adjust the beam search space continuously is described in the second chapter of this dissertation. ^ However, sometimes even a (virtually) complete distance-based method is inferior to the significantly more elaborate (and computationally expensive) maximum likelihood (ML) method. In fact, depending on the nature of the sequence data in question either method might prove to be superior. Therefore, it is difficult (even for an expert) to tell a priori which phylogenetic reconstruction method—distance-based, ML or maybe maximum parsimony (MP)—should be chosen for any particular data set. ^ A number of factors, often hidden, influence the performance of a method. For example, it is generally understood that for a phylogenetically “difficult” data set more sophisticated methods (e.g., ML) tend to be more effective and thus should be chosen. However, it is the interplay of many factors that one needs to consider in order to avoid choosing an inferior method (potentially a costly mistake, both in terms of computational expenses and in terms of reconstruction accuracy.) ^ Chapter III of this dissertation details a phylogenetic reconstruction expert system that selects a superior proper method automatically. It uses a classifier (a Decision Tree-inducing algorithm) to map a new data set to the proper phylogenetic reconstruction method. ^