MATHEMATICAL STUDIES ON THE EVOLUTIONARY CHANGE OF DNA SEQUENCES

With the aim of understanding the mechanism of molecular evolution, mathematical problems on the evolutionary change of DNA sequences are studied. The problems studied and the results obtained are as follows: (1) Estimation of evolutionary distance between nucleotide sequences. Studying the pattern of nucleotide substitution for the case of unequal substitution rates, a new mathematical formula for estimating the average number of nucleotide substitutions per site between two homologous DNA sequences is developed. It is shown that this formula has a wider applicability than currently available formulae. A statistical method for estimating the number of nucleotide changes due to deletion and insertion is also developed. (2) Biases of the estimates of nucleotide substitutions obtained by the restriction enzyme method. The deviation of the estimate of nucleotide substitutions obtained by the restriction enzyme method from the true value is investigated theoretically. It is shown that the amount of the deviation depends on the nucleotides in the recognition sequence of the restriction enzyme used, unequal rates of substitution among different nucleotides, and nucleotide frequences, but the primary factor is the unequal rates of nucleotide substitution. When many different kinds of enzymes are used, however, the amount of average deviation is generally small. (3) Distribution of restriction fragment lengths. To see the effect of undetectable restriction fragments and fragment differences on the estimate of nucleotide differences, the theoretical distribution of fragment lengths is studied. This distribution depends on the type of restriction enzymes used as well as on the relative frequencies of four nucleotides. It is shown that undetectability of small fragments or fragment differences gives a serious underestimate of nucleotide substitutions when the length-difference method of estimation is used, but the extent of underestimation is small when the site-difference method is used. (4) Evolutionary relationships of DNA sequences in finite populations. A mathematical theory on the expected evolutionary relationships among DNA sequences (nucleons) randomly chosen from the same or different populations is developed under the assumption that the evolutionary change of nucleons is determined solely by mutation and random genetic drift. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of author). 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. ^

CHROMOSOMAL MAPPING, LINKAGE RELATIONSHIPS, AND EVOLUTIONARY STUDIES OF THE HUMAN ANONYMOUS DNA CLONE D1S1 (IN SITU HYBRIDIZATION, PRIMATES, GENE MAPPING, AUTOSOMAL DOMINANT RETINITIS PIGMENTOSA, GENE DUPLICATION)

D1S1, an anonymous human DNA clone originally called (lamda)Ch4-H3 or (lamda)H3, was the first single copy mapped to a human chromosome (1p36) by in situ hybridization. The chromosomal assignment has been confirmed in other laboratories by repeating the in situ hybridization but not by another method. In the present study, hybridization to a panel of hamster-human somatic cell hybrids revealed copies of D1S1 on both chromosomes 1 and 3. Subcloning D1S1 showed that the D1S1 clone itself is from chromosome 3, and the sequence detected by in situ hybridization is at least two copies of part of the chromosome 3 copy. This finding demonstrates the importance of verifying gene mapping with two methods and questions the accuracy of in situ hybridization mapping.^ Non-human mammals have only one copy of D1S1, and the non-human primate D1S1 map closely resembles the human chromosome 3 copy. Thus, the human chromosome 1 copies appear to be part of a very recent duplication that occurred after the divergence between humans and the other great apes.^ A moderately informative HindIII D1S1 RFLP was mapped to chromosome 3. This marker and 12 protein markers were applied to a linkage study of autosomal dominant retinitis pigmentosa (ADRP). None of the markers proved linkage, but adding the three families examined to previously published data raises the ADRP:Rh lod score to 1.92 at (THETA) = 0.30. ^

LINKAGE RELATIONSHIPS AMONG PROTEIN-CODING LOCI IN FISHES OF THE GENUS XIPHOPHORUS

Inbred strains of three species of fishes of the genus Xiphophorus (platyfish and swordtails) were crossed to produce intra- and interspecific F(,1) hybrids, which were then backcrossed to one or both parental stocks. Backcross hybrids were used for the analysis of segregation and linkage of 33 protein-coding loci (whose products were visualized by starch gel electrophoresis) and a sex-linked pigment pattern gene. Segregation was Mendelian for all loci with the exception of one instance of segregation distortion. Six linkage groups of enzyme-coding loci were established: LG I, ADA --6%-- G(,6)PD --24%-- 6PGD; LG II, Est-2 --27%-- Est-3 --0%-- Est-5 --23%-- LDH-1 --16%-- MPI; LG III, AcPh --38%-- G(,3)PD-1 (GUK-2 --14%-- G(,3)PD-1 is also in LG III, but the position of GUK-2 with respect to AcPh has not yet been determined); LG IV, GPI-1 --41%-- IDH-1; LG V, Est-1 --38%-- MDH-2; and LG VI, P1P --7%-- UMPK-1 (P1P is a plasma protein, very probably transferrin).^ Sex-specific recombination appeared absent in LG II and LG IV locus pairs; significantly higher male recombination was demonstrated in LG I but significantly higher female recombination was detected in LG V. Only one significant population-specific difference in recombination was detected, in the G(,6)PD - 6PGD region of LG I; the notable absence of such effects implies close correspondence of the genomes of the species used in the study. Two cases of possible evolutionary conservation of linkage groups in fishes and mammals were described, involving the G(,6)PD - 6PGD linkage in LG I and the cluster of esterase loci in LG II. One clear case of divergence was observed, that of the linkage of ADA in LG I. It was estimated that a minimum of (TURN)50% of the Xiphophorus genome was marked by the loci studied. Therefore, the prior probability that a new locus will assort independently from the markers already established is estimated to be less than 0.5. A maximum of 21 of the 24 pairs of chromosomes could be marked with at least one locus.^ Only the two LG V loci showed a significant association with a postulated gene controlling the severity of a genetically controlled melanoma caused by abnormal proliferation of macromelanophore pigment pattern cells. The independence of melanotic severity from all other informative markers implies that one or at most a few major genes are involved in control of melanotic severity in this system. ^