A Simple Method for Estimating Average Number of Nucleotide Substitutions within and between Populations from Restriction Data

A simple method is proposed for estimating the average number of nucleotide substitutions per site within and between populations for the case where a large number of individuals are examined for many restriction enzymes. This method gives essentially the same results as those obtained by Nei and Li's method but saves a large amount of computer time. The variances of the quantities estimated can be obtained by the jackknife method, and these variances are very similar to those obtained by Nei and Jin's more sophisticated method. A similar method can also be applied to DNA sequence data.     

DNA Polymorphism Detectable by Restriction Endonucleases

Data on DNA polymorphisms detected by restriction endonucleases are rapidly accumulating. With the aim of analyzing these data, several different measures of nucleon (DNA segment) diversity within and between populations are proposed, and statistical methods for estimating these quantities are developed. These statistical methods are applicable to both nuclear and nonnuclear DNAs. When evolutionary change of nucleons occurs mainly by mutation and genetic drift, all the measures can be expressed in terms of the product of mutation rate per nucleon and effective population size. A method for estimating nucleotide diversity from nucleon diversity is also presented under certain assumptions. It is shown that DNA divergence between two populations can be studied either by the average number of restriction site differences or by the average number of nucleotide differences. In either case, a large number of different restriction enzymes should be used for studying phylogenetic relationships among related organisms, since the effect of stochastic factors on these quantities is very large. The statistical methods developed have been applied to data of Shah and Langley on mitochondrial (mt)DNA from Drosophila melanogaster, simulans and virilis. This application has suggested that the evolutionary change of mtDNA in higher animals occurs mainly by nucleotide substitution rather than by deletion and insertion. The evolutionary distances among the three species have also been estimated.     

Bias-corrected paralinear and LogDet distances and tests of molecular clocks and phylogenies under nonstationary nucleotide frequencies

The statistical properties of the paralinear and LogDet distances under nonstationary nucleotide frequencies were studied. First, we developed formulas for correcting the estimation biases of the paralinear and LogDet distances, i.e., the bias-corrected distance is estimated by dc = d - 2var(d), where d and var(d) are the estimated distance and sampling variance, respectively. The performances of these formulas and the formulas for sampling variances were examined by computer simulation. Second, we developed a method for estimating the variance- covariance matrix of paralinear distances, so that statistical tests of DNA phylogenies can be conducted in the nonstationary case. Third, a new LogDet-based method for testing the molecular clock hypothesis was developed under nonstationary nucleotide frequencies.      

A rapid quantitative real-time PCR-based DNA quantification assay coupled with species--assignment capabilities for two hybridizing Macaca species

Regional populations of rhesus and long-tailed macaques exhibit fundamental differences in mitochondrial DNA, short tandem repeat and single nucleotide polymorphism variation between mainland and insular Southeast Asian populations. Some studies have revealed genetic admixture between these species due to natural hybridization and human-assisted intercrosses. A quantitative real-time PCR (qPCR) assay was developed to efficiently determine the species of origin of a macaque biological sample, and to quantify the species-specific template DNA. Prior knowledge of species identity and DNA concentrations are crucial for maintaining cost-effective methods and accurate DNA analysis. DNA from 109 regionally representative rhesus and long-tailed macaques was qPCR amplified to determine the species and template quantities. Of the 19 Vietnamese long-tailed macaques, 3 samples were discovered to be hybrids.     

Improved error bounds for genetic distances from DNA sequences

The genetic distance between two DNA sequences may be measured by the average number of nucleotide substitutions per position that has occurred since the two sequences diverged from a common ancestor. Estimates of this quantity can be derived from Markov models for the substitution process, while the variances are estimated using the delta method and confidence intervals calculated assuming normality. However, when the sampling distribution of the estimator deviates from normality, such intervals will not be accurate. For simple one-parameter models of nucleotide substitution, we propose a transformation of normal confidence intervals, which yields an almost exact approximation to the true confidence intervals of the distance estimators. To calculate confidence intervals for more complicated models, we propose the saddlepoint approximation. A simulation study shows that the saddlepoint-derived confidence intervals are a real improvement over existing methods.     

Methods for predicting rates of inbreeding in selected populations

Summary In selected populations, families superior for the selected trait are likely to contribute more offspring to the next generation than inferior families and, as a consequence, the rate of inbreeding is likely to be higher in selected populations than in randomly mated populations of the same structure. Methods to predict rates of inbreeding in selected populations are discussed. The method of Burrows based on probabilities of coselection is reappraised in conjunction with the transition matrix method of Woolliams. The method of Latter based on variances and covariances of family size is also examined. These methods are one-generation approaches in the sense that they only account for selective advantage over a single generation, from parents to offspring. Two-generation methods are developed that account for selective advantage over two generations, from grandparent to grandoffspring as well as from parent to offspring. Predictions are compared to results from simulation. The best one-generation method was found to underpredict rates of inbreeding by 10–25%, and the two-generation methods were found to underpredict rates of inbreeding by 9–18%.     

Characterization of single nucleotide polymorphism markers for the green sea turtle (Chelonia mydas)

We present data on 29 new single nucleotide polymorphism assays for the green sea turtle, Chelonia mydas. DNA extracts from 39 green turtles were used for two methods of single nucleotide polymorphism discovery. The first approach employed an amplified fragment length polymorphism technique. The second technique screened a microsatellite library. Allele-specific amplification assays were developed for high-throughput single nucleotide polymorphism genotyping and tested on two Pacific C. mydas nesting populations. Observed heterozygosities ranged from 0 to 0.95 for a Hawaiian population and from 0 to 0.85 for a Galapagos population. Each of the populations had one locus out of Hardy-Weinberg equilibrium, SSCM2b and SSCM5 for Hawaii and Galapagos, respectively. No loci showed significant genotypic linkage disequilibrium across an expanded set of four Pacific nesting populations. However, two loci, SSCM4 and SSCM10b showed linkage disequilibrium across three populations indicating possible association.     

Estimation of heterozygosity for single-probe multilocus DNA fingerprints

In spite of the increasing application of DNA fingerprinting to natural populations and to the genetic identification of humans, explicit methods for estimation of basic population genetic parameters from DNA fingerprinting data have not been developed. Contributing to this omission is the inability to determine, for multilocus fingerprinting probes, relatively important genetic information, such as the number of loci, the number of alleles, and the distribution of these alleles into specific loci. One of the most useful genetic parameters that could be derived from such data would be the average heterozygosity, which has traditionally been employed to measure the level of genetic variation within populations and to compare genetic variation among different loci. We derive here explicit formulas for both the estimation of average heterozygosity at multiple hypervariable loci and a maximum value for this estimate. These estimates are based upon the DNA restriction-pattern matrices that are typical for fingerprinting studies of humans and natural populations. For several empirical data sets from our laboratory, estimates of average and maximal heterozygosity are shown to be relatively close to each other. Furthermore, variances of these statistics based on simulation studies are relatively small. These observations, as well as consideration of the effect of missing alleles and alternate numbers of loci, suggest that the average heterozygosity can be accurately estimated using phenotypic DNA fingerprint patterns, because this parameter is relatively insensitive to the lack of certain genetic information.      

Winnowing DNA for rare sequences: highly specific sequence and methylation based enrichment

Rare mutations in cell populations are known to be hallmarks of many diseases and cancers. Similarly, differential DNA methylation patterns arise in rare cell populations with diagnostic potential such as fetal cells circulating in maternal blood. Unfortunately, the frequency of alleles with diagnostic potential, relative to wild-type background sequence, is often well below the frequency of errors in currently available methods for sequence analysis, including very high throughput DNA sequencing. We demonstrate a DNA preparation and purification method that through non-linear electrophoretic separation in media containing oligonucleotide probes, achieves 10,000 fold enrichment of target DNA with single nucleotide specificity, and 100 fold enrichment of unmodified methylated DNA differing from the background by the methylation of a single cytosine residue.     

DEVELOPMENT OF HIGH THROUGHPUT SINGLE NUCLEOTIDE POLYMORPHISM GENOTYPING FOR THE ANALYSIS OF NODULARIA (CYANOBACTERIA) POPULATION GENETICS1

Any investigation of the genetic structure of populations involves the analysis of a large number of samples and therefore benefits from the use of rapid, inexpensive, and automated methods to assign individuals to a particular genotype. We developed a high throughput SNuPE (single nucleotide primer extension) assay to assess polymorphic base variations at three loci (PC‐IGS, rDNA‐ITS, and gvpA‐IGS) in the genome of the cyanobacterium Nodularia spumigena. Using a 96‐capilliary sequencer, analysis of thirteen 96‐well plates can be performed in the same electrophoretic run, allowing the throughput of 1248 samples in 75 min. The SNuPE method can be broken down into two stages. The first stage comprises amplification of a DNA fragment containing the polymorphic sequence and its purification from un‐incorporated PCR reagents. The second stage involves the annealing and extension of a third primer, the SNuPE primer, the 3′ end of which immediately precedes the variable site in the template. This primer is extended with a single fluorescently labeled dideoxy nucleotide by DNA polymerase, followed by characterization of the extended primers on a DNA sequencing instrument. The length of the extended primer is used to define the locus, and the incorporated fluorescent dideoxy nucleotide gives the identity of the nucleotide at each polymorphic site. Details of this technique and its application to study the genetic structure of Nodularia populations are described.     

Moment estimation of population diversity and genetic distance from data on recessive markers

A moment-based method for estimating a measure of population diversity, theta or Wright's FST, is given for dominant markers such as amplified fragment length polymorphisms (AFLPs) or RAPDs in noninbred populations. Basic assumptions are that there is random mating, Hardy-Weinberg equilibrium, linkage equilibrium, no mutation from common ancestor and equally distant populations. It is based on the variances between and within populations of genotype frequencies, whereas previously moment methods for dominant markers have been indirect in that they have been based on first estimating allele frequencies and then using the variances of those frequencies. The use of genotype frequencies directly appears to be more robust. Approximate sampling errors of the estimates are given. Methods are extended to estimate genetic distances and their sampling errors. The AFLP data from samples of breeds of pig are used for illustration.     

Simple method for analyzing the pattern of DNA polymorphism and its application to SNP data of human

In order to analyze the pattern of DNA polymorphism in detail, we have developed a simple method using a new statistic theta(i) which estimates 4Nmu from the number of segregating sites whose allelic nucleotide frequency is i/n among n DNA sequences, where N is the effective population size and mu is the mutation rate per generation per nucleotide site. Under the assumption that mutations are selectively neutral and a population size is constant, the expectation of theta(i) is equal to that of theta, which estimates 4Nmu from the number of segregating sites, so that the distribution of theta(i) is flat. Therefore, the departure of the distribution of theta(i) from the horizontal line, which represents the value of theta, reflects change in population size and natural selection. Results of the coalescent simulation show that the distributions of theta(i) in the populations which experienced expansion and reduction are U-shaped and upside-down U-shaped, respectively. And the distributions of theta(i) in some populations that experienced bottleneck are W-shaped. Furthermore, we have applied this method to the SNP data in the International HapMap Project. Results of data analyses show that the distributions of theta(i) in the CEU (European), CHB and JPT (Asian) populations are different from that in the YRI population (African). From these results of data analyses in nuclear DNA and the pattern of polymorphism in human mitochondrial DNA already known, we infer that the CEU, CHB and JPT populations experienced the bottleneck.     

Assessing population genetic structure and variability with RAPD data: Application to Vaccinium macrocarpon (American Cranberry)

A method for estimating and comparing population genetic variation using random amplified polymorphic DNA (RAPD) profiling is presented. An analysis of molecular variance (AMOVA) is extended to accomodate phenotypic molecular data in diploid populations in Hardy-Weinberg equilibrium or with an assumed degree of selfing. We present a two step strategy: 1) Estimate RAPD site frequencies without preliminary assumptions on the unknown population structure, then perform significance testing for population substructuring. 2) If population structure is evident from the first step, use this data to calculate better estimates for RAPD site frequencies and sub-population variance components. A nonparametric test for the homogeneity of molecular variance (HOMOVA) is also presented. This test was designed to statistically test for differences in intrapopulational molecular variances (heteroscedasticity among populations). These theoretical developments are applied to a RAPD data set in Vaccinium macrocarpon (American cranberry) using small sample sizes, where a gradient of molecular diversity is found between central and marginal populations. The AMOVA and HOMOVA methods provide flexible population analysis tools when using data from RAPD or other DNA methods that provide many polymorphic markers with or without direct allelic data.     

A statistical test of phylogenies estimated from sequence data

A simple approach to testing the significance of the branching order, estimated from protein or DNA sequence data, of three taxa is proposed. The branching order is inferred by the transformed-distance method, under the assumption that one or two outgroups are available, and the branch lengths are estimated by the least-squares method. The inferred branching order is considered significant if the estimated internodal distance is significantly greater than zero. To test this, a formula for the variance of the internodal distance has been developed. The statistical test proposed has been checked by computer simulation. The same test also applies to the case of four taxa with no outgroup, if one considers an unrooted tree. Formulas for the variances of internodal distances have also been developed for the case of five taxa. Conditions are given under which it is more efficient to add the sequence of a fifth taxon than to do 25% more nucleotide sequencing in each of the original four. A method is presented for combining analyses of disparate data to get a single P value. Finally, the test, applied to the human-chimpanzee-gorilla problem, shows that the issue is not yet resolved.     

The Ecological Genetics of Introduced Populations of the Giant Toad BUFO MARINUS. II. Effective Population Size

The allele frequencies are described at ten polymorphic enzyme loci (of a total of 22 loci sampled) in 15 populations of the neotropical giant toad, Bufo marinus, introduced to Hawaii and Australia in the 1930s. The history of establishment of the ten populations is described and used as a framework for the analysis of allele frequency variances. The variances are used to determine the effective sizes of the populations. The estimates obtained (390 and 346) are reasonably precise, homogeneous between localities and much smaller than estimates of neighborhood size obtained previously using ecological methods. This discrepancy is discussed, and it is concluded that the estimates obtained here using genetic methods are the more reliable.     

Sampling Variances of Heterozygosity and Genetic Distance

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.     

Effects of linkage and interaction in a comparison of theoretical populations derived by diploidized haploid and single seed descent methods

Summary Comparisons were made between the genetic means and variances of a quantitative trait determined by 8 loci in simulated populations of lines derived by diploidizing haploids (DH) on the one hand and by single seed descent (SSD) on the other.In the absence of linkage no differences between the populations were observed, but when linkage was present, recombination was more frequent in the SSD populations as indicated by the relative differences in variance between these and the DH populations. In addition, differences in means between the populations derived by the two methods were observed when non-allelic interaction was present. The direction and magnitude of the differences in both means and variances depended upon the linkage phase, the recombination frequency and the presence or absence of interaction.The conclusion was drawn that the SSD method was to be preferred from theoretical considerations although in practice the choice of method will also depend upon practical and technical factors.     

A note on simulating null distributions for G matrix comparisons

Genetic variances and covariances, summarized in G matrices, are key determinants of the course of adaptive evolution. Consequently, understanding how G matrices vary among populations is critical to answering a variety of questions in evolutionary biology. A method has recently been proposed for generating null distributions of statistics pertaining to differences in G matrices among populations. The general approach facilitated by this method is likely to prove to be very important in studies of the evolution of G . We have identified an issue in the method that will cause it to create null distributions of differences in G matrices that are likely to be far too narrow. The issue arises from the fact that the method as currently used generates null distributions of statistics pertaining to differences in G matrices across populations by simulating breeding value vectors based on G matrices estimated from data, randomizing these vectors across populations, and then calculating null values of statistics from G matrices that are calculated directly from the variances and covariances among randomized vectors. This calculation treats breeding values as quantities that are directly measurable, instead of predicted from G matrices that are themselves estimated from patterns of covariance among kin. The existing method thus neglects a major source of uncertainty in G matrices, which renders it anti‐conservative. We first suggest a correction to the method. We then apply the original and modified methods to a very simple instructive scenario. Finally, we demonstrate the use of both methods in the analysis of a real data set.     

Assessing the nucleotide diversity of three aphid species by RAPD

A method is presented for the estimation of nucleotide diversity and genetic structure of populations from RAPD (random amplified polymorphic DNA) data. It involves a modification of the technique developed by Lynch and Crease (1990) for the case of restriction sites as survey data. As new elements the method incorporates (i) dominance correction, (ii) values of asexual reproduction of the populations sampled, and (iii) an analytical variance of the number of nucleotide substitutions per site. Sampling was carried out at two geographic scales for three aphid species. At a macrogeographic scale, populations of Rhopalosiphum padi did not show statistical genetic differentiation. Aphis gossypii and Myzus persicae, which were sampled at a microgeographic scale, showed a higher genetic differentiation than R. padi, it being statistically significant in M. persicae. The major sources of sampling variance within- and between-populations were found to be nucleotide (i.e., the number of alleles used as a function of the number of primers used) and population (i.e., sample size) sampling. Extremely low estimates of nucleotide diversity were obtained for the species studied here. This result is consistent with previous reports on genetic diversity for the same or other aphid species which were based on allozyme polymorphism, mitochondrial DNA variation and qualitative analyses of RAPDs.