Correlation of DNA fragment sizes within loci in the presence of non-detectable alleles

At present most forensic databases of DNA profiling of individuals consist of DNA fragment sizes measured from Southern blot restriction fragment length polymorphism (RFLP) analysis. Statistical studies of these databases have revealed that, when fragment sizes are measured from RFLP analysis, some of the single-band patterns of individuals may actually be due to heterozygosity of alleles in which fragment size resulting from one allele remains undetected. In this work, we evaluate the effect of such allelic non-detectability on correlation of fragment sizes within individuals at a locus, and its impact on the inference of independence of fragment sizes within loci. We show that when non-detectable alleles are present in a population at a locus, positive correlations of fragment sizes are expected, which increase with the proportion of non-detectable alleles at the locus. Therefore, a non-zero positive correlation is not a proof of allelic dependence within individuals. Applications of this theory to the current forensic RFLP databases within the US show that there is virtually no evidence of significant allelic dependence within any of the loci. Therefore, the assumption that DNA fragment sizes within loci are independent is valid, and hence, the population genetic principles of computing DNA profile frequencies by multiplying binned frequencies of fragment sizes are most likely to be appropriate for forensic applications of DNA typing data.Editor's commentsThe presence of non-detectable alleles for VNTR loci has plagued the use of these highly-discriminating systems in human identification. The authors take explicit account of these alleles, and are able to show independence of the frequencies of detectable alleles. They raise the troubling issue of how to account for occasional significant results when multiple tests are performed. By invoking Bonferroni corrections, they regard all tests, even those performed on different loci, as addressing the same hypothesis—the absence of dependence at any VNTR locus.     

Sampling for Microsatellite-Based Population Genetic Studies: 25 to 30 Individuals per Population Is Enough to Accurately Estimate Allele Frequencies

One of the most common questions asked before starting a new population genetic study using microsatellite allele frequencies is “how many individuals do I need to sample from each population?” This question has previously been answered by addressing how many individuals are needed to detect all of the alleles present in a population (i.e. rarefaction based analyses). However, we argue that obtaining accurate allele frequencies and accurate estimates of diversity are much more important than detecting all of the alleles, given that very rare alleles (i.e. new mutations) are not very informative for assessing genetic diversity within a population or genetic structure among populations. Here we present a comparison of allele frequencies, expected heterozygosities and genetic distances between real and simulated populations by randomly subsampling 5–100 individuals from four empirical microsatellite genotype datasets (Formica lugubris, Sciurus vulgaris, Thalassarche melanophris, and Himantopus novaezelandia) to create 100 replicate datasets at each sample size. Despite differences in taxon (two birds, one mammal, one insect), population size, number of loci and polymorphism across loci, the degree of differences between simulated and empirical dataset allele frequencies, expected heterozygosities and pairwise F_ST values were almost identical among the four datasets at each sample size. Variability in allele frequency and expected heterozygosity among replicates decreased with increasing sample size, but these decreases were minimal above sample sizes of 25 to 30. Therefore, there appears to be little benefit in sampling more than 25 to 30 individuals per population for population genetic studies based on microsatellite allele frequencies.     

Detection of linkage between marker loci and loci affecting quantitative traits in crosses between segregating populations

Summary By making use of pedigree information and information on marker-genotypes of the parent and F-1 individuals crossed to form an F-2 population, it is possible to carry out a linkage analysis between marker loci and loci affecting quantitative traits in a cross between segregating parent populations that are at fixation for alternative alleles at the QTL, but share the same alleles at the marker loci. For two-allele systems, depending on marker allele frequencies in the parent populations, 2–4 times as many F-2 offspring will have to be raised and scored for markers and quantitative traits in order to provide power equivalent to that obtained in a cross between fully inbred lines. Major savings in number of F-2 offspring raised can be achieved by scoring each parent pair for a large number of markers in each chromosomal region and scoring F-1 and F-2 offspring only for those markers for which the parents were homozygous for alternative alleles. For multiple allele systems, particularly when dealing with hypervariable loci, only 10%–20% additional F-2 offspring will have to be raised and scored to provide power equivalent to that obtained in a cross between inbred lines. When a resource population contains novel favorable alleles at quantitative trait loci that are not present (or rare) in a commercial population, analyses of this sort will enable the loci of interest to be identified, mapped and manipulated effectively in breeding programs.Contribution no. 2124-E, 1987 series from The Agricultural Research Organization, The Volcani Center, Bet Dagan, Israel     

Nondetectability of restriction fragments and independence of DNA fragment sizes within and between loci in RFLP typing of DNA.

We provide experimental evidence showing that, during the restriction-enzyme digestion of DNA samples, some of the HaeIII-digested DNA fragments are small enough to prevent their reliable sizing on a Southern gel. As a result of such nondetectability of DNA fragments, individuals who show a single-band DNA profile at a VNTR locus may not necessarily be true homozygotes. In a population database, when the presence of such nondetectable alleles is ignored, we show that a pseudodependence of alleles within as well as across loci may occur. Using a known statistical method, under the hypothesis of independence of alleles within loci, we derive an efficient estimate of null allele frequency, which may be subsequently used for testing allelic independence within and across loci. The estimates of null allele frequencies, thus derived, are shown to agree with direct experimental data on the frequencies of HaeIII-null alleles. Incorporation of null alleles into the analysis of the forensic VNTR database suggests that the assumptions of allelic independence within and between loci are appropriate. In contrast, a failure to incorporate the occurrence of null alleles would provide a wrong inference regarding the independence of alleles within and between loci.     

Analysis and Optimization of Bulk DNA Sampling with Binary Scoring for Germplasm Characterization

The strategy of bulk DNA sampling has been a valuable method for studying large numbers of individuals through genetic markers. The application of this strategy for discrimination among germplasm sources was analyzed through information theory, considering the case of polymorphic alleles scored binarily for their presence or absence in DNA pools. We defined the informativeness of a set of marker loci in bulks as the mutual information between genotype and population identity, composed by two terms: diversity and noise. The first term is the entropy of bulk genotypes, whereas the noise term is measured through the conditional entropy of bulk genotypes given germplasm sources. Thus, optimizing marker information implies increasing diversity and reducing noise. Simple formulas were devised to estimate marker information per allele from a set of estimated allele frequencies across populations. As an example, they allowed optimization of bulk size for SSR genotyping in maize, from allele frequencies estimated in a sample of 56 maize populations. It was found that a sample of 30 plants from a random mating population is adequate for maize germplasm SSR characterization. We analyzed the use of divided bulks to overcome the allele dilution problem in DNA pools, and concluded that samples of 30 plants divided into three bulks of 10 plants are efficient to characterize maize germplasm sources through SSR with a good control of the dilution problem. We estimated the informativeness of 30 SSR loci from the estimated allele frequencies in maize populations, and found a wide variation of marker informativeness, which positively correlated with the number of alleles per locus.     

Population genetic analysis of 15 autosomal STR loci in the Russian population of northeastern Inner-Mongolia, China

In the present study, we investigated the genetic polymorphisms of 15 autosomal STR loci in the Russian population of northeastern Inner-Mongolia, China as well as its genetic relationships with other populations. DNA typing for 15 autosomal STR loci was performed on 148 randomly selected healthy individuals from the Russian population living in Eerguna, northeastern Inner-Mongolia. Allelic frequencies of these loci were calculated by direct counting. The genotype data of this Russian population was moreover compared to other populations using neighbor-joining method, as such constructing a phylogenic tree. A total of 143 alleles were found in the Russian population with corresponding allele frequencies in the range from 0.0034 to 0.5372. Among all the 15 loci, D18S51 had the highest polymorphism (PIC = 0.8632), whereas TPOX had the lowest (PIC = 0.5179). In the phylogenic tree, this Russian population has a close relationship with the populations of South Siberia and northeastern Asia. This study may increase our understanding of the genetic background of the Russian population in Eerguna, China as such providing useful information for anthropological research, forensic sciences as well as disease-association studies.     

Genetic characterization and diversity among avocado (<Emphasis Type="Italic">Persea americana</Emphasis> Mill.) genotypes from INIA-CENIAP,Venezuela

Studies on Persea americana have been addressed in different ways with biochemical and molecular techniques. Microsatellites are able to detect multiple alleles for particular loci and are therefore a useful tool to study genealogical relationships, population structures and genetic mapping. Ninety-six samples from 49 cultivars including three horticultural groups and hybrids were collected from the avocado germplasm bank at INIA-CENIAP (Venezuela). A modified DNA extraction protocol was performed. Forty microsatellites were selected from previous references, PCR amplifications were performed, and presence/absence, size, and number of alleles were evaluated on polyacrylamide gels. Attributes for polymorphic alleles were analyzed with POPGENE, and genetic diversity was calculated by effective sample size, number of alleles per locus (Na), effective number of alleles (Ne), Shannon information index (In), observed heterozygosis (H), expected heterozygosity (He), Wright’s fixation index (Fis), and allele frequencies. Only 14 primers were amplified, and AVT106 primer resulted monomorphic. Unique genotypes for each sample were obtained. Nine loci showed allele patterns that can be useful for taxonomic identification of cultivars or varieties. Comparing values of Fis with Ho and He, we found a direct relationship where low heterozygosis alleles identified in the population may affect the expected level. Allele frequencies ranged from 0.5632 to 0.0105. For all loci, at least one rare allele was observed. With the available information from genetic analysis, an identifying system was implemented for selected avocado cultivars maintained at the INIA-CENIAP Venezuelan germplasm bank on the basis of molecular data.     

Statistical genetic considerations for maintaining germ plasm collections

One objective of the regeneration of genetic populations is to maintain at least one copy of each allele present in the original population. Genetic diversity within populations depends on the number and frequency of alleles across all loci. The objectives of this study on outbreeding crops are: (1) to use probability models to determine optimal sample sizes for the regeneration for a number of alleles at independent loci; and (2) to examine theoretical considerations in choosing core subsets of a collection. If we assume that k-1 alleles occur at an identical low frequency of p₀ and that the k^th allele occurs at a frequency of 1-[(k-1)p₀], for loci with two, three, or four alleles, each with a p₀ of 0.05, 89–110 additional individuals are required if at least one allele at each of 10 loci is to be retained with a 90% probability; if 100 loci are involved, 134–155 individuals are required. For two, three, or four alleles, when p₀ is 0.03 at each of 10 loci, the sample size required to include at least one of the alleles from each class in each locus is 150–186 individuals; if 100 loci are involved, 75 additional individuals are required. Sample sizes of 160–210 plants are required to capture alleles at frequencies of 0.05 or higher in each of 150 loci, with a 90–95% probability. For rare alleles widespread throughout the collection, most alleles with frequencies of 0.03 and 0.05 per locus will be included in a core subset of 25–100 accessions.     

Identification of individuals by analysis of biallelic DNA markers, using PCR and solid-phase minisequencing.

We have developed a new method for forensic identification of individuals, in which a panel of biallelic DNA markers are amplified by the PCR, and the variable nucleotides are detected in the amplified DNA fragments by the solid-phase minisequencing method. A panel of 12 common polymorphic nucleotides located on different chromosomes with reported allele frequencies close to .5 were chosen for the test. The allele frequencies for most of the markers were found to be similar in the Finnish and other Caucasian populations. We also introduce a novel approach for rapid determination of the population frequencies of biallelic markers. By this approach we were able to determine the allele frequencies of the markers in the Finnish population, by quantitative analysis of three pooled DNA samples representing 3,000 individuals. The power of discrimination and exclusion of the solid-phase minisequencing typing test with 12 markers was similar to that of three VNTR markers that are routinely used in forensic analyses at our institute. The solid-phase minisequencing method was successfully applied to type paternity and forensic case samples. We also show that the quantitative nature of our method allows typing of mixed samples.     

Estimation of allele frequencies for VNTR loci

VNTR loci provide valuable information for a number of fields of study involving human genetics, ranging from forensics (DNA fingerprinting and paternity testing) to linkage analysis and population genetics. Alleles of a VNTR locus are simply fragments obtained from a particular portion of the DNA molecule and are defined in terms of their length. The essential element of a VNTR fragment is the repeat, which is a short sequence of basepairs. The core of the fragment is composed of a variable number of identical repeats that are linked in tandem. A sample of fragments from a population of individuals exhibits substantial variation in length because of variation in the number of repeats. Each distinct fragment length defines an allele, but any given fragment is measured with error. Therefore the observed distribution of fragment lengths is not discrete but is continuous, and determination of distinct allele classes is not straightforward. A mixture model is the natural statistical method for estimating the allele frequencies of VNTR loci. In this article we develop nonparametric methods for obtaining the distribution of allele sizes and estimates of their frequencies. Methods for obtaining maximum-likelihood estimates are developed. In addition, we suggest an empirical Bayes method to improve the maximum-likelihood estimates of the gene frequencies; the empirical Bayes procedure effects a local smoothing. The latter method works particularly well when measurement error is large relative to the repeat size, because the estimated distribution of allele frequencies when maximum likelihood is used is unreliable because of an alternating pattern of over- and underestimation. We define alleles and estimate the allele frequencies for two VNTR loci from the human genome (D17S79 and D2S44), from data obtained from Lifecodes, Inc.     

Simultaneous estimation of all the parameters of a stepwise mutation model.

Minisatellite and microsatellite are short tandemly repetitive sequences dispersed in eukaryotic genomes, many of which are highly polymorphic due to copy number variation of the repeats. Because mutation changes copy numbers of the repeat sequences in a generalized stepwise fashion, stepwise mutation models are widely used for studying the dynamics of these loci. We propose a minimum chi-square (MCS) method for simultaneous estimation of all the parameters in a stepwise mutation model and the ancestral allelic type of a sample. The MCS estimator requires knowing the mean number of alleles of a certain size in a sample, which can be estimated using Monte Carlo samples generated by a coalescent algorithm. The method is applied to samples of seven (CA)n repeat loci from eight human populations and one chimpanzee population. The estimated values of parameters suggest that there is a general tendency for microsatellite alleles to expand in size, because (1) each mutation has a slight tendency to cause size increase and (2) the mean size increase is larger than the mean size decrease for a mutation. Our estimates also suggest that most of these CA-repeat loci evolve according to multistep mutation models rather than single-step mutation models. We also introduced several quantities for measuring the quality of the estimation of ancestral allelic type, and it appears that the majority of the estimated ancestral allelic types are reasonably accurate. Implications of our analysis and potential extensions of the method are discussed.SINCE the discovery that a large number of loci with tandemly repeated sequences in human and many eukaryote species are highly polymorphic because of copy number variation of the repeats in different individuals (Jeffreys 1985; Litt and Luty 1989; Weber and May 1989), allele size data from such loci are rapidly becoming the dominant source of genetic markers for genome mapping, forensic testing, and population studies. Loci with repeat sequences longer than 5 bp are generally referred to as minisatellite or variable number tandem repeat loci, and those with repeat sequences between 2 to 5 bp are referred to as microsatellite or short tandem repeat loci (Tautz 1993). Because mutations change the copy number of such loci in a stepwise fashion, rapid accumulation of population samples from minisatellite and microsatellite loci has resurrected the interest of the stepwise mutation model (SMM), which was popular in the 1970s.     

An estimator for pairwise relatedness using molecular markers

I propose a new estimator for jointly estimating two-gene and four-gene coefficients of relatedness between individuals from an outbreeding population with data on codominant genetic markers and compare it, by Monte Carlo simulations, to previous ones in precision and accuracy for different distributions of population allele frequencies, numbers of alleles per locus, actual relationships, sample sizes, and proportions of relatives included in samples. In contrast to several previous estimators, the new estimator is well behaved and applies to any number of alleles per locus and any allele frequency distribution. The estimates for two- and four-gene coefficients of relatedness from the new estimator are unbiased irrespective of the sample size and have sampling variances decreasing consistently with an increasing number of alleles per locus to the minimum asymptotic values determined by the variation in identity-by-descent among loci per se, regardless of the actual relationship. The new estimator is also robust for small sample sizes and for unknown relatives being included in samples for estimating allele frequencies. Compared to previous estimators, the new one is generally advantageous, especially for highly polymorphic loci and/or small sample sizes.     

Amplification of reproducible allele markers for amplified fragment length polymorphism analysis.

A procedure for amplification by PCR of reproducible allele markers for amplified fragment length polymorphism (Amp-FLP) analysis is presented. We have prepared markers for the allelic products of the VNTR loci D1S80 (MCT118) and D17S30 (YNZ22) and for the hypervariable VNTR locus close to the 3' end of the apolipoprotein B gene (apoB) by re-amplifying a mixture of PCR products from individuals with known alleles. These allele markers allow precise and discrete determination of the VNTR alleles at these loci using the Amp-FLP technique that should prove suitable in forensic analyses, paternity testing and population studies.     

Genetic analysis of the 10 ChrX STRs loci in Chinese Han nationality from Guangdong province

This study is to explore the polymorphic nature of X-Chromosome short tandem repeats (ChrX STRs) loci, and to determine its application in kinship tests for forensic cases. A new fluorescent multiplex PCR that simultaneously amplifies the 10 ChX STRs loci in the same PCR reaction had been set up. DXS7132, DXS981, DXS6801, DXS6809, DXS6789, DXS7424, DXS101, DXS7133, GATA165B12 and GATA31E08 were analyzed in a sample of 511 (399 males and 112 females) unrelated individuals from Guangdong Han nationality in China. One hundred and one alleles were observed in all the loci. Here, we investigated the allele frequencies and mutation rates of the ten loci, and then made the comparison of allele frequencies distribution among different populations. The results show the ten loci in the multiplex systems may provide high polymorphism information for kinship testing and relationship investigations, and it is necessary to gain allele frequency and mutation rate of different population for forensic application.     

Characteristics of polymorphism at a VNTR locus 3' to the apolipoprotein B gene in five human populations.

We have analyzed the allele frequency distribution at the hypervariable locus 3' to the apolipoprotein B gene (ApoB 3' VNTR) in five well-defined human populations (Kacharis of northeast India, New Guinea Highlanders of Papua New Guinea, Dogrib Indians of Canada, Pehuenche Indians of Chile, and a relatively homogeneous Caucasian population of northern German extraction) by using the PCR technique. A total of 12 segregating alleles were detected in the pooled sample of 319 individuals. A fairly consistent bimodal pattern of allele frequency distribution, apparent in most of these geographically and genetically diverse populations, suggests that the ApoB 3' VNTR polymorphism predates the geographic dispersal of ancestral human populations. In spite of the observed high degree of polymorphism at this locus (expected heterozygosity levels 55%-78%), the genotype distributions in all populations (irrespective of their tribal or cosmopolitan nature) conform to their respective Hardy-Weinberg predictions. Furthermore, analysis of the congruence between expected heterozygosity and the observed number of alleles reveals that, in general, the allele frequency distributions at this locus are in agreement with the predictions of the classical mutation-drift models. The data also show that alleles that are shared by all populations have the highest average frequency within populations. These findings demonstrate the potential utility of highly informative hypervariable loci such as the ApoB 3' VNTR locus in population genetic research, as well as in forensic medicine and determination of biological relatedness of individuals.     

Polymorphisms at VNTR loci suggest homogeneity of the white population of Utah

Apparent departure from equilibrium of genetic parameters measured for multiallelic single-locus markers such as VNTR (variable number of tandem repeat) loci has been suggested as evidence of underlying heterogeneity of the tested population. Using allele frequency distributions at eight VNTR loci from the white population of Utah, we show that the observed number of alleles and the gene diversity at each locus are congruent according to expectations of the neutral mutation model. This demonstrates the genetic homogeneity of the white population of Utah with reference to the allele (total and rare) frequency distribution at eight VNTR loci. The importance of such procedures is discussed in the context of using VNTR polymorphism data for forensic and medicolegal applications. Recommendations for reporting population data for hypervariable loci are also made to aid potential users in conducting similar analyses.     

Sample size considerations in genetic polymorphism studies.

OBJECTIVES: Molecular studies for genetic polymorphisms are being carried out for a number of different applications, such as genetic disorders in different populations, pharmacogenomics, genetic identification of ethnic groups for forensic and legal applications, genetic identification of breed/stock in animals and plants for commercial applications and conservation of germ plasm. In this paper, for a random sampling scheme, we address two questions: (A) What should be the minimum size of the sample so that, with a prespecified probability, all alleles at a given locus (or haplotypes at a given set of loci) are detected? (B) What should be the sample size so that the allele frequency distribution at a given locus (or haplotype frequency distribution at a given set of loci) is estimated reliably within permissible error limits? METHODS: We have used combinatorial probabilistic arguments and Monte Carlo simulations to answer these questions. RESULTS: We found that the minimum sample size required in case A depends mainly on the prespecified probability of detecting all alleles, while in case B, it varies greatly depending on the permissible error in estimation (which will vary with the application). We have obtained the minimum sample sizes for different degrees of polymorphism at a locus under high stringency, as well as a relaxed level of permissible error. We present a detailed sampling procedure for estimating allele frequencies at a given locus, which will be of use in practical applications. CONCLUSION: Since the sample size required for reliable estimation of allele frequency distribution increases with the number of alleles at the locus, there is a strong case for using biallelic markers (like single nucleotide polymorphisms) when the available sample size is about 800 or less.     

Unbiased estimator for genetic drift and effective population size

Amounts of genetic drift and the effective size of populations can be estimated from observed temporal shifts in sample allele frequencies. Bias in this so-called temporal method has been noted in cases of small sample sizes and when allele frequencies are highly skewed. We characterize bias in commonly applied estimators under different sampling plans and propose an alternative estimator for genetic drift and effective size that weights alleles differently. Numerical evaluations of exact probability distributions and computer simulations verify that this new estimator yields unbiased estimates also when based on a modest number of alleles and loci. At the cost of a larger standard deviation, it thus eliminates the bias associated with earlier estimators. The new estimator should be particularly useful for microsatellite loci and panels of SNPs, representing a large number of alleles, many of which will occur at low frequencies.     

种群微卫星DNA分析中样本量对各种遗传多样性度量指标的影响

我们以中国飞蝗种群的微卫星遗传分析数据为例 ,评估了取样对种群遗传多样性指标的影响 ,结果显示 :样本大小与所观测到的每位点等位基因数、平均等位基因数及基因丰富度指数均呈显著正相关 ,而与期望杂合度无显著相关 ;微卫星位点多态性的高低直接影响所观测到的种群基因丰富度及其检测所需的样本量 ;对大多数种群遗传和分子生态学研究而言 ,30 - 5 0个个体是微卫星DNA分析所需要的最小样本量。基因丰富度经过稀疏法或多次随机抽样法校正后 ,可适用于瓶颈效应等种群历史数量变动的检测。另外 ,在研究中 ,还应避免采集时间的不同及样本的性比构成所可能造成的对种群遗传结构的影响     

Methodologies for estimating the sample size required for genetic conservation of outbreeding crops

Summary The main purpose of germplasm banks is to preserve the genetic variability existing in crop species. The effectiveness of the regeneration of collections stored in gene banks is affected by factors such as sample size, random genetic drift, and seed viability. The objective of this paper is to review probability models and population genetics theory to determine the choice of sample size used for seed regeneration. A number of conclusions can be drawn from the results. First, the size of the sample depends largely on the frequency of the least common allele or genotype. Genotypes or alleles occurring at frequencies of more than 10% can be preserved with a sample size of 40 individuals. A sample size of 100 individuals will preserve genotypes (alleles) that occur at frequencies of 5%. If the frequency of rare genotypes (alleles) drops below 5%, larger sample sizes are required. A second conclusion is that for two, three, and four alleles per locus the sample size required to include a copy of each allele depends more on the frequency of the rare allele or alleles than on the number. Samples of 300 to 400 are required to preserve alleles that are present at a frequency of 1%. Third, if seed is bulked, the expected number of parents involved in any sample drawn from the bulk will be less than the number of parents included in the bulk. Fourth, to maintain a rate of breeding (F) of 1 %, the effective population size (N _e) should be at least 150 for three alleles, and 300 for four alleles. Fifth, equalizing the reproductive output of each family to two progeny doubles the effective size of the population. Based on the results presented here, a practical option is considered for regenerating maize seed in a program constrained by limited funds.Part of this paper was presented at the Global Maize Germplasm Workshop, CIMMYT, El Batan, Mexico, March 6–12, 1988