Quantitative determination of allele frequency in pooled DNA by using sequencing method

Quantitative determination of the allele frequency of single-nucleotide polymorphism (SNP) in pooled DNA samples is a promising approach to clarify the relationships between SNPs and diseases. Here, we present such a simple, accurate, and inexpensive method for quantitative determining the allele frequency in pooled DNA samples. Three steps of DNA pooling, PCR amplification and sequencing are involved in this assay. Although direct determination of the allele frequency from the two allele-specific fluorescence intensities is possible, correction for differential response of alleles is important. We explored the effect of differential response of alleles on test statistics and provide a solution to this problem based on heterozygous fluorescence intensities. We demonstrate the accuracy and reliability of this assay on pooled DNA samples with pre-determined allele frequencies from 7.1% to 53.9%. The accuracy of allele frequency measurements is high, with a correlation coefficient of r2 = 0.997 between measured and known frequencies. We believe that by providing a means for SNP genotyping up to hundreds of samples simultaneously, inexpensively, and reproducibly, this method is a powerful strategy for detecting meaningful polymorphic differences in candidate gene association studies.     

Determining SNP allele frequencies in DNA pools

Single nucleotide polymorphisms (SNPs) are among the most common types of polymorphism used for genetic association studies. A method to allow the accurate quantitation of their allele frequencies from DNA pools would both increase throughput and decrease costs for large-scale genotyping. However, to date, most DNA pooling studies have concentrated on the use of microsatellite polymorphisms. In the case of SNPs that are restriction fragment length polymorphisms (RFLPs), studies have tended to use methods for the quantitation of allele frequency from pools that rely on densitometric evaluation of bands on an autoradiograph. Radiation-based methods have well-known drawbacks, and we present two alternative methods for the determination of SNP allele frequencies. For RFLPs, we used agarose gel electrophoresis of digested PCR products with ethidium bromide staining combined with densitometric analysis of gel images on a PC. For all types of SNP, we used allele-specific fluorescent probes in the Taqman assay to determine the relative frequencies of two different alleles. Both methods gave accurate and reproducible results, suggesting they are suitable for use in DNA pooling experiments.     

DNA pooling: a comprehensive, multi-stage association analysis of ACSL6 and SIRT5 polymorphisms in schizophrenia

Many candidate gene association studies have evaluated incomplete, unrepresentative sets of single nucleotide polymorphisms (SNPs), producing non-significant results that are difficult to interpret. Using a rapid, efficient strategy designed to investigate all common SNPs, we tested associations between schizophrenia and two positional candidate genes: ACSL6 (Acyl-Coenzyme A synthetase long-chain family member 6) and SIRT5 (silent mating type information regulation 2 homologue 5). We initially evaluated the utility of DNA sequencing traces to estimate SNP allele frequencies in pooled DNA samples. The mean variances for the DNA sequencing estimates were acceptable and were comparable to other published methods (mean variance: 0.0008, range 0-0.0119). Using pooled DNA samples from cases with schizophrenia/schizoaffective disorder (Diagnostic and Statistical Manual of Mental Disorders edition IV criteria) and controls (n=200, each group), we next sequenced all exons, introns and flanking upstream/downstream sequences for ACSL6 and SIRT5. Among 69 identified SNPs, case-control allele frequency comparisons revealed nine suggestive associations (P<0.2). Each of these SNPs was next genotyped in the individual samples composing the pools. A suggestive association with rs 11743803 at ACSL6 remained (allele-wise P=0.02), with diminished evidence in an extended sample (448 cases, 554 controls, P=0.062). In conclusion, we propose a multi-stage method for comprehensive, rapid, efficient and economical genetic association analysis that enables simultaneous SNP detection and allele frequency estimation in large samples. This strategy may be particularly useful for research groups lacking access to high throughput genotyping facilities. Our analyses did not yield convincing evidence for associations of schizophrenia with ACSL6 or SIRT5.     

Estimation of allele frequency in pooled DNA by using PCR–RFLP combined with microchip electrophoresis

Biallelic marker, most commonly single nucleotide polymorphism (SNP), is widely utilized in genetic association analysis, which can be speeded up by estimating allele frequency in pooled DNA instead of individual genotyping. Several methods have shown high accuracy and precision for allele frequency estimation in pools. Here, we explored PCR restriction fragment length polymorphism (PCR–RFLP) combined with microchip electrophoresis as a possible strategy for allele frequency estimation in DNA pools. We have used the commercial available Agilent 2100 microchip electrophoresis analysis system for quantifying the enzymatically digested DNA fragments and the fluorescence intensities to estimate the allele frequencies in the DNA pools. In this study, we have estimated the allele frequencies of five SNPs in a DNA pool composed of 141 previously genotyped health controls and a DNA pool composed of 96 previously genotyped gastric cancer patients with a frequency representation of 10–90% for the variant allele. Our studies show that accurate, quantitative data on allele frequencies, suitable for investigating the association of SNPs with complex disorders, can be estimated from pooled DNA samples by using this assay. This approach, being independent of the number of samples, promises to drastically reduce the labor and cost of genotyping in the initial association analysis.     

Ethnic differences in the linkage disequilibrium and distribution of single-nucleotide polymorphisms in 35 candidate genes for cardiovascular diseases

Single-nucleotide polymorphisms (SNPs) are commonly used to study genetics for common diseases and predict pharmacological response. The selection of likely informative SNPs in association studies depends on their allele frequencies and on the linkage disequilibrium (LD) between SNPs, both of which may show interethnic differences. Among three populations consisting of 207 Chinese, 858 French, and 395 Spanish, we compared the allele frequency distributions of 64 intragenic SNPs of 35 candidate genes for cardiovascular diseases. Twenty-eight of these SNPs from 12 genes were also examined for intragenic LD. About 20% of SNPs were restricted to Europeans, being monomorphic in Chinese, among them mostly nonsynonymous coding SNPs and noncoding SNPs. Only 1.6% of SNPs were specific in Chinese, commensurate with the detection of these SNPs almost exclusively in Caucasians. Similarly, these SNPs were more often rare (<0.1 minor allele frequency) in Chinese (44.3%) than in Europeans (31.1%). The variant allele frequencies and intermarker LDs in terms of D' and Delta(2) were highly correlated between French and Spanish populations (r = 0.98-0.99, p < 0.001). However, only moderate correlations of allele frequencies and D' were found between the Chinese and the European populations (r = 0.7 and 0.3, respectively) despite a high correlation of Delta(2) values (r = 0.8). These results suggest that ethnic considerations are important in the selection of SNPs for association studies of candidate genes, as this may affect the power of the study as well as the likelihood of asking relevant questions and getting medically meaningful answers.     

Multiplex SNP genotyping in pooled DNA samples by a four-colour microarray system

We selected 125 candidate single nucleotide polymorphisms (SNPs) in genes belonging to the human type 1 interferon (IFN) gene family and the genes coding for proteins in the main type 1 IFN signalling pathway by screening databases and by in silico comparison of DNA sequences. Using quantitative analysis of pooled DNA samples by solid-phase mini-sequencing, we found that only 20% of the candidate SNPs were polymorphic in the Finnish and Swedish populations. To allow more effective validation of candidate SNPs, we developed a four-colour microarray-based mini-sequencing assay for multiplex, quantitative allele frequency determination in pooled DNA samples. We used cyclic mini-sequencing reactions with primers carrying 5′-tag sequences, followed by capture of the products on microarrays by hybridisation to complementary tag oligonucleotides. Standard curves prepared from mixtures of known amounts of SNP alleles demonstrate the applicability of the system to quantitative analysis, and showed that for about half of the tested SNPs the limit of detection for the minority allele was below 5%. The microarray-based genotyping system established here is universally applicable for genotyping and quantification of any SNP, and the validated system for SNPs in type 1 IFN-related genes should find many applications in genetic studies of this important immunoregulatory pathway.     

Kinetic FP-TDI assay for SNP allele frequency determination

Strategies for identifying genetic risk factors in complex diseases by association studies require the comparison of allele frequencies of numerous SNPs between affected and control populations. Theoretically, hundreds of thousands of SNP markers across the genome will have to be genotyped in these studies. Genotyping SNPs one sample at a time is extremely costly and time consuming. To streamline whole genome association studies, some have proposed to screen SNPs by pooling the DNA samples initially for allele frequency determination and perform individual genotyping only when there is a significant discrepancy in allele frequencies between the affected and control populations. Here we describe a new method for determining the allele frequency of SNPs in pooled DNA samples using a two-color primer extension assay with real-time monitoring of fluorescence polarization (named kinetic FP-TDI assay). By comparing the ratio of the rate of incorporation of the two allele-specific dye-terminators, one can calculate the relative amounts of each allele in the pooled sample. The accuracy of allele frequency determination with pooled samples is within 3.3 +/- 0.8% of that determined by genotyping individual samples that make up the pool.     

Cheap, accurate and rapid allele frequency estimation of single nucleotide polymorphisms by primer extension and DHPLC in DNA pools

At present, the cost of genotyping single nucleotide polymorphisms (SNPs) in large numbers of subjects poses a formidable problem for molecular genetic approaches to complex diseases. We have tested the possibility of using primer extension and denaturing high performance liquid chromatography to estimate allele frequencies of SNPs in pooled DNA samples. Our data show that this method should allow the accurate estimation of absolute allele frequencies in pooled samples of DNA and also of the difference in allele frequency between different pooled DNA samples. This technique therefore offers an efficient and cheap method for genotyping SNPs in large case-control and family-based association samples.     

The prostate cancer risk locus at 10q11 is associated with DNA repair capacity

Genome-wide association studies (GWAS) have identified several single nucleotide polymorphisms (SNPs) that mildly predict prostate cancer risk. These SNPs are local tagging markers for causal gene alterations. Consideration of candidate genes in the tagged regions would be facilitated by additional information on the particular pathomechanisms which contribute to the observed risk increase. In this study we test for an association of prostate cancer tagging SNPs with alterations in DNA repair capacity, a phenotype that is frequently involved in cancer predisposition. DNA repair capacity was assessed on blood lymphocytes from 128 healthy probands after ionizing irradiation. We used the micronucleus (MN) assay to determine the cellular DNA double-strand break repair capacity and flow cytometry to measure damage induced mitotic delay (MD). Probands were genotyped for a panel of 14 SNPs, each representing an independent prostate cancer risk locus previously identified by GWAS. Associations between germline variants and DNA repair capacity were found for the SNPs rs1512268 (8p21), rs6983267 (8q24) and rs10993994 (10q11). The most significant finding was an association of homozygous rs10993994 T-allele carriers with a lower MN frequency (p=0.0003) and also a decreased MD index (p=0.0353). Cells with prostate cancer risk alleles at rs10993994 seem to cope more efficiently with DNA double strand breaks (less MN) in a shorter time (decreased MD index). This intriguing finding imposes concern about the accuracy of repair, with respect to the cancer risk that is mediated by T genotypes. To date, MSMB (microseminoprotein β) is favored as the causal gene at the 10q11 risk locus, since it was the first candidate gene known to be expressionally altered by rs10993994. Based on the present observation, candidate genes from the contexts of DNA repair and apoptosis may be more promising targets for expression studies with respect to the rs10993994 genotype.     

True pedigree errors more frequent than apparent errors for single nucleotide polymorphisms

Single nucleotide polymorphisms (SNPs) are currently being developed for use in disequilibrium analyses. These SNPs consist of two alleles with varying degrees of polymorphism. A natural design for use with SNPs is the 'haplotype relative risk' sampling design in which a father, mother, and child are typed at an SNP locus. Given such a trio of genotypes, we ask: what is the probability that a pedigree error (a change from one allele to the other) at an SNP locus will be detected using only Mendel's laws as a check? We calculate the probability of detecting such errors for a hypothetical SNP locus with varying degrees of polymorphism and for various true error rates. For the sets of allele frequencies considered, we find that the detection rates range between 25 and 30%, the detection rate being lowest when the two alleles have equal frequencies and the highest when one allele has a frequency of 10%. Based on this detection rate, we determine that the true error rate is roughly 3.3-4 times that of the apparent error rate at an SNP locus. The greatest discrepancy between true and apparent error rates occurs when allele frequencies are equal.     

High-throughput SNP detection by using DNA pooling and denaturing high performance liquid chromatography (DHPLC)

One of the critical steps in the positional cloning of a complex disease gene involves association analysis between a phenotype and a set of densely spaced diallelic markers, typically single nucleotide repeats (SNPs), covering the region of interest. However, the effort and cost of detecting sufficient numbers of SNPs across relatively large physical distances represents a significant rate-limiting step. We have explored DNA pooling, in conjunction with denaturing high performance liquid chromatography (DHPLC), as a possible strategy for augmenting the efficiency, economy, and throughput of SNP detection. DHPLC is traditionally used to detect variants in polymerase chain reaction products containing both allelic forms of a polymorphism (e.g., heterozygotes or a 1:1 mix of both alleles) via heteroduplex separation and thereby requires separate analyses of multiple individual test samples. We have adapted this technology to identify variants in pooled DNA. To evaluate the utility and sensitivity of this approach, we constructed DNA pools comprised of 20 previously genotyped individuals with a frequency representation of 0%-50% for the variant allele. Mutation detection was performed by using temperature-modulated heteroduplex formation/DHPLC and dye-terminator sequencing. Using DHPLC, we could consistently detect SNPs at lower than 5% frequency, corresponding to the detection of one variant allele in a pool of 20 alleles. In contrast, fluorescent sequencing detected variants in the same pools only if the frequency of the less common allele was at least 10%. We conclude that DNA pooling of samples for DHPLC analysis is an effective way to increase throughput efficiency of SNP detection.     

In the presence of population structure: From genomics to candidate genes underlying local adaptation

Understanding the genomic signatures, genes, and traits underlying local adaptation of organisms to heterogeneous environments is of central importance to the field evolutionary biology. To identify loci underlying local adaptation, models that combine allelic and environmental variation while controlling for the effects of population structure have emerged as the method of choice. Despite being evaluated in simulation studies, there has not been a thorough investigation of empirical evidence supporting local adaptation across these alleles. To evaluate these methods, we use 875 Arabidopsis thaliana Eurasian accessions and two mixed models (GEMMA and LFMM) to identify candidate SNPs underlying local adaptation to climate. Subsequently, to assess evidence of local adaptation and function among significant SNPs, we examine allele frequency differentiation and recent selection across Eurasian populations, in addition to their distribution along quantitative trait loci (QTL) explaining fitness variation between Italy and Sweden populations and cis‐regulatory/nonsynonymous sites showing significant selective constraint. Our results indicate that significant LFMM/GEMMA SNPs show low allele frequency differentiation and linkage disequilibrium across locally adapted Italy and Sweden populations, in addition to a poor association with fitness QTL peaks (highest logarithm of odds score). Furthermore, when examining derived allele frequencies across the Eurasian range, we find that these SNPs are enriched in low‐frequency variants that show very large climatic differentiation but low levels of linkage disequilibrium. These results suggest that their enrichment along putative functional sites most likely represents deleterious variation that is independent of local adaptation. Among all the genomic signatures examined, only SNPs showing high absolute allele frequency differentiation (AFD) and linkage disequilibrium (LD) between Italy and Sweden populations showed a strong association with fitness QTL peaks and were enriched along selectively constrained cis‐regulatory/nonsynonymous sites. Using these SNPs, we find strong evidence linking flowering time, freezing tolerance, and the abscisic‐acid pathway to local adaptation.     

Relative quantitation of restriction fragment length polymorphic DNAs via DNA melting analysis provides an effective way to determine allele frequencies

To accurately and precisely estimate the allele frequencies in DNA pools for a cost-effective approach to correlate genetic variations to phenotypic traits, we exploited differential melting kinetics between restriction fragment length polymorphic DNAs. The allele frequencies of two SNPs in a series of DNA mixtures with known allelic compositions of the SNPs were determined by analyzing the meltings of restricted PCR amplicons, yielding a result with a root mean square error (RMSE) of 0.014 relative to the expected values and a standard deviation (SD) of 0.018 from triplicate measurements. This method was then applied in the measurement of genotype frequencies in DNA pools in which varying numbers of genomic DNAs were intermingled while maintaining uniform quantitative contribution. Analyses of 10 SNPs demonstrated the feasibility of this method in an economical and highly accurate manner as the results yielded an RMSE value of 0.027 and a SD of 0.019.     

SNPs in stress-responsive rice genes: validation, genotyping, functional relevance and population structure

ABSTRACT: BACKGROUND: Single nucleotide polymorphism (SNP) validation and large-scale genotyping are required to maximize the use of DNA sequence variation and determine the functional relevance of candidate genes for complex stress tolerance traits through genetic association in rice. We used the bead array platform-based Illumina GoldenGate assay to validate and genotype SNPs in a select set of stress-responsive genes to understand their functional relevance and study the population structure in rice. RESULTS: Of the 384 putative SNPs assayed, we successfully validated and genotyped 362 (94.3%). Of these 325 (84.6%) showed polymorphism among the 91 rice genotypes examined. Physical distribution, degree of allele sharing, admixtures and introgression, and amino acid replacement of SNPs in 263 abiotic and 62 biotic stress-responsive genes provided clues for identification and targeted mapping of trait-associated genomic regions. We assessed the functional and adaptive significance of validated SNPs in a set of contrasting drought tolerant upland and sensitive lowland rice genotypes by correlating their allelic variation with amino acid sequence alterations in catalytic domains and three-dimensional secondary protein structure encoded by stress-responsive genes. We found a strong genetic association among SNPs in the nine stress-responsive genes with upland and lowland ecological adaptation. Higher nucleotide diversity was observed in indica accessions compared with other rice sub-populations based on different population genetic parameters. The inferred ancestry of 16% among rice genotypes was derived from admixed populations with the maximum between upland aus and wild Oryza species. CONCLUSIONS: SNPs validated in biotic and abiotic stress-responsive rice genes can be used in association analyses to identify candidate genes and develop functional markers for stress tolerance in rice.     

Precise estimation of allele frequencies of single-nucleotide polymorphisms by a quantitative SSCP analysis of pooled DNA

We show that single-nucleotide polymorphisms (SNPs) of moderate to high heterozygosity (minor allele frequencies >10%) can be efficiently detected, and their allele frequencies accurately estimated, by pooling the DNA samples and applying a capillary-based SSCP analysis. In this method, alleles are separated into peaks, and their frequencies can be reliably and accurately quantified from their peak heights (SD <1.8%). We found that as many as 40% of publicly available SNPs that were analyzed by this method have widely differing allele frequency distributions among groups of different ethnicity (parents of Centre d'Etude Polymorphisme Humaine families vs. Japanese individuals). These results demonstrate the effectiveness of the present pooling method in the reevaluation of candidate SNPs that have been collected by examination of limited numbers of individuals. The method should also serve as a robust quantitative technique for studies in which a precise estimate of SNP allele frequencies is essential-for example, in linkage disequilibrium analysis.     

Allele frequency matching between SNPs reveals an excess of linkage disequilibrium in genic regions of the human genome

Significant interest has emerged in mapping genetic susceptibility for complex traits through whole-genome association studies. These studies rely on the extent of association, i.e., linkage disequilibrium (LD), between single nucleotide polymorphisms (SNPs) across the human genome. LD describes the nonrandom association between SNP pairs and can be used as a metric when designing maximally informative panels of SNPs for association studies in human populations. Using data from the 1.58 million SNPs genotyped by Perlegen, we explored the allele frequency dependence of the LD statistic r(2) both empirically and theoretically. We show that average r(2) values between SNPs unmatched for allele frequency are always limited to much less than 1 (theoretical approximately 0.46 to 0.57 for this dataset). Frequency matching of SNP pairs provides a more sensitive measure for assessing the average decay of LD and generates average r(2) values across nearly the entire informative range (from 0 to 0.89 through 0.95). Additionally, we analyzed the extent of perfect LD (r(2) = 1.0) using frequency-matched SNPs and found significant differences in the extent of LD in genic regions versus intergenic regions. The SNP pairs exhibiting perfect LD showed a significant bias for derived, nonancestral alleles, providing evidence for positive natural selection in the human genome.     

The affected-/discordant-sib-pair design can guarantee validity of multipoint model-free linkage analysis of incomplete pedigrees when there is marker-marker disequilibrium

Genomewide linkage studies are tending toward the use of single-nucleotide polymorphisms (SNPs) as the markers of choice. However, linkage disequilibrium (LD) between tightly linked SNPs violates the fundamental assumption of linkage equilibrium (LE) between markers that underlies most multipoint calculation algorithms currently available, and this leads to inflated affected-relative-pair allele-sharing statistics when founders' multilocus genotypes are unknown. In this study, we investigate the impact that the degree of LD, marker allele frequency, and association type have on estimating the probabilities of sharing alleles identical by descent in multipoint calculations and hence on type I error rates of different sib-pair linkage approaches that assume LE. We show that marker-marker LD does not inflate type I error rates of affected sib pair (ASP) statistics in the whole parameter space, and that, in any case, discordant sib pairs (DSPs) can be used to control for marker-marker LD in ASPs. We advocate the ASP/DSP design with appropriate sib-pair statistics that test the difference in allele sharing between ASPs and DSPs.     

Positive correlation between DNA polymerase alpha-primase pausing and mutagenesis within polypyrimidine/polypurine microsatellite sequences

Microsatellite DNA sequences are ubiquitous in the human genome, and mutation rates of these repetitive sequences vary with respect to DNA sequence as well as length. We have analyzed polymerase-DNA interactions as a function of microsatellite sequence, using polypyrimidine/polypurine di- and tetranucleotide alleles representative of those found in the human genome. Using an in vitro primer extension assay and the mammalian DNA polymerase alpha-primase complex, we have observed a polymerase termination profile for each microsatellite that is unique to that allele. Interestingly, a periodic termination profile with an interval size (9-11 nucleotides) unrelated to microsatellite unit length was observed for the [TC](20) and [TTCC](9) templates. In contrast, a unit-punctuated polymerase termination profile was found for the longer polypurine templates. We detected strong polymerase pauses within the [TC](20) allele at low reaction pH which were eliminated by the addition of deaza-dGTP, consistent with these specific pauses being a consequence of triplex DNA formation during DNA synthesis. Quantitatively, a strand bias was observed in the primer extension assay, in that polymerase synthesis termination is more intense when the polypurine sequence serves as the template, relative to its complementary polypyrimidine sequence. The HSV-tk forward mutation assay was utilized to determine the corresponding polymerase alpha-primase error frequencies and specificities at the microsatellite alleles. A higher microsatellite polymerase error frequency (50x10(-4) to 60x10(-4)) was measured when polypurine sequences serve as templates for DNA synthesis, relative to the polypyrimidine template (18x10(-4)). Thus, a positive correlation exists between polymerase alpha-primase pausing and mutagenesis within microsatellite DNA alleles.     

Different real time PCR approaches for the fine quantification of SNP's alleles in DNA pools: assays development, characterization and pre-validation

Single nucleotide polymorphisms (SNPs) are becoming the most common type of markers used in genetic analysis. In the present report a SNP has been chosen to test the applicability of Real Time PCR to discriminate and quantify SNPs alleles on DNA pools. Amplification Refractory Mutation System (ARMS) and Mismatch Amplification Mutation Assay (MAMA) has been applied. Each assay has been pre-validated testing specificity and performances (linearity, PCR efficiency, interference limit, limit of detection, limit of quantification, precision and accuracy). Both the approaches achieve a precise and accurate estimation of the allele frequencies on pooled DNA samples in the range from 5 % to 95 % and don't require standard curves or calibrators. The lowest measurement that could be significantly distinguished from the background noise has been determined around the 1 % for both the approaches, allowing to extend the range of quantifications from 1 % to 99 %. Furthermore applicability of Real Time PCR assays for general diagnostic purposes is discussed.     

Genotyping pooled DNA using 100K SNP microarrays: a step towards genomewide association scans

The identification of quantitative trait loci (QTLs) of small effect size that underlie complex traits poses a particular challenge for geneticists due to the large sample sizes and large numbers of genetic markers required for genomewide association scans. An efficient solution for screening purposes is to combine single nucleotide polymorphism (SNP) microarrays and DNA pooling (SNP-MaP), an approach that has been shown to be valid, reliable and accurate in deriving relative allele frequency estimates from pooled DNA for groups such as cases and controls for 10K SNP microarrays. However, in order to conduct a genomewide association study many more SNP markers are needed. To this end, we assessed the validity and reliability of the SNP-MaP method using Affymetrix GeneChip^® Mapping 100K Array set. Interpretable results emerged for 95% of the SNPs (nearly 110000 SNPs). We found that SNP-MaP allele frequency estimates correlated 0.939 with allele frequencies for 97605 SNPs that were genotyped individually in an independent population; the correlation was 0.971 for 26 SNPs that were genotyped individually for the 1028 individuals used to construct the DNA pools. We conclude that extending the SNP-MaP method to the Affymetrix GeneChip^® Mapping 100K Array set provides a useful screen of >100000 SNP markers for QTL association scans.