Allele Frequency Estimates Research Articles

Comparing the van Oosterhout and Chybicki‐Burczyk methods of estimating null allele frequencies for inbred populations

In spite of the usefulness of codominant markers in population genetics, the existence of null alleles raises challenging estimation issues in natural populations that are characterized by positive inbreeding coefficients (F > 0). Disregarding the possibility of F > 0 in a population will generally lead to overestimates of null allele frequencies. Conversely, estimates of inbreeding coefficients (F) may be strongly biased upwards (excess homozygotes), in the presence of nontrivial frequencies of null alleles. An algorithm has been presented for the estimation of null allele frequencies in inbred populations (van Oosterhout method), using external estimates of the F-statistics. The goal of this study is to introduce a modification of this method and to provide a formal comparison with an alternative likelihood-based method (Chybicki-Burczyk). Using simulated data, we illustrate the strengths and limitations of these competing methods. Under most circumstances, the likelihood method is preferable, but for highly inbred organisms, a modified van Oosterhout method offers some advantages.

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 FST 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.

An empirical Bayes mixture model for SNP detection in pooled sequencing data

Detecting single-nucleotide polymorphism (SNP) in pooled sequencing data is more challenging than in individual sequencing because of sampling variations across pools. To effectively differentiate SNP signal from sequencing error, appropriate estimation of the sequencing error is necessary. In this article, we propose an empirical Bayes mixture (EBM) model for SNP detection and allele frequency estimation in pooled sequencing data. The proposed model reliably learns the error distribution by pooling information across pools and genomic positions. In addition, the proposed EBM model builds in characteristics unique to the pooled sequencing data, boosting the sensitivity of SNP detection. For large-scale inference in SNP detection, the EBM model provides a flexible and robust way for estimation and control of local false discovery rate. We demonstrate the performance of the proposed method through simulation studies and real data application. Implementation of this method is available at https://sites.google.com/site/zhouby98.

Empirical Validation of Pooled Whole Genome Population Re-Sequencing in Drosophila melanogaster

The sequencing of pooled non-barcoded individuals is an inexpensive and efficient means of assessing genome-wide population allele frequencies, yet its accuracy has not been thoroughly tested. We assessed the accuracy of this approach on whole, complex eukaryotic genomes by resequencing pools of largely isogenic, individually sequenced Drosophila melanogaster strains. We called SNPs in the pooled data and estimated false positive and false negative rates using the SNPs called in individual strain as a reference. We also estimated allele frequency of the SNPs using “pooled” data and compared them with “true” frequencies taken from the estimates in the individual strains. We demonstrate that pooled sequencing provides a faithful estimate of population allele frequency with the error well approximated by binomial sampling, and is a reliable means of novel SNP discovery with low false positive rates. However, a sufficient number of strains should be used in the pooling because variation in the amount of DNA derived from individual strains is a substantial source of noise when the number of pooled strains is low. Our results and analysis confirm that pooled sequencing is a very powerful and cost-effective technique for assessing of patterns of sequence variation in populations on genome-wide scales, and is applicable to any dataset where sequencing individuals or individual cells is impossible, difficult, time consuming, or expensive.

SNP Calling, Genotype Calling, and Sample Allele Frequency Estimation from New-Generation Sequencing Data

We present a statistical framework for estimation and application of sample allele frequency spectra from New-Generation Sequencing (NGS) data. In this method, we first estimate the allele frequency spectrum using maximum likelihood. In contrast to previous methods, the likelihood function is calculated using a dynamic programming algorithm and numerically optimized using analytical derivatives. We then use a Bayesian method for estimating the sample allele frequency in a single site, and show how the method can be used for genotype calling and SNP calling. We also show how the method can be extended to various other cases including cases with deviations from Hardy-Weinberg equilibrium. We evaluate the statistical properties of the methods using simulations and by application to a real data set.

Late‐onset progressive retinal atrophy in the Gordon and Irish Setter breeds is associated with a frameshift mutation in C2orf71

Progressive retinal atrophy (PRA) in dogs is characterised by the degeneration of the photoreceptor cells of the retina, resulting in vision loss and eventually complete blindness. The condition affects more than 100 dog breeds and is known to be genetically heterogeneous between breeds. Around 14 mutations have now been identified that are associated with PRA in around 49 breeds, but for the majority of breeds the mutation(s) responsible have yet to be identified. Using genome-wide association with 16 Gordon Setter PRA cases and 22 controls, we identified a novel PRA locus, termed rod-cone degeneration 4 (rcd4), on CFA17 (Praw =2.22×10(-8) , Pgenome =2.00×10(-5) ), where a 3.2-Mb region was homozygous within cases. A frameshift mutation was identified in C2orf71, a gene located within this region. This variant was homozygous in 19 of 21 PRA cases and was at a frequency of approximately 0.37 in the Gordon Setter population. Approximately 10% of cases in our study (2 of 21) are not associated with this C2orf71 mutation, indicating that PRA in this breed is genetically heterogeneous and caused by at least two mutations. This variant is also present in a number of Irish Setter dogs with PRA and has an estimated allele frequency of 0.26 in the breed. The function of C2orf71 remains unknown, but it is important for retinal development and function and has previously been associated with autosomal recessive retinitis pigmentosa in humans.

Biases and Errors on Allele Frequency Estimation and Disease Association Tests of Next‐Generation Sequencing of Pooled Samples

Next-generation sequencing is widely used to study complex diseases because of its ability to identify both common and rare variants without prior single nucleotide polymorphism (SNP) information. Pooled sequencing of implicated target regions can lower costs and allow more samples to be analyzed, thus improving statistical power for disease-associated variant detection. Several methods for disease association tests of pooled data and for optimal pooling designs have been developed under certain assumptions of the pooling process, for example, equal/unequal contributions to the pool, sequencing depth variation, and error rate. However, these simplified assumptions may not portray the many factors affecting pooled sequencing data quality, such as PCR amplification during target capture and sequencing, reference allele preferential bias, and others. As a result, the properties of the observed data may differ substantially from those expected under the simplified assumptions. Here, we use real datasets from targeted sequencing of pooled samples, together with microarray SNP genotypes of the same subjects, to identify and quantify factors (biases and errors) affecting the observed sequencing data. Through simulations, we find that these factors have a significant impact on the accuracy of allele frequency estimation and the power of association tests. Furthermore, we develop a workflow protocol to incorporate these factors in data analysis to reduce the potential biases and errors in pooled sequencing data and to gain better estimation of allele frequencies. The workflow, Psafe, is available at http://bioinformatics.med.yale.edu/group/.

Maximum likelihood estimation of individual inbreeding coefficients and null allele frequencies

In this paper, we developed and compared several expectation-maximization (EM) algorithms to find maximum likelihood estimates of individual inbreeding coefficients using molecular marker information. The first method estimates the inbreeding coefficient for a single individual and assumes that allele frequencies are known without error. The second method jointly estimates inbreeding coefficients and allele frequencies for a set of individuals that have been genotyped at several loci. The third method generalizes the second method to include the case in which null alleles may be present. In particular, it is able to jointly estimate individual inbreeding coefficients and allele frequencies, including the frequencies of null alleles, and accounts for missing data. We compared our methods with several other estimation procedures using simulated data and found that our methods perform well. The maximum likelihood estimators consistently gave among the lowest root-mean-square-error (RMSE) of all the estimators that were compared. Our estimator that accounts for null alleles performed particularly well and was able to tease apart the effects of null alleles, randomly missing genotypes and differing degrees of inbreeding among members of the datasets we analysed. To illustrate the performance of our estimators, we analysed previously published datasets on mice (Mus musculus) and white-tailed deer (Odocoileus virginianus).

Synteny‐based mapping‐by‐sequencing enabled by targeted enrichment

Mapping-by-sequencing, as implemented in SHOREmap ('SHOREmapping'), is greatly accelerating the identification of causal mutations. The original SHOREmap approach based on resequencing of bulked segregants required a highly accurate and complete reference sequence. However, current whole-genome or transcriptome assemblies from next-generation sequencing data of non-model organisms do not produce chromosome-length scaffolds. We have therefore developed a method that exploits synteny with a related genome for genetic mapping. We first demonstrate how mapping-by-sequencing can be performed using a reduced number of markers, and how the associated decrease in the number of markers can be compensated for by enrichment of marker sequences. As proof of concept, we apply this method to Arabidopsis thaliana gene models ordered by synteny with the genome sequence of the distant relative Brassica rapa, whose genome has several large-scale rearrangements relative to A.thaliana. Our approach provides an alternative method for high-resolution genetic mapping in species that lack finished genome reference sequences or for which only RNA-seq assemblies are available. Finally, for improved identification of causal mutations by fine-mapping, we introduce a new likelihood ratio test statistic, transforming local allele frequency estimations into a confidence interval similar to conventional mapping intervals.

Practical capability of a DNA pool‐based genome‐wide association study using BovineSNP50 array in a cattle population

ABSTRACTGenome‐wide association mapping for complex traits in cattle populations is a powerful, but expensive, selection tool. The DNA pooling technique can potentially reduce the cost of genome‐wide association studies. However, in DNA pooling design, the additional variance generated by pooling‐specific errors must be taken into account. Therefore, this study aimed to investigate factors such as: (i) the accuracy of allele frequency estimation; (ii) the magnitude of errors in pooling construction and in the array; and (iii) the effect of the number of replicate arrays on P‐values estimated by a genome‐wide association study. Results showed that the Illumina correction method is the most effective method to correct the allele frequency estimation; pooling errors, especially array variance, should be taken into account in DNA pooling design; and the risk of a type I error can be reduced by using at least two replicate arrays. These results indicate the practical capability and cost‐effectiveness of pool‐based genome‐wide association studies using the BovineSNP50 array in a cattle population.

Determination of the obesity-associated gene variants within the entire FTO gene by ultra-deep targeted sequencing in obese and lean children

Background:The Fat mass and obesity-associated gene (FTO) was the first gene reliably associated with body mass index in genome-wide association studies on a population level. At present, the genetic variations within the FTO gene are still the common variants that have the largest influence on body mass index.Methods:In the current study, we amplified the entire FTO gene, in total 412 Kbp, in over 200 long-range PCR fragments from each individual, from 524 severely obese and 527 lean Swedish children, and sequenced the products as two DNA pools using massive parallel sequencing (SOLiD).Results:The sequencing achieved very high coverage (median 18 000 reads) and we detected and estimated allele frequencies for 705 single nucleotide polymorphisms (SNPs) (19 novel) and 40 indels (24 novel) using a sophisticated statistical approach to remove false-positive SNPs. We identified 19 obesity-associated SNPs within intron one of the FTO gene, and validated our findings with genotyping. Ten of the validated obesity-associated SNPs have a stronger obesity association (P<0.007) than the commonly studied rs9939609 SNP (P<0.012).Conclusions:This study provides a comprehensive obesity-associated variation map of FTO, identifies novel lead SNPs and evaluates putative causative variants. We conclude that intron one is the only region within the FTO gene associated with obesity, and finally, we establish next generation sequencing of pooled DNA as a powerful method to investigate genetic association with complex diseases and traits.

Estimating the effect of SNP genotype on quantitative traits from pooled DNA samples

BackgroundStudies to detect associations between DNA markers and traits of interest in humans and livestock benefit from increasing the number of individuals genotyped. Performing association studies on pooled DNA samples can provide greater power for a given cost. For quantitative traits, the effect of an SNP is measured in the units of the trait and here we propose and demonstrate a method to estimate SNP effects on quantitative traits from pooled DNA data.MethodsTo obtain estimates of SNP effects from pooled DNA samples, we used logistic regression of estimated allele frequencies in pools on phenotype. The method was tested on a simulated dataset, and a beef cattle dataset using a model that included principal components from a genomic correlation matrix derived from the allele frequencies estimated from the pooled samples. The performance of the obtained estimates was evaluated by comparison with estimates obtained using regression of phenotype on genotype from individual samples of DNA.ResultsFor the simulated data, the estimates of SNP effects from pooled DNA are similar but asymptotically different to those from individual DNA data. Error in estimating allele frequencies had a large effect on the accuracy of estimated SNP effects. For the beef cattle dataset, the principal components of the genomic correlation matrix from pooled DNA were consistent with known breed groups, and could be used to account for population stratification. Correctly modeling the contemporary group structure was essential to achieve estimates similar to those from individual DNA data, and pooling DNA from individuals within groups was superior to pooling DNA across groups. For a fixed number of assays, pooled DNA samples produced results that were more correlated with results from individual genotyping data than were results from one random individual assayed from each pool.ConclusionsUse of logistic regression of allele frequency on phenotype makes it possible to estimate SNP effects on quantitative traits from pooled DNA samples. With pooled DNA samples, genotyping costs are reduced, and in cases where trait records are abundant this approach is promising to obtain SNP associations for marker-assisted selection.

Polymorphism discovery and allele frequency estimation using high-throughput DNA sequencing of target-enriched pooled DNA samples

BackgroundThe central role of the somatotrophic axis in animal post-natal growth, development and fertility is well established. Therefore, the identification of genetic variants affecting quantitative traits within this axis is an attractive goal. However, large sample numbers are a pre-requisite for the identification of genetic variants underlying complex traits and although technologies are improving rapidly, high-throughput sequencing of large numbers of complete individual genomes remains prohibitively expensive. Therefore using a pooled DNA approach coupled with target enrichment and high-throughput sequencing, the aim of this study was to identify polymorphisms and estimate allele frequency differences across 83 candidate genes of the somatotrophic axis, in 150 Holstein-Friesian dairy bulls divided into two groups divergent for genetic merit for fertility.ResultsIn total, 4,135 SNPs and 893 indels were identified during the resequencing of the 83 candidate genes. Nineteen percent (n = 952) of variants were located within 5' and 3' UTRs. Seventy-two percent (n = 3,612) were intronic and 9% (n = 464) were exonic, including 65 indels and 236 SNPs resulting in non-synonymous substitutions (NSS). Significant (P < 0.01) mean allele frequency differentials between the low and high fertility groups were observed for 720 SNPs (58 NSS). Allele frequencies for 43 of the SNPs were also determined by genotyping the 150 individual animals (Sequenom® MassARRAY). No significant differences (P > 0.1) were observed between the two methods for any of the 43 SNPs across both pools (i.e., 86 tests in total).ConclusionsThe results of the current study support previous findings of the use of DNA sample pooling and high-throughput sequencing as a viable strategy for polymorphism discovery and allele frequency estimation. Using this approach we have characterised the genetic variation within genes of the somatotrophic axis and related pathways, central to mammalian post-natal growth and development and subsequent lactogenesis and fertility. We have identified a large number of variants segregating at significantly different frequencies between cattle groups divergent for calving interval plausibly harbouring causative variants contributing to heritable variation. To our knowledge, this is the first report describing sequencing of targeted genomic regions in any livestock species using groups with divergent phenotypes for an economically important trait.

Reducing bias of allele frequency estimates by modeling SNP genotype data with informative missingness.

The presence of missing single-nucleotide polymorphism (SNP) genotypes is common in genetic studies. For studies with low-density SNPs, the most commonly used approach to dealing with genotype missingness is to simply remove the observations with missing genotypes from the analyses. This naïve method is straightforward but is valid only when the missingness is random. However, a given assay often has a different capability in genotyping heterozygotes and homozygotes, causing the phenomenon of “differential dropout” in the sense that the missing rates of heterozygotes and homozygotes are different. In practice, differential dropout among genotypes exists in even carefully designed studies, such as the data from the HapMap project and the Wellcome Trust Case Control Consortium. Under the assumption of Hardy–Weinberg equilibrium and no genotyping error, we here propose a statistical method to model the differential dropout among different genotypes. Compared with the naïve method, our method provides more accurate allele frequency estimates when the differential dropout is present. To demonstrate its practical use, we further apply our method to the HapMap data and a scleroderma data set.

Estimates of array and pool-construction variance for planning efficient DNA-pooling genome wide association studies

BackgroundUntil recently, genome-wide association studies (GWAS) have been restricted to research groups with the budget necessary to genotype hundreds, if not thousands, of samples. Replacing individual genotyping with genotyping of DNA pools in Phase I of a GWAS has proven successful, and dramatically altered the financial feasibility of this approach. When conducting a pool-based GWAS, how well SNP allele frequency is estimated from a DNA pool will influence a study's power to detect associations. Here we address how to control the variance in allele frequency estimation when DNAs are pooled, and how to plan and conduct the most efficient well-powered pool-based GWAS.MethodsBy examining the variation in allele frequency estimation on SNP arrays between and within DNA pools we determine how array variance [var(earray)] and pool-construction variance [var(econstruction)] contribute to the total variance of allele frequency estimation. This information is useful in deciding whether replicate arrays or replicate pools are most useful in reducing variance. Our analysis is based on 27 DNA pools ranging in size from 74 to 446 individual samples, genotyped on a collective total of 128 Illumina beadarrays: 24 1M-Single, 32 1M-Duo, and 72 660-Quad.ResultsFor all three Illumina SNP array types our estimates of var(earray) were similar, between 3-4 × 10-4 for normalized data. Var(econstruction) accounted for between 20-40% of pooling variance across 27 pools in normalized data.ConclusionsWe conclude that relative to var(earray), var(econstruction) is of less importance in reducing the variance in allele frequency estimation from DNA pools; however, our data suggests that on average it may be more important than previously thought. We have prepared a simple online tool, PoolingPlanner (available at http://www.kchew.ca/PoolingPlanner/), which calculates the effective sample size (ESS) of a DNA pool given a range of replicate array values. ESS can be used in a power calculator to perform pool-adjusted calculations. This allows one to quickly calculate the loss of power associated with a pooling experiment to make an informed decision on whether a pool-based GWAS is worth pursuing.

Malic enzyme gene polymorphism is associated with responsiveness in circulating parathyroid hormone after long-term calcium supplementation.

To identify genetic variations associated with parathyroid hormone (PTH) suppression after long-term calcium supplementation. For high throughput SNP screening, subjects consisted of 171 postmenopausal women without osteoporosis at the lumbar spine. A separate group of 19 premenpausal women were recruited for calcium absorption study. Postmenopausal women in the screening group were given 500 mg/day calcium supplementation. Bangkok, Thailand. Parathyroid hormone (PTH) and bone mineral density (BMD) were measured at baseline and 2 years after calcium supplementation. High throughput single-nucleotide polymorphism (SNP) screening was performed by comparing estimated allele frequencies derived from hybridization signal intensities of pooled DNA samples on Affymetrix's 10K SNP genotyping microarrays based responsiveness in PTH after calcium supplementation. Genotyping of SNP rs1112482 in malic enzyme gene (ME1) gene, a SNP among those with highest odds ratio of being related to PTH suppression after calcium, was performed in all postmenopausal subjects in the screening group and premenopausal women in the calcium absorption study group in which fractional calcium absorption was assessed by stable isotope dilution. Data were expressed as mean +/- SEM. PTH significantly decreased after 2 years of calcium supplementation (4.7 ± 1.9 vs. 4.4 ± 1.6 pmol/L, P < 0.01). There was a significant increase in lumbar spine BMD (1.03 ± 0.01 vs. 1.01 ± 0.01 g/cm2, P < 0.001) but not femoral neck BMD. In 108 subjects whose PTH levels decreased after calcium, the suppression of PTH was higher in those with at least one C allele in rs1112482 of ME1 gene (-26.3 ± 2.1 vs. -16.9 ± 1.4%, P < 0.001). Fractional calcium absorption also tends to the higher in subjects in the calcium absorption study group with at least one C allele (n = 6) compared to those without the C allele (n = 13) (58.0 ± 4.9 vs. 49.3 ± 2.8%, P = 0.054). Cytosolic malic enzyme 1 gene polymorphism is associated with the degree of suppression of parathyroid hormone after long-term calcium supplementation. The effect is probably mediated through an increase in intestinal calcium absorption.

The Statistics of Bulk Segregant Analysis Using Next Generation Sequencing

We describe a statistical framework for QTL mapping using bulk segregant analysis (BSA) based on high throughput, short-read sequencing. Our proposed approach is based on a smoothed version of the standard statistic, and takes into account variation in allele frequency estimates due to sampling of segregants to form bulks as well as variation introduced during the sequencing of bulks. Using simulation, we explore the impact of key experimental variables such as bulk size and sequencing coverage on the ability to detect QTLs. Counterintuitively, we find that relatively large bulks maximize the power to detect QTLs even though this implies weaker selection and less extreme allele frequency differences. Our simulation studies suggest that with large bulks and sufficient sequencing depth, the methods we propose can be used to detect even weak effect QTLs and we demonstrate the utility of this framework by application to a BSA experiment in the budding yeast Saccharomyces cerevisiae.

Distribution of allele frequencies and effect sizes and their interrelationships for common genetic susceptibility variants

Recent discoveries of hundreds of common susceptibility SNPs from genome-wide association studies provide a unique opportunity to examine population genetic models for complex traits. In this report, we investigate distributions of various population genetic parameters and their interrelationships using estimates of allele frequencies and effect-size parameters for about 400 susceptibility SNPs across a spectrum of qualitative and quantitative traits. We calibrate our analysis by statistical power for detection of SNPs to account for overrepresentation of variants with larger effect sizes in currently known SNPs that are expected due to statistical power for discovery. Across all qualitative disease traits, minor alleles conferred "risk" more often than "protection." Across all traits, an inverse relationship existed between "regression effects" and allele frequencies. Both of these trends were remarkably strong for type I diabetes, a trait that is most likely to be influenced by selection, but were modest for other traits such as human height or late-onset diseases such as type II diabetes and cancers. Across all traits, the estimated effect-size distribution suggested the existence of increasingly large numbers of susceptibility SNPs with decreasingly small effects. For most traits, the set of SNPs with intermediate minor allele frequencies (5-20%) contained an unusually small number of susceptibility loci and explained a relatively small fraction of heritability compared with what would be expected from the distribution of SNPs in the general population. These trends could have several implications for future studies of common and uncommon variants.

Sampling method for estimating neutral allele frequency in a pedigreed population

The estimated allele frequency at neutral DNA marker loci is a fundamental parameter for establishing a conservation scheme for a set of livestock breeds. In this study, we propose a novel 'minimum distance (MD) method' for estimating neutral allele frequencies, which minimizes the error by the use of pedigree information. Using computer simulation and actual microsatellite data for a pedigreed cattle population, the performance of the proposed method was compared with that of conventional random sampling (RND). MD manifests a promising superiority to RND, irrespective of the sample size and the depth of pedigree. It is theoretically demonstrated that the error of the estimates depends on both the sample size and the distance of founder allele frequencies between the sampled and the non-sampled individuals. MD samples individuals so as to minimize the latter source of estimation error.

Database sample size effect on minimum allele frequency estimation: Database comparison analysis of samples of 4652 and 560 individuals for 22 microsatellites in Colombian population

With the aim of studying the effect of the database size on the frequency estimations of minimum and rare alleles, a comparative analysis was undertaken between two different size samples from a Colombian mestizo population living in Antioquia region. In this work, minimum allele frequencies (calculated using two different methods) were compared in samples with (a) size n = 560, the total number of individuals in our database from Antioquia in 2008, and (b) size n = 4652, the new size of the same database in 2010. When database size was increased, the total number of alleles increased in 17%, going from 257 up to 313 alleles. Although the number of alleles with low frequency became higher for an enlarged database, as it could be expected, the minimum allele frequency decreased and, therefore, the final number of alleles with a frequency below this estimate did not changed significantly.