Inference of site frequency spectra from high-throughput sequence data: quantification of selection on nonsynonymous and synonymous sites in humans

Sequencing errors and random sampling of nucleotide types among sequencing reads at heterozygous sites present challenges for accurate, unbiased inference of single-nucleotide polymorphism genotypes from high-throughput sequence data. Here, we develop a maximum-likelihood approach to estimate the frequency distribution of the number of alleles in a sample of individuals (the site frequency spectrum), using high-throughput sequence data. Our method assumes binomial sampling of nucleotide types in heterozygotes and random sequencing error. By simulations, we show that close to unbiased estimates of the site frequency spectrum can be obtained if the error rate per base read does not exceed the population nucleotide diversity. We also show that these estimates are reasonably robust if errors are nonrandom. We then apply the method to infer site frequency spectra for zerofold degenerate, fourfold degenerate, and intronic sites of protein-coding genes using the low coverage human sequence data produced by the 1000 Genomes Project phase-one pilot. By fitting a model to the inferred site frequency spectra that estimates parameters of the distribution of fitness effects of new mutations, we find evidence for significant natural selection operating on fourfold sites. We also find that a model with variable effects of mutations at synonymous sites fits the data significantly better than a model with equal mutational effects. Under the variable effects model, we infer that 11% of synonymous mutations are subject to strong purifying selection.     

Haplotype Estimation Using Sequencing Reads

High-throughput sequencing technologies produce short sequence reads that can contain phase information if they span two or more heterozygote genotypes. This information is not routinely used by current methods that infer haplotypes from genotype data. We have extended the SHAPEIT2 method to use phase-informative sequencing reads to improve phasing accuracy. Our model incorporates the read information in a probabilistic model through base quality scores within each read. The method is primarily designed for high-coverage sequence data or data sets that already have genotypes called. One important application is phasing of single samples sequenced at high coverage for use in medical sequencing and studies of rare diseases. Our method can also use existing panels of reference haplotypes. We tested the method by using a mother-father-child trio sequenced at high-coverage by Illumina together with the low-coverage sequence data from the 1000 Genomes Project (1000GP). We found that use of phase-informative reads increases the mean distance between switch errors by 22% from 274.4 kb to 328.6 kb. We also used male chromosome X haplotypes from the 1000GP samples to simulate sequencing reads with varying insert size, read length, and base error rate. When using short 100 bp paired-end reads, we found that using mixtures of insert sizes produced the best results. When using longer reads with high error rates (5–20 kb read with 4%–15% error per base), phasing performance was substantially improved.     

Extending rare-variant testing strategies: analysis of noncoding sequence and imputed genotypes

Next Generation Sequencing Technology has revolutionized our ability to study the contribution of rare genetic variation to heritable traits. However, existing single-marker association tests are underpowered for detecting rare risk variants. A more powerful approach involves pooling methods that combine multiple rare variants from the same gene into a single test statistic. Proposed pooling methods can be limited because they generally assume high-quality genotypes derived from deep-coverage sequencing, which may not be available. In this paper, we consider an intuitive and computationally efficient pooling statistic, the cumulative minor-allele test (CMAT). We assess the performance of the CMAT and other pooling methods on datasets simulated with population genetic models to contain realistic levels of neutral variation. We consider study designs ranging from exon-only to whole-gene analyses that contain noncoding variants. For all study designs, the CMAT achieves power comparable to that of previously proposed methods. We then extend the CMAT to probabilistic genotypes and describe application to low-coverage sequencing and imputation data. We show that augmenting sequence data with imputed samples is a practical method for increasing the power of rare-variant studies. We also provide a method of controlling for confounding variables such as population stratification. Finally, we demonstrate that our method makes it possible to use external imputation templates to analyze rare variants imputed into existing GWAS datasets. As proof of principle, we performed a CMAT analysis of more than 8 million SNPs that we imputed into the GAIN psoriasis dataset by using haplotypes from the 1000 Genomes Project.     

Distinct error rates for reference and nonreference genotypes estimated by pedigree analysis

Errors in genotype calling can have perverse effects on genetic analyses, confounding association studies, and obscuring rare variants. Analyses now routinely incorporate error rates to control for spurious findings. However, reliable estimates of the error rate can be difficult to obtain because of their variance between studies. Most studies also report only a single estimate of the error rate even though genotypes can be miscalled in more than one way. Here, we report a method for estimating the rates at which different types of genotyping errors occur at biallelic loci using pedigree information. Our method identifies potential genotyping errors by exploiting instances where the haplotypic phase has not been faithfully transmitted. The expected frequency of inconsistent phase depends on the combination of genotypes in a pedigree and the probability of miscalling each genotype. We develop a model that uses the differences in these frequencies to estimate rates for different types of genotype error. Simulations show that our method accurately estimates these error rates in a variety of scenarios. We apply this method to a dataset from the whole-genome sequencing of owl monkeys (Aotus nancymaae) in three-generation pedigrees. We find significant differences between estimates for different types of genotyping error, with the most common being homozygous reference sites miscalled as heterozygous and vice versa. The approach we describe is applicable to any set of genotypes where haplotypic phase can reliably be called and should prove useful in helping to control for false discoveries.     

Rare Variant Association Testing Under Low-Coverage Sequencing

Deep sequencing technologies enable the study of the effects of rare variants in disease risk. While methods have been developed to increase statistical power for detection of such effects, detecting subtle associations requires studies with hundreds or thousands of individuals, which is prohibitively costly. Recently, low-coverage sequencing has been shown to effectively reduce the cost of genome-wide association studies, using current sequencing technologies. However, current methods for disease association testing on rare variants cannot be applied directly to low-coverage sequencing data, as they require individual genotype data, which may not be called correctly due to low-coverage and inherent sequencing errors. In this article, we propose two novel methods for detecting association of rare variants with disease risk, using low coverage, error-prone sequencing. We show by simulation that our methods outperform previous methods under both low- and high-coverage sequencing and under different disease architectures. We use real data and simulation studies to demonstrate that to maximize the power to detect associations for a fixed budget, it is desirable to include more samples while lowering coverage and to perform an analysis using our suggested methods.     

A Maximum-Likelihood Method to Correct for Allelic Dropout in Microsatellite Data with No Replicate Genotypes

Allelic dropout is a commonly observed source of missing data in microsatellite genotypes, in which one or both allelic copies at a locus fail to be amplified by the polymerase chain reaction. Especially for samples with poor DNA quality, this problem causes a downward bias in estimates of observed heterozygosity and an upward bias in estimates of inbreeding, owing to mistaken classifications of heterozygotes as homozygotes when one of the two copies drops out. One general approach for avoiding allelic dropout involves repeated genotyping of homozygous loci to minimize the effects of experimental error. Existing computational alternatives often require replicate genotyping as well. These approaches, however, are costly and are suitable only when enough DNA is available for repeated genotyping. In this study, we propose a maximum-likelihood approach together with an expectation-maximization algorithm to jointly estimate allelic dropout rates and allele frequencies when only one set of nonreplicated genotypes is available. Our method considers estimates of allelic dropout caused by both sample-specific factors and locus-specific factors, and it allows for deviation from Hardy–Weinberg equilibrium owing to inbreeding. Using the estimated parameters, we correct the bias in the estimation of observed heterozygosity through the use of multiple imputations of alleles in cases where dropout might have occurred. With simulated data, we show that our method can (1) effectively reproduce patterns of missing data and heterozygosity observed in real data; (2) correctly estimate model parameters, including sample-specific dropout rates, locus-specific dropout rates, and the inbreeding coefficient; and (3) successfully correct the downward bias in estimating the observed heterozygosity. We find that our method is fairly robust to violations of model assumptions caused by population structure and by genotyping errors from sources other than allelic dropout. Because the data sets imputed under our model can be investigated in additional subsequent analyses, our method will be useful for preparing data for applications in diverse contexts in population genetics and molecular ecology.     

Estimating Individual Admixture Proportions from Next Generation Sequencing Data

Inference of population structure and individual ancestry is important both for population genetics and for association studies. With next generation sequencing technologies it is possible to obtain genetic data for all accessible genetic variations in the genome. Existing methods for admixture analysis rely on known genotypes. However, individual genotypes cannot be inferred from low-depth sequencing data without introducing errors. This article presents a new method for inferring an individual’s ancestry that takes the uncertainty introduced in next generation sequencing data into account. This is achieved by working directly with genotype likelihoods that contain all relevant information of the unobserved genotypes. Using simulations as well as publicly available sequencing data, we demonstrate that the presented method has great accuracy even for very low-depth data. At the same time, we demonstrate that applying existing methods to genotypes called from the same data can introduce severe biases. The presented method is implemented in the NGSadmix software available at http://www.popgen.dk/software.     

Improved Ancestry Estimation for both Genotyping and Sequencing Data using Projection Procrustes Analysis and Genotype Imputation

Accurate estimation of individual ancestry is important in genetic association studies, especially when a large number of samples are collected from multiple sources. However, existing approaches developed for genome-wide SNP data do not work well with modest amounts of genetic data, such as in targeted sequencing or exome chip genotyping experiments. We propose a statistical framework to estimate individual ancestry in a principal component ancestry map generated by a reference set of individuals. This framework extends and improves upon our previous method for estimating ancestry using low-coverage sequence reads (LASER 1.0) to analyze either genotyping or sequencing data. In particular, we introduce a projection Procrustes analysis approach that uses high-dimensional principal components to estimate ancestry in a low-dimensional reference space. Using extensive simulations and empirical data examples, we show that our new method (LASER 2.0), combined with genotype imputation on the reference individuals, can substantially outperform LASER 1.0 in estimating fine-scale genetic ancestry. Specifically, LASER 2.0 can accurately estimate fine-scale ancestry within Europe using either exome chip genotypes or targeted sequencing data with off-target coverage as low as 0.05×. Under the framework of LASER 2.0, we can estimate individual ancestry in a shared reference space for samples assayed at different loci or by different techniques. Therefore, our ancestry estimation method will accelerate discovery in disease association studies not only by helping model ancestry within individual studies but also by facilitating combined analysis of genetic data from multiple sources.     

Accounting for bias from sequencing error in population genetic estimates

Sequencing error presents a significant challenge to population genetic analyses using low-coverage sequence in general and single-pass reads in particular. Bias in parameter estimates becomes severe when the level of polymorphism (signal) is low relative to the amount of error (noise). Choosing an arbitrary quality score cutoff yields biased estimates, particularly with newer, non-Sanger sequencing technologies that have different quality score distributions. We propose a rule of thumb to judge when a given threshold will lead to significant bias and suggest alternative approaches that reduce bias.     

MSACompro: protein multiple sequence alignment using predicted secondary structure, solvent accessibility, and residue-residue contacts

Background

Estimation of allele frequency is of fundamental importance in population genetic analyses and in association mapping. In most studies using next-generation sequencing, a cost effective approach is to use medium or low-coverage data (e.g., < 15X). However, SNP calling and allele frequency estimation in such studies is associated with substantial statistical uncertainty because of varying coverage and high error rates.

Results

We evaluate a new maximum likelihood method for estimating allele frequencies in low and medium coverage next-generation sequencing data. The method is based on integrating over uncertainty in the data for each individual rather than first calling genotypes. This method can be applied to directly test for associations in case/control studies. We use simulations to compare the likelihood method to methods based on genotype calling, and show that the likelihood method outperforms the genotype calling methods in terms of: (1) accuracy of allele frequency estimation, (2) accuracy of the estimation of the distribution of allele frequencies across neutrally evolving sites, and (3) statistical power in association mapping studies. Using real re-sequencing data from 200 individuals obtained from an exon-capture experiment, we show that the patterns observed in the simulations are also found in real data.

Conclusions

Overall, our results suggest that association mapping and estimation of allele frequencies should not be based on genotype calling in low to medium coverage data. Furthermore, if genotype calling methods are used, it is usually better not to filter genotypes based on the call confidence score.     

Population Genetic Inference from Personal Genome Data: Impact of Ancestry and Admixture on Human Genomic Variation

Full sequencing of individual human genomes has greatly expanded our understanding of human genetic variation and population history. Here, we present a systematic analysis of 50 human genomes from 11 diverse global populations sequenced at high coverage. Our sample includes 12 individuals who have admixed ancestry and who have varying degrees of recent (within the last 500 years) African, Native American, and European ancestry. We found over 21 million single-nucleotide variants that contribute to a 1.75-fold range in nucleotide heterozygosity across diverse human genomes. This heterozygosity ranged from a high of one heterozygous site per kilobase in west African genomes to a low of 0.57 heterozygous sites per kilobase in segments inferred to have diploid Native American ancestry from the genomes of Mexican and Puerto Rican individuals. We show evidence of all three continental ancestries in the genomes of Mexican, Puerto Rican, and African American populations, and the genome-wide statistics are highly consistent across individuals from a population once ancestry proportions have been accounted for. Using a generalized linear model, we identified subtle variations across populations in the proportion of neutral versus deleterious variation and found that genome-wide statistics vary in admixed populations even once ancestry proportions have been factored in. We further infer that multiple periods of gene flow shaped the diversity of admixed populations in the Americas—70% of the European ancestry in today’s African Americans dates back to European gene flow happening only 7–8 generations ago.     

Attack of the PCR clones: Rates of clonality have little effect on RAD‐seq genotype calls

Interpretation of high‐throughput sequence data requires an understanding of how decisions made during bioinformatic data processing can influence results. One source of bias that is often cited is PCR clones (or PCR duplicates). PCR clones are common in restriction site‐associated sequencing (RAD‐seq) data sets, which are increasingly being used for molecular ecology. To determine the influence PCR clones and the bioinformatic handling of clones have on genotyping, we evaluate four RAD‐seq data sets. Data sets were compared before and after clones were removed to estimate the number of clones present in RAD‐seq data, quantify how often the presence of clones in a data set causes genotype calls to change compared to when clones were removed, investigate the mechanisms that lead to genotype call changes and test whether clones bias heterozygosity estimates. Our RAD‐seq data sets contained 30%–60% PCR clones, but 95% of RAD‐tags had five or fewer clones. Relatively few genotypes changed once clones were removed (5%–10%), and the vast majority of these changes (98%) were associated with genotypes switching from a called to no‐call state or vice versa. PCR clones had a larger influence on genotype calls in individuals with low read depth but appeared to influence genotype calls at all loci similarly. Removal of PCR clones reduced the number of called genotypes by 2% but had almost no influence on estimates of heterozygosity. As such, while steps should be taken to limit PCR clones during library preparation, PCR clones are likely not a substantial source of bias for most RAD‐seq studies.     

Inferring recent migration rates from individual genotypes

We present a novel and straightforward method for estimating recent migration rates between discrete populations using multilocus genotype data. The approach builds upon a two-step sampling design, where individual genotypes are sampled before and after dispersal. We develop a model that estimates all pairwise backwards migration rates ( m_ij , the probability that an individual sampled in population i is a migrant from population j ) between a set of populations. The method is validated with simulated data and compared with the methods of BayesAss and Structure. First, we use data for an island model and then we consider more realistic data simulations for a metapopulation of the greater white-toothed shrew ( Crocidura russula ). We show that the precision and bias of estimates primarily depend upon the proportion of individuals sampled in each population. Weak sampling designs may particularly affect the quality of the coverage provided by 95% highest posterior density intervals. We further show that it is relatively insensitive to the number of loci sampled and the overall strength of genetic structure. The method can easily be extended and makes fewer assumptions about the underlying demographic and genetic processes than currently available methods. It allows backwards migration rates to be estimated across a wide range of realistic conditions.     

Accounting for genotype uncertainty in the estimation of allele frequencies in autopolyploids

Despite the increasing opportunity to collect large‐scale data sets for population genomic analyses, the use of high‐throughput sequencing to study populations of polyploids has seen little application. This is due in large part to problems associated with determining allele copy number in the genotypes of polyploid individuals (allelic dosage uncertainty–ADU), which complicates the calculation of important quantities such as allele frequencies. Here, we describe a statistical model to estimate biallelic SNP frequencies in a population of autopolyploids using high‐throughput sequencing data in the form of read counts. We bridge the gap from data collection (using restriction enzyme based techniques [e.g. GBS, RADseq]) to allele frequency estimation in a unified inferential framework using a hierarchical Bayesian model to sum over genotype uncertainty. Simulated data sets were generated under various conditions for tetraploid, hexaploid and octoploid populations to evaluate the model's performance and to help guide the collection of empirical data. We also provide an implementation of our model in the R package polyfreqs and demonstrate its use with two example analyses that investigate (i) levels of expected and observed heterozygosity and (ii) model adequacy. Our simulations show that the number of individuals sampled from a population has a greater impact on estimation error than sequencing coverage. The example analyses also show that our model and software can be used to make inferences beyond the estimation of allele frequencies for autopolyploids by providing assessments of model adequacy and estimates of heterozygosity.     

Joint Estimation of Contamination,Error and Demography for Nuclear DNA from Ancient Humans

When sequencing an ancient DNA sample from a hominin fossil, DNA from present-day humans involved in excavation and extraction will be sequenced along with the endogenous material. This type of contamination is problematic for downstream analyses as it will introduce a bias towards the population of the contaminating individual(s). Quantifying the extent of contamination is a crucial step as it allows researchers to account for possible biases that may arise in downstream genetic analyses. Here, we present an MCMC algorithm to co-estimate the contamination rate, sequencing error rate and demographic parameters—including drift times and admixture rates—for an ancient nuclear genome obtained from human remains, when the putative contaminating DNA comes from present-day humans. We assume we have a large panel representing the putative contaminant population (e.g. European, East Asian or African). The method is implemented in a C++ program called ‘Demographic Inference with Contamination and Error’ (DICE). We applied it to simulations and genome data from ancient Neanderthals and modern humans. With reasonable levels of genome sequence coverage (>3X), we find we can recover accurate estimates of all these parameters, even when the contamination rate is as high as 50%.     

Unbiased Functional Clustering of Gene Variants with a Phenotypic-Linkage Network

Groupwise functional analysis of gene variants is becoming standard in next-generation sequencing studies. As the function of many genes is unknown and their classification to pathways is scant, functional associations between genes are often inferred from large-scale omics data. Such data types—including protein–protein interactions and gene co-expression networks—are used to examine the interrelations of the implicated genes. Statistical significance is assessed by comparing the interconnectedness of the mutated genes with that of random gene sets. However, interconnectedness can be affected by confounding bias, potentially resulting in false positive findings. We show that genes implicated through de novo sequence variants are biased in their coding-sequence length and longer genes tend to cluster together, which leads to exaggerated p-values in functional studies; we present here an integrative method that addresses these bias. To discern molecular pathways relevant to complex disease, we have inferred functional associations between human genes from diverse data types and assessed them with a novel phenotype-based method. Examining the functional association between de novo gene variants, we control for the heretofore unexplored confounding bias in coding-sequence length. We test different data types and networks and find that the disease-associated genes cluster more significantly in an integrated phenotypic-linkage network than in other gene networks. We present a tool of superior power to identify functional associations among genes mutated in the same disease even after accounting for significant sequencing study bias and demonstrate the suitability of this method to functionally cluster variant genes underlying polygenic disorders.     

Assembly-free quantification of vagrant DNA inserts

Inserts of DNA from extranuclear sources, such as organelles and microbes, are common in eukaryote nuclear genomes. However, sequence similarity between the nuclear and extranuclear DNA, and a history of multiple insertions, make the assembly of these regions challenging. Consequently, the number, sequence and location of these vagrant DNAs cannot be reliably inferred from the genome assemblies of most organisms. We introduce two statistical methods to estimate the abundance of nuclear inserts even in the absence of a nuclear genome assembly. The first (intercept method) only requires low-coverage (<1×) sequencing data, as commonly generated for population studies of organellar and ribosomal DNAs. The second method additionally requires that a subset of the individuals carry extranuclear DNA with diverged genotypes. We validated our intercept method using simulations and by re-estimating the frequency of human NUMTs (nuclear mitochondrial inserts). We then applied it to the grasshopper Podisma pedestris, exceptional for both its large genome size and reports of numerous NUMT inserts, estimating that NUMTs make up 0.056% of the nuclear genome, equivalent to >500 times the mitochondrial genome size. We also re-analysed a museomics data set of the parrot Psephotellus varius, obtaining an estimate of only 0.0043%, in line with reports from other species of bird. Our study demonstrates the utility of low-coverage high-throughput sequencing data for the quantification of nuclear vagrant DNAs. Beyond quantifying organellar inserts, these methods could also be used on endosymbiont-derived sequences. We provide an R implementation of our methods called “vagrantDNA” and code to simulate test data sets.     

Bias and Sensitivity Analysis When Estimating Treatment Effects from the Cox Model with Omitted Covariates

Summary

Omission of relevant covariates can lead to bias when estimating treatment or exposure effects from survival data in both randomized controlled trials and observational studies. This paper presents a general approach to assessing bias when covariates are omitted from the Cox model. The proposed method is applicable to both randomized and non‐randomized studies. We distinguish between the effects of three possible sources of bias: omission of a balanced covariate, data censoring and unmeasured confounding. Asymptotic formulae for determining the bias are derived from the large sample properties of the maximum likelihood estimator. A simulation study is used to demonstrate the validity of the bias formulae and to characterize the influence of the different sources of bias. It is shown that the bias converges to fixed limits as the effect of the omitted covariate increases, irrespective of the degree of confounding. The bias formulae are used as the basis for developing a new method of sensitivity analysis to assess the impact of omitted covariates on estimates of treatment or exposure effects. In simulation studies, the proposed method gave unbiased treatment estimates and confidence intervals with good coverage when the true sensitivity parameters were known. We describe application of the method to a randomized controlled trial and a non‐randomized study.     

Long insert whole genome sequencing for copy number variant and translocation detection

As next-generation sequencing continues to have an expanding presence in the clinic, the identification of the most cost-effective and robust strategy for identifying copy number changes and translocations in tumor genomes is needed. We hypothesized that performing shallow whole genome sequencing (WGS) of 900–1000-bp inserts (long insert WGS, LI-WGS) improves our ability to detect these events, compared with shallow WGS of 300–400-bp inserts. A priori analyses show that LI-WGS requires less sequencing compared with short insert WGS to achieve a target physical coverage, and that LI-WGS requires less sequence coverage to detect a heterozygous event with a power of 0.99. We thus developed an LI-WGS library preparation protocol based off of Illumina’s WGS library preparation protocol and illustrate the feasibility of performing LI-WGS. We additionally applied LI-WGS to three separate tumor/normal DNA pairs collected from patients diagnosed with different cancers to demonstrate our application of LI-WGS on actual patient samples for identification of somatic copy number alterations and translocations. With the evolution of sequencing technologies and bioinformatics analyses, we show that modifications to current approaches may improve our ability to interrogate cancer genomes.     

Gap statistics for whole genome shotgun DNA sequencing projects

MOTIVATION: Investigators utilize gap estimates for DNA sequencing projects. Standard theories assume sequences are independently and identically distributed, leading to appreciable under-prediction of gaps. RESULTS: Using a statistical scaling factor and data from 20 representative whole genome shotgun projects, we construct regression equations that relate coverage to a normalized gap measure. Prokaryotic genomes do not correlate to sequence coverage, while eukaryotes show strong correlation if the chaff is ignored. Gaps decrease at an exponential rate of only about one-third of that predicted via theory alone. Case studies suggest that departure from theory can largely be attributed to assembly difficulties for repeat-rich genomes, but bias and coverage anomalies are also important when repeats are sparse. Such factors cannot be readily characterized a priori, suggesting upper limits on the accuracy of gap prediction. We also find that diminishing coverage probability discussed in other studies is a theoretical artifact that does not arise for the typical project.