Quantifying Population Genetic Differentiation from Next-Generation Sequencing Data

Over the past few years, new high-throughput DNA sequencing technologies have dramatically increased speed and reduced sequencing costs. However, the use of these sequencing technologies is often challenged by errors and biases associated with the bioinformatical methods used for analyzing the data. In particular, the use of naïve methods to identify polymorphic sites and infer genotypes can inflate downstream analyses. Recently, explicit modeling of genotype probability distributions has been proposed as a method for taking genotype call uncertainty into account. Based on this idea, we propose a novel method for quantifying population genetic differentiation from next-generation sequencing data. In addition, we present a strategy for investigating population structure via principal components analysis. Through extensive simulations, we compare the new method herein proposed to approaches based on genotype calling and demonstrate a marked improvement in estimation accuracy for a wide range of conditions. We apply the method to a large-scale genomic data set of domesticated and wild silkworms sequenced at low coverage. We find that we can infer the fine-scale genetic structure of the sampled individuals, suggesting that employing this new method is useful for investigating the genetic relationships of populations sampled at low coverage.     

Pollen flow in the wildservice tree, Sorbus torminalis (L.) Crantz. I. Evaluating the paternity analysis procedure in continuous populations

The joint development of polymorphic molecular markers and paternity analysis methods provides new approaches to investigate ongoing patterns of pollen flow in natural plant populations. However, paternity studies are hindered by false paternity assignment and the nondetection of true fathers. To gauge the risk of these two types of errors, we performed a simulation study to investigate the impact on paternity analysis of: (i) the assumed values for the size of the breeding male population (NBMP), and (ii) the rate of scoring error in genotype assessment. Our simulations were based on microsatellite data obtained from a natural population of the entomophilous wild service tree, Sorbus torminalis (L.) Crantz. We show that an accurate estimate of NBMP is required to minimize both types of errors, and we assess the reliability of a technique used to estimate NBMP based on parent-offspring genetic data. We then show that scoring errors in genotype assessment only slightly affect the assessment of paternity relationships, and conclude that it is generally better to neglect the scoring error rate in paternity analyses within a nonisolated population.     

Maximum-likelihood estimation of allelic dropout and false allele error rates from microsatellite genotypes in the absence of reference data

The importance of quantifying and accounting for stochastic genotyping errors when analyzing microsatellite data is increasingly being recognized. This awareness is motivating the development of data analysis methods that not only take errors into consideration but also recognize the difference between two distinct classes of error, allelic dropout and false alleles. Currently methods to estimate rates of allelic dropout and false alleles depend upon the availability of error-free reference genotypes or reliable pedigree data, which are often not available. We have developed a maximum-likelihood-based method for estimating these error rates from a single replication of a sample of genotypes. Simulations show it to be both accurate and robust to modest violations of its underlying assumptions. We have applied the method to estimating error rates in two microsatellite data sets. It is implemented in a computer program, Pedant, which estimates allelic dropout and false allele error rates with 95% confidence regions from microsatellite genotype data and performs power analysis. Pedant is freely available at http://www.stats.gla.ac.uk/ approximately paulj/pedant.html.     

Evaluating pedigree data. II. Identifying the cause of error in families with inconsistencies

Pedigree data can be evaluated, and subsequently corrected, by analysis of the distribution of genetic markers, taking account of the possibility of mistyping . Using a model of pedigree error developed previously, we obtained the maximum likelihood estimates of error parameters in pedigree data from Tokelau. Posterior probabilities for the possible true relationships in each family are conditional on the putative relationships and the marker data are calculated using the parameter estimates. These probabilities are used as a basis for discriminating between pedigree error and genetic marker errors in families where inconsistencies have been observed. When applied to the Tokelau data and compared with the results of retyping inconsistent families, these statistical procedures are able to discriminate between pedigree and marker error, with approximately 90% accuracy, for families with two or more offspring. The large proportion of inconsistencies inferred to be due to marker error (61%) indicates the importance of discriminating between error sources when judging the reliability of putative relationship data. Application of our model of pedigree error has proved to be an efficient way of determining and subsequently correcting sources of error in extensive pedigree data collected in large surveys.     

Identifying marker typing incompatibilities in linkage analysis.

A common problem encountered in linkage analyses is that execution of the computer program is halted because of genotypes in the data that are inconsistent with Mendelian inheritance. Such inconsistencies may arise because of pedigree errors or errors in typing. In some cases, the source of the inconsistencies is easily identified by examining the pedigree. In others, the error is not obvious, and substantial time and effort are required to identify the responsible genotypes. We have developed two methods for automatically identifying those individuals whose genotypes are most likely the cause of the inconsistencies. First, we calculate the posterior probability of genotyping error for each member of the pedigree, given the marker data on all pedigree members and allowing anyone in the pedigree to have an error. Second, we identify those individuals whose genotypes could be solely responsible for the inconsistency in the pedigree. We illustrate these methods with two examples: one a pedigree error, the second a genotyping error. These methods have been implemented as a module of the pedigree analysis program package MENDEL.     

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.     

Likelihood-based genetic mark-recapture estimates when genotype samples are incomplete and contain typing errors

Genotypes produced from samples collected non-invasively in harsh field conditions often lack the full complement of data from the selected microsatellite loci. The application to genetic mark-recapture methodology in wildlife species can therefore be prone to misidentifications leading to both ‘true non-recaptures’ being falsely accepted as recaptures (Type I errors) and ‘true recaptures’ being undetected (Type II errors). Here we present a new likelihood method that allows every pairwise genotype comparison to be evaluated independently. We apply this method to determine the total number of recaptures by estimating and optimising the balance between Type I errors and Type II errors. We show through simulation that the standard error of recapture estimates can be minimised through our algorithms. Interestingly, the precision of our recapture estimates actually improved when we included individuals with missing genotypes, as this increased the number of pairwise comparisons potentially uncovering more recaptures. Simulations suggest that the method is tolerant to per locus error rates of up to 5% per locus and can theoretically work in datasets with as little as 60% of loci genotyped. Our methods can be implemented in datasets where standard mismatch analyses fail to distinguish recaptures. Finally, we show that by assigning a low Type I error rate to our matching algorithms we can generate a dataset of individuals of known capture histories that is suitable for the downstream analysis with traditional mark-recapture methods.     

Estimating genotyping error rates from Mendelian errors in SNP array genotypes and their impact on inference

A simple method of inferring the genotyping error rate of SNP arrays and similar high-throughput genotyping methods from Mendelian errors is described. Application to genotypes from small families using the Affymetrix GeneChip Human Mapping 50 k Array indicates an error rate of about 0.1%, and this rate can be reduced by increasing the quality criterion for calls, though at the cost of a reduced genotype call rate, which limits the benefit available. Simulated data are used to show that the number of SNPs on this array is sufficient for such a low error rate to have little impact on identical by descent-based inference for disease linkage in sib-pair studies.     

Susceptibility of biallelic haplotype and genotype frequencies to genotyping error

With the availability of fast genotyping methods and genomic databases, the search for statistical association of single nucleotide polymorphisms with a complex trait has become an important methodology in medical genetics. However, even fairly rare errors occurring during the genotyping process can lead to spurious association results and decrease in statistical power. We develop a systematic approach to study how genotyping errors change the genotype distribution in a sample. The general M-marker case is reduced to that of a single-marker locus by recognizing the underlying tensor-product structure of the error matrix. Both method and general conclusions apply to the general error model; we give detailed results for allele-based errors of size depending both on the marker locus and the allele present. Multiple errors are treated in terms of the associated diffusion process on the space of genotype distributions. We find that certain genotype and haplotype distributions remain unchanged under genotyping errors, and that genotyping errors generally render the distribution more similar to the stable one. In case-control association studies, this will lead to loss of statistical power for nondifferential genotyping errors and increase in type I error for differential genotyping errors. Moreover, we show that allele-based genotyping errors do not disturb Hardy-Weinberg equilibrium in the genotype distribution. In this setting we also identify maximally affected distributions. As they correspond to situations with rare alleles and marker loci in high linkage disequilibrium, careful checking for genotyping errors is advisable when significant association based on such alleles/haplotypes is observed in association studies.     

Modeling population genetic data in autotetraploid species

Allozyme and PCR-based molecular markers have been widely used to investigate genetic diversity and population genetic structure in autotetraploid species. However, an empirical but inaccurate approach was often used to infer marker genotype from the pattern and intensity of gel bands. Obviously, this introduces serious errors in prediction of the marker genotypes and severely biases the data analysis. This article developed a theoretical model to characterize genetic segregation of alleles at genetic marker loci in autotetraploid populations and a novel likelihood-based method to estimate the model parameters. The model properly accounts for segregation complexities due to multiple alleles and double reduction at autotetrasomic loci in natural populations, and the method takes appropriate account of incomplete marker phenotype information with respect to genotype due to multiple-dosage allele segregation at marker loci in tetraploids. The theoretical analyses were validated by making use of a computer simulation study and their utility is demonstrated by analyzing microsatellite marker data collected from two populations of sycamore maple (Acer pseudoplatanus L.), an economically important autotetraploid tree species. Numerical analyses based on simulation data indicate that the model parameters can be adequately estimated and double reduction is detected with good power using reasonable sample size.     

Incorporating genotyping uncertainty in haplotype inference for single-nucleotide polymorphisms

The accuracy of the vast amount of genotypic information generated by high-throughput genotyping technologies is crucial in haplotype analyses and linkage-disequilibrium mapping for complex diseases. To date, most automated programs lack quality measures for the allele calls; therefore, human interventions, which are both labor intensive and error prone, have to be performed. Here, we propose a novel genotype clustering algorithm, GeneScore, based on a bivariate t-mixture model, which assigns a set of probabilities for each data point belonging to the candidate genotype clusters. Furthermore, we describe an expectation-maximization (EM) algorithm for haplotype phasing, GenoSpectrum (GS)-EM, which can use probabilistic multilocus genotype matrices (called "GenoSpectrum") as inputs. Combining these two model-based algorithms, we can perform haplotype inference directly on raw readouts from a genotyping machine, such as the TaqMan assay. By using both simulated and real data sets, we demonstrate the advantages of our probabilistic approach over the current genotype scoring methods, in terms of both the accuracy of haplotype inference and the statistical power of haplotype-based association analyses.     

Bayesian haplotype inference via the Dirichlet process.

The problem of inferring haplotypes from genotypes of single nucleotide polymorphisms (SNPs) is essential for the understanding of genetic variation within and among populations, with important applications to the genetic analysis of disease propensities and other complex traits. The problem can be formulated as a mixture model, where the mixture components correspond to the pool of haplotypes in the population. The size of this pool is unknown; indeed, knowing the size of the pool would correspond to knowing something significant about the genome and its history. Thus methods for fitting the genotype mixture must crucially address the problem of estimating a mixture with an unknown number of mixture components. In this paper we present a Bayesian approach to this problem based on a nonparametric prior known as the Dirichlet process. The model also incorporates a likelihood that captures statistical errors in the haplotype/genotype relationship trading off these errors against the size of the pool of haplotypes. We describe an algorithm based on Markov chain Monte Carlo for posterior inference in our model. The overall result is a flexible Bayesian method, referred to as DP-Haplotyper, that is reminiscent of parsimony methods in its preference for small haplotype pools. We further generalize the model to treat pedigree relationships (e.g., trios) between the population's genotypes. We apply DP-Haplotyper to the analysis of both simulated and real genotype data, and compare to extant methods.     

Molecular and statistical approaches to the detection and correction of errors in genotype databases.

Errors in genotyping data have been shown to have a significant effect on the estimation of recombination fractions in high-resolution genetic maps. Previous estimates of errors in existing databases have been limited to the analysis of relatively few markers and have suggested rates in the range 0.5%-1.5%. The present study capitalizes on the fact that within the Centre d'Etude du Polymorphisme Humain (CEPH) collection of reference families, 21 individuals are members of more than one family, with separate DNA samples provided by CEPH for each appearance of these individuals. By comparing the genotypes of these individuals in each of the families in which they occur, an estimated error rate of 1.4% was calculated for all loci in the version 4.0 CEPH database. Removing those individuals who were clearly identified by CEPH as appearing in more than one family resulted in a 3.0% error rate for the remaining samples, suggesting that some error checking of the identified repeated individuals may occur prior to data submission. An error rate of 3.0% for version 4.0 data was also obtained for four chromosome 5 markers that were retyped through the entire CEPH collection. The effects of these errors on a multipoint map were significant, with a total sex-averaged length of 36.09 cM with the errors, and 19.47 cM with the errors corrected. Several statistical approaches to detect and allow for errors during linkage analysis are presented. One method, which identified families containing possible errors on the basis of the impact on the maximum lod score, showed particular promise, especially when combined with the limited retyping of the identified families. The impact of the demonstrated error rate in an established genotype database on high-resolution mapping is significant, raising the question of the overall value of incorporating such existing data into new genetic maps.     

The origin and diversification of eukaryotes: problems with molecular phylogenetics and molecular clock estimation

Determining the relationships among and divergence times for the major eukaryotic lineages remains one of the most important and controversial outstanding problems in evolutionary biology. The sequencing and phylogenetic analyses of ribosomal RNA (rRNA) genes led to the first nearly comprehensive phylogenies of eukaryotes in the late 1980s, and supported a view where cellular complexity was acquired during the divergence of extant unicellular eukaryote lineages. More recently, however, refinements in analytical methods coupled with the availability of many additional genes for phylogenetic analysis showed that much of the deep structure of early rRNA trees was artefactual. Recent phylogenetic analyses of a multiple genes and the discovery of important molecular and ultrastructural phylogenetic characters have resolved eukaryotic diversity into six major hypothetical groups. Yet relationships among these groups remain poorly understood because of saturation of sequence changes on the billion-year time-scale, possible rapid radiations of major lineages, phylogenetic artefacts and endosymbiotic or lateral gene transfer among eukaryotes. Estimating the divergence dates between the major eukaryote lineages using molecular analyses is even more difficult than phylogenetic estimation. Error in such analyses comes from a myriad of sources including: (i) calibration fossil dates, (ii) the assumed phylogenetic tree, (iii) the nucleotide or amino acid substitution model, (iv) substitution number (branch length) estimates, (v) the model of how rates of evolution change over the tree, (vi) error inherent in the time estimates for a given model and (vii) how multiple gene data are treated. By reanalysing datasets from recently published molecular clock studies, we show that when errors from these various sources are properly accounted for, the confidence intervals on inferred dates can be very large. Furthermore, estimated dates of divergence vary hugely depending on the methods used and their assumptions. Accurate dating of divergence times among the major eukaryote lineages will require a robust tree of eukaryotes, a much richer Proterozoic fossil record of microbial eukaryotes assignable to extant groups for calibration, more sophisticated relaxed molecular clock methods and many more genes sampled from the full diversity of microbial eukaryotes.     

GIbPSs: a toolkit for fast and accurate analyses of genotyping‐by‐sequencing data without a reference genome

Genotyping‐by‐sequencing (GBS) and related methods are increasingly used for studies of non‐model organisms from population genetic to phylogenetic scales. We present GIbPSs, a new genotyping toolkit for the analysis of data from various protocols such as RAD, double‐digest RAD, GBS, and two‐enzyme GBS without a reference genome. GIbPSs can handle paired‐end GBS data and is able to assign reads from both strands of a restriction fragment to the same locus. GIbPSs is most suitable for population genetic and phylogeographic analyses. It avoids genotyping errors due to indel variation by identifying and discarding affected loci. GIbPSs creates a genotype database that offers rich functionality for data filtering and export in numerous formats. We performed comparative analyses of simulated and real GBS data with GIbPSs and another program, pyRAD. This program accounts for indel variation by aligning homologous sequences. GIbPSs performed better than pyRAD in several aspects. It required much less computation time and displayed higher genotyping accuracy. GIbPSs retained smaller numbers of loci overall in analyses of real GBS data. It nevertheless delivered more complete genotype matrices with greater locus overlap between individuals and greater numbers of loci sampled in all individuals.     

Are Guinea Pigs Rodents? The Importance of Adequate Models in Molecular Phylogenetics

The monophyly of Rodentia has repeatedly been challenged based on several studies of molecular sequence data. Most recently, D'Erchia et al. (1996) analyzed complete mtDNA sequences of 16 mammals and concluded that rodents are not monophyletic. We have reanalyzed these data using maximum-likelihood methods. We use two methods to test for significance of differences among alternative topologies and show that (1) models that incorporate variation in evolutionary rates across sites fit the data dramatically better than models used in the original analyses, (2) the mtDNA data fail to refute rodent monophyly, and (3) the original interpretation of strong support for nonmonophyly results from systematic error associated with an oversimplified model of sequence evolution. These analyses illustrate the importance of incorporating recent theoretical advances into molecular phylogenetic analyses, especially when results of these analyses conflict with classical hypotheses of relationships.     

Analyses and comparison of accuracy of different genotype imputation methods

The power of genetic association analyses is often compromised by missing genotypic data which contributes to lack of significant findings, e.g., in in silico replication studies. One solution is to impute untyped SNPs from typed flanking markers, based on known linkage disequilibrium (LD) relationships. Several imputation methods are available and their usefulness in association studies has been demonstrated, but factors affecting their relative performance in accuracy have not been systematically investigated. Therefore, we investigated and compared the performance of five popular genotype imputation methods, MACH, IMPUTE, fastPHASE, PLINK and Beagle, to assess and compare the effects of factors that affect imputation accuracy rates (ARs). Our results showed that a stronger LD and a lower MAF for an untyped marker produced better ARs for all the five methods. We also observed that a greater number of haplotypes in the reference sample resulted in higher ARs for MACH, IMPUTE, PLINK and Beagle, but had little influence on the ARs for fastPHASE. In general, MACH and IMPUTE produced similar results and these two methods consistently outperformed fastPHASE, PLINK and Beagle. Our study is helpful in guiding application of imputation methods in association analyses when genotype data are missing.     

Allele frequency‐free inference of close familial relationships from genotypes or low‐depth sequencing data

Knowledge of how individuals are related is important in many areas of research, and numerous methods for inferring pairwise relatedness from genetic data have been developed. However, the majority of these methods were not developed for situations where data are limited. Specifically, most methods rely on the availability of population allele frequencies, the relative genomic position of variants and accurate genotype data. But in studies of non‐model organisms or ancient samples, such data are not always available. Motivated by this, we present a new method for pairwise relatedness inference, which requires neither allele frequency information nor information on genomic position. Furthermore, it can be applied not only to accurate genotype data but also to low‐depth sequencing data from which genotypes cannot be accurately called. We evaluate it using data from a range of human populations and show that it can be used to infer close familial relationships with a similar accuracy as a widely used method that relies on population allele frequencies. Additionally, we show that our method is robust to SNP ascertainment and applicable to low‐depth sequencing data generated using different strategies, including resequencing and RADseq, which is important for application to a diverse range of populations and species.     

The spleen colony technique. I. Correction for the overlap effect and sources of error in CFU-s determination

A linear model for the errors of the 'spleen colony' assay for haemopoietic stem cells has been derived. The components emerging from the model are interpreted and practical recommendations given for interpreting measurements made with this assay. The model permits correction for the effect of overlapping colonies and gives average errors for single measurements of the number of CFU-s. More reliable and more precise information can be obtained using this model. The spleen colony technique detects a population of immature precursor cells designated as CFU-s (Till & McCulloch, 1961). The relative error of measurement is often large when compared with the changes in the phenomena studied. Consequently a better knowledge of the errors of this technique is highly desirable. This paper should be regarded as an extension of the previous analysis of Till (1972). The theory for the errors of the spleen colony technique was applied to 905 determinations of the CFU-s numbers performed on random-bred mice. Data from random-bred mice rather than those from inbred mice have been used because the error components can be expected to be larger and, consequently, more easily detectable. The model of errors has also been validated using data published by Till (1972) and has subsequently been applied to data from several inbred mice strains (Znojil & Necas, 1988).     

Allowing for random errors in radiation dose estimates for the atomic bomb survivor data

The presence of random errors in the individual radiation dose estimates for the A-bomb survivors causes underestimation of radiation effects in dose-response analyses, and also distorts the shape of dose-response curves. Statistical methods are presented which will adjust for these biases, provided that a valid statistical model for the dose estimation errors is used. Emphasis is on clarifying some rather subtle statistical issues. For most of this development the distinction between radiation dose and exposure is not critical. The proposed methods involve downward adjustment of dose estimates, but this does not imply that the dosimetry system is faulty. Rather, this is a part of the dose-response analysis required to remove biases in the risk estimates. The primary focus of this report is on linear dose-response models, but methods for linear-quadratic models are also considered briefly. Some plausible models for the dose estimation errors are considered, which have typical errors in a range of 30-40% of the true values, and sensitivity analysis of the resulting bias corrections is provided. It is found that for these error models the resulting estimates of excess cancer risk based on linear models are about 6-17% greater than estimates that make no allowance for dose estimation errors. This increase in risk estimates is reduced to about 4-11% if, as has often been done recently, survivors with dose estimates above 4 Gy are eliminated from the analysis.