A new approach for efficient genotype imputation using information from relatives

Background

Genotype imputation can help reduce genotyping costs particularly for implementation of genomic selection. In applications entailing large populations, recovering the genotypes of untyped loci using information from reference individuals that were genotyped with a higher density panel is computationally challenging. Popular imputation methods are based upon the Hidden Markov model and have computational constraints due to an intensive sampling process. A fast, deterministic approach, which makes use of both family and population information, is presented here. All individuals are related and, therefore, share haplotypes which may differ in length and frequency based on their relationships. The method starts with family imputation if pedigree information is available, and then exploits close relationships by searching for long haplotype matches in the reference group using overlapping sliding windows. The search continues as the window size is shrunk in each chromosome sweep in order to capture more distant relationships.

Results

The proposed method gave higher or similar imputation accuracy than Beagle and Impute2 in cattle data sets when all available information was used. When close relatives of target individuals were present in the reference group, the method resulted in higher accuracy compared to the other two methods even when the pedigree was not used. Rare variants were also imputed with higher accuracy. Finally, computing requirements were considerably lower than those of Beagle and Impute2. The presented method took 28 minutes to impute from 6 k to 50 k genotypes for 2,000 individuals with a reference size of 64,429 individuals.

Conclusions

The proposed method efficiently makes use of information from close and distant relatives for accurate genotype imputation. In addition to its high imputation accuracy, the method is fast, owing to its deterministic nature and, therefore, it can easily be used in large data sets where the use of other methods is impractical.     

A coalescent model of recombination hotspots

Recent experimental findings suggest that the assumption of a homogeneous recombination rate along the human genome is too naive. These findings point to block-structured recombination rates; certain regions (called hotspots) are more prone than other regions to recombination. In this report a coalescent model incorporating hotspot or block-structured recombination is developed and investigated analytically as well as by simulation. Our main results can be summarized as follows: (1) The expected number of recombination events is much lower in a model with pure hotspot recombination than in a model with pure homogeneous recombination, (2) hotspots give rise to large variation in recombination rates along the genome as well as in the number of historical recombination events, and (3) the size of a (nonrecombining) block in the hotspot model is likely to be overestimated grossly when estimated from SNP data. The results are discussed with reference to the current debate about block-structured recombination and, in addition, the results are compared to genome-wide variation in recombination rates. A number of new analytical results about the model are derived.     

A coalescent model of ancestry for a rare allele

In disequilibrium mapping from data on a rare allele, interest may focus on the ancestry of a random sample of current descendants of a mutation. The mutation is assumed to have been introduced into the population as a single copy a known time ago and to have reached a given copy number within the population. Theory has been developed to describe the ancestral distribution under arbitrary patterns of population expansion. Further results permit convenient realization of the ancestry for a random sample of copies of a rare allele within populations of constant size or within populations growing or shrinking at constant exponential rate. In this article, we present an efficient approximate method for realizing coalescence times under more general patterns of population growth. We also apply diagnostics, checking the age of the mutation. In the course of the derivation, some additional insight is gained into the dynamics of the descendants of the mutation.     

Exact coalescent for the Wright-Fisher model

The Kingman coalescent, which has become the foundation for a wide range of theoretical as well as empirical studies, was derived as an approximation of the Wright-Fisher (WF) model. The approximation heavily relies on the assumption that population size is large and sample size is much smaller than the population size. Whether the sample size is too large compared to the population size is rarely questioned in practice when applying statistical methods based on the Kingman coalescent. Since WF model is the most widely used population genetics model for reproduction, it is desirable to develop a coalescent framework for the WF model, which can be used whenever there are concerns about the accuracy of the Kingman coalescent as an approximation. This paper described the exact coalescent theory for the WF model and develops a simulation algorithm, which is then used, together with an analytical approach, to study the properties of the exact coalescent as well as its differences to the Kingman coalescent. We show that the Kingman coalescent differs from the exact coalescent by: (1) shorter waiting time between successive coalescent events; (2) different probability of observing a topological relationship among sequences in a sample; and (3) slightly smaller tree length in the genealogy of a large sample. On the other hand, there is little difference in the age of the most recent common ancestor (MRCA) of the sample. The exact coalescent makes up the longer waiting time between successive coalescent events by having multiple coalescence at the same time. The most significant difference among various summary statistics of a coalescent examined is the sum of lengths of external branches, which can be more than 10% larger for exact coalescent than that for the Kingman coalescent. As a whole, the Kingman coalescent is a remarkably accurate approximation to the exact coalescent for sample and population sizes falling considerably outside the region that was originally anticipated.     

Accuracy of genotype imputation in sheep breeds

Although genomic selection offers the prospect of improving the rate of genetic gain in meat, wool and dairy sheep breeding programs, the key constraint is likely to be the cost of genotyping. Potentially, this constraint can be overcome by genotyping selection candidates for a low density (low cost) panel of SNPs with sparse genotype coverage, imputing a much higher density of SNP genotypes using a densely genotyped reference population. These imputed genotypes would then be used with a prediction equation to produce genomic estimated breeding values. In the future, it may also be desirable to impute very dense marker genotypes or even whole genome re‐sequence data from moderate density SNP panels. Such a strategy could lead to an accurate prediction of genomic estimated breeding values across breeds, for example. We used genotypes from 48 640 (50K) SNPs genotyped in four sheep breeds to investigate both the accuracy of imputation of the 50K SNPs from low density SNP panels, as well as prospects for imputing very dense or whole genome re‐sequence data from the 50K SNPs (by leaving out a small number of the 50K SNPs at random). Accuracy of imputation was low if the sparse panel had less than 5000 (5K) markers. Across breeds, it was clear that the accuracy of imputing from sparse marker panels to 50K was higher if the genetic diversity within a breed was lower, such that relationships among animals in that breed were higher. The accuracy of imputation from sparse genotypes to 50K genotypes was higher when the imputation was performed within breed rather than when pooling all the data, despite the fact that the pooled reference set was much larger. For Border Leicesters, Poll Dorsets and White Suffolks, 5K sparse genotypes were sufficient to impute 50K with 80% accuracy. For Merinos, the accuracy of imputing 50K from 5K was lower at 71%, despite a large number of animals with full genotypes (2215) being used as a reference. For all breeds, the relationship of individuals to the reference explained up to 64% of the variation in accuracy of imputation, demonstrating that accuracy of imputation can be increased if sires and other ancestors of the individuals to be imputed are included in the reference population. The accuracy of imputation could also be increased if pedigree information was available and was used in tracking inheritance of large chromosome segments within families. In our study, we only considered methods of imputation based on population‐wide linkage disequilibrium (largely because the pedigree for some of the populations was incomplete). Finally, in the scenarios designed to mimic imputation of high density or whole genome re‐sequence data from the 50K panel, the accuracy of imputation was much higher (86–96%). This is promising, suggesting that in silico genome re‐sequencing is possible in sheep if a suitable pool of key ancestors is sequenced for each breed.     

Accuracy of genotype imputation in Labrador Retrievers

The dog is a valuable model species for the genetic analysis of complex traits, and the use of genotype imputation in dogs will be an important tool for future studies. It is of particular interest to analyse the effect of factors like single nucleotide polymorphism (SNP) density of genotyping arrays and relatedness between dogs on imputation accuracy due to the acknowledged genetic and pedigree structure of dog breeds. In this study, we simulated different genotyping strategies based on data from 1179 Labrador Retriever dogs. The study involved 5826 SNPs on chromosome 1 representing the high density (HighD) array; the low‐density (LowD) array was simulated by masking different proportions of SNPs on the HighD array. The correlations between true and imputed genotypes for a realistic masking level of 87.5% ranged from 0.92 to 0.97, depending on the scenario used. A correlation of 0.92 was found for a likely scenario (10% of dogs genotyped using HighD, 87.5% of HighD SNPs masked in the LowD array), which indicates that genotype imputation in Labrador Retrievers can be a valuable tool to reduce experimental costs while increasing sample size. Furthermore, we show that genotype imputation can be performed successfully even without pedigree information and with low relatedness between dogs in the reference and validation sets. Based on these results, the impact of genotype imputation was evaluated in a genome‐wide association analysis and genomic prediction in Labrador Retrievers.     

Accuracy of genotype imputation in Nelore cattle

Background

Genotype imputation from low-density (LD) to high-density single nucleotide polymorphism (SNP) chips is an important step before applying genomic selection, since denser chips tend to provide more reliable genomic predictions. Imputation methods rely partially on linkage disequilibrium between markers to infer unobserved genotypes. Bos indicus cattle (e.g. Nelore breed) are characterized, in general, by lower levels of linkage disequilibrium between genetic markers at short distances, compared to taurine breeds. Thus, it is important to evaluate the accuracy of imputation to better define which imputation method and chip are most appropriate for genomic applications in indicine breeds.

Methods

Accuracy of genotype imputation in Nelore cattle was evaluated using different LD chips, imputation software and sets of animals. Twelve commercial and customized LD chips with densities ranging from 7 K to 75 K were tested. Customized LD chips were virtually designed taking into account minor allele frequency, linkage disequilibrium and distance between markers. Software programs FImpute and BEAGLE were applied to impute genotypes. From 995 bulls and 1247 cows that were genotyped with the Illumina® BovineHD chip (HD), 793 sires composed the reference set, and the remaining 202 younger sires and all the cows composed two separate validation sets for which genotypes were masked except for the SNPs of the LD chip that were to be tested.

Results

Imputation accuracy increased with the SNP density of the LD chip. However, the gain in accuracy with LD chips with more than 15 K SNPs was relatively small because accuracy was already high at this density. Commercial and customized LD chips with equivalent densities presented similar results. FImpute outperformed BEAGLE for all LD chips and validation sets. Regardless of the imputation software used, accuracy tended to increase as the relatedness between imputed and reference animals increased, especially for the 7 K chip.

Conclusions

If the Illumina® BovineHD is considered as the target chip for genomic applications in the Nelore breed, cost-effectiveness can be improved by genotyping part of the animals with a chip containing around 15 K useful SNPs and imputing their high-density missing genotypes with FImpute.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-014-0069-1) contains supplementary material, which is available to authorized users.     

Fast accurate missing SNP genotype local imputation

ABSTRACT: BACKGROUND: Single nucleotide polymorphism (SNP) genotyping assays normally give rise to certain percents of no-calls; the problem becomes severe when the target organisms, such as cattle, do not have a high resolution genomic sequence. Missing SNP genotypes, when related to target traits, would confound downstream data analyses such as genome-wide association studies (GWAS). Existing methods for recovering the missing values are successful to some extent --- either accurate but not fast enough or fast but not accurate enough. RESULTS: To a target missing genotype, we take only the SNP loci within a genetic distance vicinity and only the samples within a similarity vicinity into our local imputation process. For missing genotype imputation, the comparative performance evaluations through extensive simulation studies using real human and cattle genotype datasets demonstrated that our nearest neighbor based local imputation method was one of the most efficient methods, and outperformed existing methods except the time-consuming fastPHASE; for missing haplotype allele imputation, the comparative performance evaluations using real mouse haplotype datasets demonstrated that our method was not only one of the most efficient methods, but also one of the most accurate methods. CONCLUSIONS: Given that fastPHASE requires a long imputation time on medium to high density datasets, and that our nearest neighbor based local imputation method only performed slightly worse, yet better than all other methods, one might want to adopt our method as an alternative missing SNP genotype or missing haplotype allele imputation method.     

MagicalRsq: Machine-learning-based genotype imputation quality calibration

1. Download : Download high-res image (200KB)
2. Download : Download full-size image

     

A maximum pseudo-likelihood approach for estimating species trees under the coalescent model

Background  

Several phylogenetic approaches have been developed to estimate species trees from collections of gene trees. However, maximum likelihood approaches for estimating species trees under the coalescent model are limited. Although the likelihood of a species tree under the multispecies coalescent model has already been derived by Rannala and Yang, it can be shown that the maximum likelihood estimate (MLE) of the species tree (topology, branch lengths, and population sizes) from gene trees under this formula does not exist. In this paper, we develop a pseudo-likelihood function of the species tree to obtain maximum pseudo-likelihood estimates (MPE) of species trees, with branch lengths of the species tree in coalescent units.     

The ChinaMAP reference panel for the accurate genotype imputation in Chinese populations

Dear Editor, The genotype imputation is an efficient and pivotal approach to estimate the unobserved genotypes in the genomic data from the single nucleotide po...     

Design of low density SNP chips for genotype imputation in layer chicken

Background

The main goal of selection is to achieve genetic gain for a population by choosing the best breeders among a set of selection candidates. Since 2013, the use of a high density genotyping chip (600K Affymetrix® Axiom® HD genotyping array) for chicken has enabled the implementation of genomic selection in layer and broiler breeding, but the genotyping costs remain high for a routine use on a large number of selection candidates. It has thus been deemed interesting to develop a low density genotyping chip that would induce lower costs. In this perspective, various simulation studies have been conducted to find the best way to select a set of SNPs for low density genotyping of two laying hen lines.

Results

To design low density SNP chips, two methodologies, based on equidistance (EQ) or on linkage disequilibrium (LD) were compared. Imputation accuracy was assessed as the mean correlation between true and imputed genotypes. The results showed correlations more sensitive to false imputation of SNPs having low Minor Allele Frequency (MAF) when the EQ methodology was used. An increase in imputation accuracy was obtained when SNP density was increased, either through an increase in the number of selected windows on a chromosome or through the rise of the LD threshold. Moreover, the results varied depending on the type of chromosome (macro or micro-chromosome). The LD methodology enabled to optimize the number of SNPs, by reducing the SNP density on macro-chromosomes and by increasing it on micro-chromosomes. Imputation accuracy also increased when the size of the reference population was increased. Conversely, imputation accuracy decreased when the degree of kinship between reference and candidate populations was reduced. Finally, adding selection candidates’ dams in the reference population, in addition to their sire, enabled to get better imputation results.

Conclusions

Whichever the SNP chip, the methodology, and the scenario studied, highly accurate imputations were obtained, with mean correlations higher than 0.83. The key point to achieve good imputation results is to take into account chicken lines’ LD when designing a low density SNP chip, and to include the candidates’ direct parents in the reference population.

     

A coalescent dual process in a Moran model with genic selection, and the lambda coalescent limit

The genealogical structure of neutral populations in which reproductive success is highly-skewed has been the subject of many recent studies. Here we derive a coalescent dual process for a related class of continuous-time Moran models with viability selection. In these models, individuals can give birth to multiple offspring whose survival depends on both the parental genotype and the brood size. This extends the dual process construction for a multi-type Moran model with genic selection described in Etheridge and Griffiths (2009). We show that in the limit of infinite population size the non-neutral Moran models converge to a Markov jump process which we call the Λ-Fleming-Viot process with viability selection and we derive a coalescent dual for this process directly from the generator and as a limit from the Moran models. The dual is a branching-coalescing process similar to the Ancestral Selection Graph which follows the typed ancestry of genes backwards in time with real and virtual lineages. As an application, the transition functions of the non-neutral Moran and Λ-coalescent models are expressed as mixtures of the transition functions of the dual process.     

Comparison of genotype imputation strategies using a combined reference panel for chicken population

Using whole-genome sequence (WGS) data are supposed to be optimal for genome-wide association studies and genomic predictions. However, sequencing thousands of individuals of interest is expensive. Imputation from single nucleotide polymorphisms panels to WGS data is an attractive approach to obtain highly reliable WGS data at low cost. Here, we conducted a genotype imputation study with a combined reference panel in yellow-feather dwarf broiler population. The combined reference panel was assembled by sequencing 24 key individuals of a yellow-feather dwarf broiler population (internal reference panel) and WGS data from 311 chickens in public databases (external reference panel). Three scenarios were investigated to determine how different factors affect the accuracy of imputation from 600 K array data to WGS data, including: genotype imputation with internal, external and combined reference panels; the number of internal reference individuals in the combined reference panel; and different reference sizes and selection strategies of an external reference panel. Results showed that imputation accuracy from 600 K to WGS data were 0.834±0.012, 0.920±0.007 and 0.982±0.003 for the internal, external and combined reference panels, respectively. Increasing the reference size from 50 to 250 improved the accuracy of genotype imputation from 0.848 to 0.974 for the combined reference panel and from 0.647 to 0.917 for the external reference panel. The selection strategies for the external reference panel had no impact on the accuracy of imputation using the combined reference panel. However, if only an external reference panel with reference size >50 was used, the selection strategy of minimizing the average distance to the closest leaf had the greatest imputation accuracy compared with other methods. Generally, using a combined reference panel provided greater imputation accuracy, especially for low-frequency variants. In conclusion, the optimal imputation strategy with a combined reference panel should comprehensively consider genetic diversity of the study population, availability and properties of external reference panels, sequencing and computing costs, and frequency of imputed variants. This work sheds light on how to design and execute genotype imputation with a combined external reference panel in a livestock population.     

Exome sequence genotype imputation in globally diverse hexaploid wheat accessions

Key message

Imputing genotypes from the 90K SNP chip to exome sequence in wheat was moderately accurate. We investigated the factors that affect imputation and propose several strategies to improve accuracy.

Abstract

Imputing genetic marker genotypes from low to high density has been proposed as a cost-effective strategy to increase the power of downstream analyses (e.g. genome-wide association studies and genomic prediction) for a given budget. However, imputation is often imperfect and its accuracy depends on several factors. Here, we investigate the effects of reference population selection algorithms, marker density and imputation algorithms (Beagle4 and FImpute) on the accuracy of imputation from low SNP density (9K array) to the Infinium 90K single-nucleotide polymorphism (SNP) array for a collection of 837 hexaploid wheat Watkins landrace accessions. Based on these results, we then used the best performing reference selection and imputation algorithms to investigate imputation from 90K to exome sequence for a collection of 246 globally diverse wheat accessions. Accession-to-nearest-entry and genomic relationship-based methods were the best performing selection algorithms, and FImpute resulted in higher accuracy and was more efficient than Beagle4. The accuracy of imputing exome capture SNPs was comparable to imputing from 9 to 90K at approximately 0.71. This relatively low imputation accuracy is in part due to inconsistency between 90K and exome sequence formats. We also found the accuracy of imputation could be substantially improved to 0.82 when choosing an equivalent number of exome SNP, instead of 90K SNPs on the existing array, as the lower density set. We present a number of recommendations to increase the accuracy of exome imputation.

     

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.     

A sequential coalescent algorithm for chromosomal inversions

Chromosomal inversions are common in natural populations and are believed to be involved in many important evolutionary phenomena, including speciation, the evolution of sex chromosomes and local adaptation. While recent advances in sequencing and genotyping methods are leading to rapidly increasing amounts of genome-wide sequence data that reveal interesting patterns of genetic variation within inverted regions, efficient simulation methods to study these patterns are largely missing. In this work, we extend the sequential Markovian coalescent, an approximation to the coalescent with recombination, to include the effects of polymorphic inversions on patterns of recombination. Results show that our algorithm is fast, memory-efficient and accurate, making it feasible to simulate large inversions in large populations for the first time. The SMC algorithm enables studies of patterns of genetic variation (for example, linkage disequilibria) and tests of hypotheses (using simulation-based approaches) that were previously intractable.     

A coalescent dual process in a Moran model with genic selection

A coalescent dual process for a multi-type Moran model with genic selection is derived using a generator approach. This leads to an expansion of the transition functions in the Moran model and the Wright–Fisher diffusion process limit in terms of the transition functions for the coalescent dual. A graphical representation of the Moran model (in the spirit of Harris) identifies the dual as a strong dual process following typed lines backwards in time. An application is made to the harmonic measure problem of finding the joint probability distribution of the time to the first loss of an allele from the population and the distribution of the surviving alleles at the time of loss. Our dual process mirrors the Ancestral Selection Graph of [Krone, S. M., Neuhauser, C., 1997. Ancestral processes with selection. Theoret. Popul. Biol. 51, 210–237; Neuhauser, C., Krone, S. M., 1997. The genealogy of samples in models with selection. Genetics 145, 519–534], which allows one to reconstruct the genealogy of a random sample from a population subject to genic selection. In our setting, we follow [Stephens, M., Donnelly, P., 2002. Ancestral inference in population genetics models with selection. Aust. N. Z. J. Stat. 45, 395–430] in assuming that the types of individuals in the sample are known. There are also close links to [Fearnhead, P., 2002. The common ancestor at a nonneutral locus. J. Appl. Probab. 39, 38–54]. However, our methods and applications are quite different. This work can also be thought of as extending a dual process construction in a Wright–Fisher diffusion in [Barbour, A.D., Ethier, S.N., Griffiths, R.C., 2000. A transition function expansion for a diffusion model with selection. Ann. Appl. Probab. 10, 123–162]. The application to the harmonic measure problem extends a construction provided in the setting of a neutral diffusion process model in [Ethier, S.N., Griffiths, R.C., 1991. Harmonic measure for random genetic drift. In: Pinsky, M.A. (Ed.), Diffusion Processes and Related Problems in Analysis, vol. 1. In: Progress in Probability Series, vol. 22, Birkhäuser, Boston, pp. 73–81].