90 research outputs found
A second-level diagonal preconditionerfor single-step SNPBLUP
No full textBackgroundThe preconditioned conjugate gradient (PCG) method is an iterative solver of linear equations systems commonly used in animal breeding. However, the PCG method has been shown to encounter convergence issues when applied to single-step single nucleotide polymorphism BLUP (ssSNPBLUP) models. Recently, we proposed a deflated PCG (DPCG) method for solving ssSNPBLUP efficiently. The DPCG method introduces a second-level preconditioner that annihilates the effect of the largest unfavourable eigenvalues of the ssSNPBLUP preconditioned coefficient matrix on the convergence of the iterative solver. While it solves the convergence issues of ssSNPBLUP, the DPCG method requires substantial additional computations, in comparison to the PCG method. Accordingly, the aim of this study was to develop a second-level preconditioner that decreases the largest eigenvalues of the ssSNPBLUP preconditioned coefficient matrix at a lower cost than the DPCG method, in addition to comparing its performance to the (D)PCG methods applied to two different ssSNPBLUP models.ResultsBased on the properties of the ssSNPBLUP preconditioned coefficient matrix, we proposed a second-level diagonal preconditioner that decreases the largest eigenvalues of the ssSNPBLUP preconditioned coefficient matrix under some conditions. This proposed second-level preconditioner is easy to implement in current software and does not result in additional computing costs as it can be combined with the commonly used (block-)diagonal preconditioner. Tested on two different datasets and with two different ssSNPBLUP models, the second-level diagonal preconditioner led to a decrease of the largest eigenvalues and the condition number of the preconditioned coefficient matrices. It resulted in an improvement of the convergence pattern of the iterative solver. For the largest dataset, the convergence of the PCG method with the proposed second-level diagonal preconditioner was slower than the DPCG method, but it performed better than the DPCG method in terms of total computing time.ConclusionsThe proposed second-level diagonal preconditioner can improve the convergence of the (D)PCG methods applied to two ssSNPBLUP models. Based on our results, the PCG method combined with the proposed second-level diagonal preconditioner seems to be more efficient than the DPCG method in solving ssSNPBLUP. However, the optimal combination of ssSNPBLUP and solver will most likely be situation-dependent.greenNumerical Analysi
Deflated preconditioned conjugate gradient method for solving single-step BLUP models efficiently
No full textBackground: The single-step single nucleotide polymorphism best linear unbiased prediction (ssSNPBLUP) method, such as single-step genomic BLUP (ssGBLUP), simultaneously analyses phenotypic, pedigree, and genomic information of genotyped and non-genotyped animals. In contrast to ssGBLUP, SNP effects are fitted explicitly as random effects in the ssSNPBLUP model. Similarly, principal components associated with the genomic information can be fitted explicitly as random effects in a single-step principal component BLUP (ssPCBLUP) model to remove noise in genomic information. Single-step genomic BLUP is solved efficiently by using the preconditioned conjugate gradient (PCG) method. Unfortunately, convergence issues have been reported when solving ssSNPBLUP by using PCG. Poor convergence may be linked with poor spectral condition numbers of the preconditioned coefficient matrices of ssSNPBLUP. These condition numbers, and thus convergence, could be improved through the deflated PCG (DPCG) method, which is a two-level PCG method for ill-conditioned linear systems. Therefore, the first aim of this study was to compare the properties of the preconditioned coefficient matrices of ssGBLUP and ssSNPBLUP, and to document convergence patterns that are obtained with the PCG method. The second aim was to implement and test the efficiency of a DPCG method for solving ssSNPBLUP and ssPCBLUP. Results: For two dairy cattle datasets, the smallest eigenvalues obtained for ssSNPBLUP (ssPCBLUP) and ssGBLUP, both solved with the PCG method, were similar. However, the largest eigenvalues obtained for ssSNPBLUP and ssPCBLUP were larger than those for ssGBLUP, which resulted in larger condition numbers and in slow convergence for both systems solved by the PCG method. Different implementations of the DPCG method led to smaller condition numbers, and faster convergence for ssSNPBLUP and for ssPCBLUP, by deflating the largest unfavourable eigenvalues. Conclusions: Poor convergence of ssSNPBLUP and ssPCBLUP when solved by the PCG method are related to larger eigenvalues and larger condition numbers in comparison to ssGBLUP. These convergence issues were solved with a DPCG method that annihilates the effect of the largest unfavourable eigenvalues of the preconditioned coefficient matrix of ssSNPBLUP and of ssPCBLUP on the convergence of the PCG method. It resulted in a convergence pattern, at least, similar to that of ssGBLUP.</p
Genomic prediction using individual-level data and summary statistics from multiple populations
No full textThis study presents a method for genomic prediction that uses individual-level data and summary statistics from multiple populations. Genome-wide markers are nowadays widely used to predict complex traits, and genomic prediction using multi-population data are an appealing approach to achieve higher prediction accuracies. However, sharing of individual-level data across populations is not always possible. We present a method that enables integration of summary statistics from separate analyses with the available individual-level data. The data can either consist of individuals with single or multiple (weighted) phenotype records per individual. We developed a method based on a hypothetical joint analysis model and absorption of population-specific information. We show that population-specific information is fully captured by estimated allele substitution effects and the accuracy of those estimates, i.e., the summary statistics. The method gives identical result as the joint analysis of all individual-level data when complete summary statistics are available. We provide a series of easy-to-use approximations that can be used when complete summary statistics are not available or impractical to share. Simulations show that approximations enable integration of different sources of information across a wide range of settings, yielding accurate predictions. The method can be readily extended to multiple-traits. In summary, the developed method enables integration of genome-wide data in the individual-level or summary statistics from multiple populations to obtain more accurate estimates of allele substitution effects and genomic predictions.</p
Genomic prediction using individual-level data and summary statistics from multiple populations
No full textABSTRACTThis study presents a method for genomic prediction that uses individual-level data and summary statistics from multiple populations. Genome-wide markers are nowadays widely used to predict complex traits, and genomic prediction using multi-population data is an appealing approach to achieve higher prediction accuracies. However, sharing of individual-level data across populations is not always possible. We present a method that enables integration of summary statistics from separate analyses with the available individual-level data. The data can either consist of individuals with single or multiple (weighted) phenotype records per individual. We developed a method based on a hypothetical joint analysis model and absorption of population specific information. We show that population specific information is fully captured by estimated allele substitution effects and the accuracy of those estimates, i.e. the summary statistics. The method gives identical result as the joint analysis of all individual-level data when complete summary statistics are available. We provide a series of easy-to-use approximations that can be used when complete summary statistics are not available or impractical to share. Simulations show that approximations enables integration of different sources of information across a wide range of settings yielding accurate predictions. The method can be readily extended to multiple-traits. In summary, the developed method enables integration of genome-wide data in the individual-level or summary statistics form from multiple populations to obtain more accurate estimates of allele substitution effects and genomic predictions.</jats:p
Technical note : Genetic groups in single-step single nucleotide polymorphism best linear unbiased predictor
No full textGenetic groups, also called unknown or phantom parents groups, are often used in dairy cattle genetic evaluations to account for selection that cannot be accounted for by known genetic relationships. With the advent of genomic evaluations, the theory of genetic groups was extended to the so-called single-step genomic BLUP (ssGBLUP). In short, genetic groups can be fitted in ssGBLUP through regression effects, or by including them in the pedigree and computing the adequate combined pedigree and genomic relationship matrix. In this study, we applied the so-called Quaas and Pollak transformation to a system of equations for single-step SNP BLUP (ssSNPBLUP), such that genetic groups can thereafter be included in the pedigree. The example in this study showed that including the genetic groups in the pedigree for ssSNPBLUP allowed reduced memory burden and computational costs in comparison to genetic groups fitted as covariates
Genetic diversity in the barn. Updates in livestock genetic diversity conservation and its potential use for wildlife conservation
No full textInternational audienc
SNPrune: an efficient algorithm to prune large SNP array and sequence datasets based on high linkage disequilibrium
No full textBackground: High levels of pairwise linkage disequilibrium (LD) in single nucleotide polymorphism (SNP) array or whole-genome sequence data may affect both performance and efficiency of genomic prediction models. Thus, this warrants pruning of genotyping data for high LD. We developed an algorithm, named SNPrune, which enables the rapid detection of any pair of SNPs in complete or high LD throughout the genome. Methods: LD, measured as the squared correlation between phased alleles (r 2), can only reach a value of 1 when both loci have the same count of the minor allele. Sorting loci based on the minor allele count, followed by comparison of their alleles, enables rapid detection of loci in complete LD. Detection of loci in high LD can be optimized by computing the range of the minor allele count at another locus for each possible value of the minor allele count that can yield LD values higher than a predefined threshold. This efficiently reduces the number of pairs of loci for which LD needs to be computed, instead of considering all pairwise combinations of loci. The implemented algorithm SNPrune considered bi-allelic loci either using phased alleles or allele counts as input. SNPrune was validated against PLINK on two datasets, using an r 2 threshold of 0.99. The first dataset contained 52k SNP genotypes on 3534 pigs and the second dataset contained simulated whole-genome sequence data with 10.8 million SNPs and 2500 animals. Results: SNPrune removed a similar number of SNPs as PLINK from the pig data but SNPrune was almost 12 times faster than PLINK. From the simulated sequence data with 10.8 million SNPs, SNPrune removed 6.4 and 1.4 million SNPs due to complete and high LD. Results were very similar regardless of whether phased alleles or allele counts were used. Using allele counts and multi-threading with 10 threads, SNPrune completed the analysis in 21 min. Using a sliding window of up to 500,000 SNPs, PLINK removed ~ 43,000 less SNPs (0.6%) in the sequence data and SNPrune was 24 to 170 times faster, using one or ten threads, respectively. Conclusions: The SNPrune algorithm developed here is able to remove SNPs in high LD throughout the genome very efficiently in large datasets.</p
Factors affecting accuracy of estimated effective number of chromosome segments for numerically small breeds
No full textFor numerically small breeds, obtaining a sufficiently large breed-specific reference population for genomic prediction is challenging or simply not possible, but may be overcome by adding individuals from another breed. To prioritize among available breeds, the effective number of chromosome segments (Me) can be used as an indicator of relatedness between individuals from different breeds. The Me is also an important parameter in determining the accuracy of genomic prediction. The Me can be estimated both within a population and between two populations or breeds, as the reciprocal of the variance of genomic relationships. However, the threshold for number of individuals needed to accurately estimate within or between populations Me is currently unknown. It is also unknown if a discrepancy in number of genotyped individuals in two breeds affects the estimates of Me between populations. In this study, we conducted a simulation that mimics current domestic cattle populations in order to investigate how estimated Me is affected by number of genotyped individuals, single-nucleotide polymorphism (SNP) density and pedigree availability. Our results show that a small sample of 10 genotyped individuals may result in substantial over or underestimation of Me. While estimates of within population Me were hardly affected by SNP density, between population Me values were highly dependent on the number of available SNPs, with higher SNP densities being able to detect more independent chromosome segments. When subtracting pedigree from genomic relationships before computing Me, estimates of within population Me were three to four times higher than estimates with genotypes only; however, between Me estimates remained the same. For accurate estimation of within and between population Me, at least 50 individuals should be genotyped per population. Estimates of within Me were highly affected by whether pedigree was used or not. For within Me, even the smallest SNP density (~11k) resulted in accurate representation of family relationships in the population; however, for between Me, many more markers are needed to capture all independent segments
Convergence behavior of single-step GBLUP and SNPBLUP for different termination criteria
No full textBackgroundThe preconditioned conjugate gradient (PCG) method is the current method of choice for iterative solving of genetic evaluations. The relative difference between two successive iterates and the relative residual of the system of equations are usually chosen as a termination criterion for the PCG method in animal breeding. However, our initial analyses showed that these two commonly used termination criteria may report that a PCG method applied to a single-step single nucleotide polymorphism best linear unbiased prediction (ssSNPBLUP) is not converged yet, whereas the solutions are accurate enough for practical use. Therefore, the aim of this study was to propose two termination criteria that have been (partly) developed in other fields, but are new in animal breeding, and to compare their behavior to that of the two termination criteria widely used in animal breeding for the PCG method applied to ssSNPBLUP. The convergence patterns of ssSNPBLUP were also compared to the convergence patterns of single-step genomic BLUP (ssGBLUP).ResultsBuilding upon previous work, we propose two termination criteria that take the properties of the system of equations into account. These two termination criteria are directly related to the relative error of the iterates with respect to the true solutions. Based on pig and dairy cattle datasets, we show that the preconditioned coefficient matrices of ssSNPBLUP and ssGBLUP have similar properties when using a second-level preconditioner for ssSNPBLUP. Therefore, the PCG method applied to ssSNPBLUP and ssGBLUP converged similarly based on the relative error of the iterates with respect to the true solutions. This similar convergence behavior between ssSNPBLUP and ssGBLUP was observed for both proposed termination criteria. This was, however, not the case for the termination criterion defined as the relative residual when applied to the dairy cattle evaluations.ConclusionOur results showed that the PCG method can converge similarly when applied to ssSNPBLUP and to ssGBLUP. The two proposed termination criteria always depicted these similar convergence behaviors, and we recommend them for comparing convergence properties of different models and for routine evaluations.Numerical Analysi
Effects of data structure on the estimation of covariance functions to describe genotype by envrironment interactions in a reaction norm model
No full textCovariance functions have been proposed to predict breeding values and genetic (co)variances as a function of phenotypic within herd-year averages (environmental parameters) to include genotype by environment interaction. The objective of this paper was to investigate the influence of definition of environmental parameters and non-random use of sires on expected breeding values and estimated genetic variances across environments. Breeding values were simulated as a linear function of simulated herd effects. The definition of environmental parameters hardly influenced the results. In situations with random use of sires, estimated genetic correlations between the trait expressed in different environments were 0.93, 0.93 and 0.97 while simulated at 0.89 and estimated genetic variances deviated up to 30% from the simulated values. Non random use of sires, poor genetic connectedness and small herd size had a large impact on the estimated covariance functions, expected breeding values and calculated environmental parameters. Estimated genetic correlations between a trait expressed in different environments were biased upwards and breeding values were more biased when genetic connectedness became poorer and herd composition more diverse. The best possible solution at this stage is to use environmental parameters combining large numbers of animals per herd, while losing some information on genotype by environment interaction in the dat
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