128 research outputs found
Assessment of genomic selection for introgression of polledness into Holstein Friesian cattle by simulation
No full textNaturally hornless cattle are called polled. The possibility to introgress the allele responsible (P) for polledness in a cattle population that is more intensively selected for other traits is investigated in this paper. Gene introgression, generally carried out by several steps of backcrossing and selection, takes a long time and may lead to unacceptable genetic loss in other traits or inbreeding. The main objective of the current study was to evaluate the use of genomic selection to speed up the introgression of a target allele in a conventional dairy cattle breeding scheme with overlapping generations. A cattle population and a breeding program were simulated and run over a 12 year selection period. Assuming that the polled population was inferior for overall genetic merit , two selection strategies were evaluated: i) selection on conventional BLUP-EBV (CBLUP); ii) selection on genomic EBV (GEBV) obtained with the genomic relationship matrix used in BLUP (GBLUP). Both selection strategies were applied with (PSEL) and without (NOPSEL) selection for the single polled locus (P). The overall level of genetic merit, the P allele frequency and the inbreeding level (F) in the new born animals were monitored each year, as well as the average genetic gain per year of selection (¿G). The overall genetic level of new born animals was higher for GBLUP compared to CBLUP, with an average ¿G/year of 8.34% (GBLUP) against 7.49% (CBLUP). The PSEL scenario reduced genetic gain, but P allele frequency increased from 0.130 to 0.415 (CBLUP) and from 0.128 to 0.440 (GBLUP) for PSEL, after 12 years of selection. No substantial changes in allele frequency were recorded for NOPSEL scenarios, both for CBLUP and GBLUP breeding schemes. The overall inbreeding rates for GBLUP were 0.28%/y (NOPSEL) and 0.30%/y (PSEL) and for CBLUP 0.52%/y (NOPSEL) and 0.44%/y (PSEL). In conclusion, application of GS to gene introgression helped to speed up the process of introgression of a gene while simultaneously increasing the genetic gain and reducing the inbreeding rate
Accuracy of multi-trait genomic selection using different methods
No full textAbstract Background Genomic selection has become a very important tool in animal genetics and is rapidly emerging in plant genetics. It holds the promise to be particularly beneficial to select for traits that are difficult or expensive to measure, such as traits that are measured in one environment and selected for in another environment. The objective of this paper was to develop three models that would permit multi-trait genomic selection by combining scarcely recorded traits with genetically correlated indicator traits, and to compare their performance to single-trait models, using simulated datasets. Methods Three (SNP) Single Nucleotide Polymorphism based models were used. Model G and BCπ0 assumed that contributed (co)variances of all SNP are equal. Model BSSVS sampled SNP effects from a distribution with large (or small) effects to model SNP that are (or not) associated with a quantitative trait locus. For reasons of comparison, model A including pedigree but not SNP information was fitted as well. Results In terms of accuracies for animals without phenotypes, the models generally ranked as follows: BSSVS > BCπ0 > G > > A. Using multi-trait SNP-based models, the accuracy for juvenile animals without any phenotypes increased up to 0.10. For animals with phenotypes on an indicator trait only, accuracy increased up to 0.03 and 0.14, for genetic correlations with the evaluated trait of 0.25 and 0.75, respectively. Conclusions When the indicator trait had a genetic correlation lower than 0.5 with the trait of interest in our simulated data, the accuracy was higher if genotypes rather than phenotypes were obtained for the indicator trait. However, when genetic correlations were higher than 0.5, using an indicator trait led to higher accuracies for selection candidates. For different combinations of traits, the level of genetic correlation below which genotyping selection candidates is more effective than obtaining phenotypes for an indicator trait, needs to be derived considering at least the heritabilities and the numbers of animals recorded for the traits involved.</p
Partial least square regression applied to the QTLMAS 2010 dataset
No full textDetection of genomic regions affecting traits is a goal in many genetic studies. Studies applying distinct methods for detection of these regions, called quantitative trait loci (QTL), have been described, ranging from single marker regression [1] to methods that enable to fit several markers simultaneously [2,3]. Simultaneously fitting all markers leads to more accurate detection of QTL compared to independent fitting of single markers in a regression model when there is linkage disequilibrium (LD) between the genomic regions that affect the trait but comes at the cost of increased computational requirements [2]. Partial least square regression (PLSR) is one method for simultaneously fitting multiple markers and was applied by Bjornstad et al. for detection of QTL [3]. An interesting characteristic of PLSR its straightforward application of to simultaneous analysis of data of multiple traits [3]. The objectives of this study were to use PLSR to search for QTL and to estimate breeding values in the dataset of the QTLMAS 2010 worksho
Comparison of analyses of the QTLMAS XIII common dataset. II: QTL analysis
No full textBackground - Five participants of the QTL-MAS 2009 workshop applied QTL analyses to the workshop common data set which contained a time-related trait: cumulative yield. Underlying the trait were 18 QTLs for three parameters of a logistic growth curve that was used for simulating the trait. Methods - Different statistical models and methods were employed to detect QTLs and estimate position and effect sizes of QTLs. Here we compare the results with respect to the numbers of QTLs detected, estimated positions and percentage explained variance. Furthermore, limiting factors in the QTL detection are evaluated. Results - All QTLs for the asymptote and the scaling factor of the logistic curve were detected by at least one of the participants. Only one out of six of the QTLs for the inflection point was detected. None of the QTLs were detected by all participants. Dominant, epistatic and imprinted QTLs were reported while only additive QTLs were simulated. The power to map QTLs for the inflection point increased when more time points were added. Conclusions - For the detection of QTLs related to the asymptote and the scaling factor, there were no strong differences between the methods used here. Also, it did not matter much whether the time course data were analyzed per single time point or whether parameters of a growth curve were first estimated and then analyzed. In contrast, the power for detection of QTLs for the inflection point was very low and the frequency of time points appeared to be a limiting factor. This can be explained by a low accuracy in estimating the inflection point from a limited time range and a limited number of time points, and by the low correlation between the simulated values for this parameter and the phenotypic data available for the individual time point
Supplemental Material for Vandenplas, Calus, and Gorjanc, 2018
No full textSupplemental figures are available in File S1. A description of the simulated genotype and phenotype datasets for each scenario is provided in File S2. Simulated genotype and phenotype datasets for the 5 replicates of each scenario are provided in Files S3, S4, and S5
Prediction of haplotypes for ungenotyped animals and its effect on marker-assisted breeding value estimation
No full textBackground: In livestock populations, missing genotypes on a large proportion of animals are a major problem to implement the estimation of marker-assisted breeding values using haplotypes. The objective of this article is to develop a method to predict haplotypes of animals that are not genotyped using mixed model equations and to investigate the effect of using these predicted haplotypes on the accuracy of marker-assisted breeding value estimation. Methods: For genotyped animals, haplotypes were determined and for each animal the number of haplotype copies (nhc) was counted, i.e. 0, 1 or 2 copies. In a mixed model framework, nhc for each haplotype were predicted for ungenotyped animals as well as for genotyped animals using the additive genetic relationship matrix. The heritability of nhc was assumed to be 0.99, allowing for minor genotyping and haplotyping errors. The predicted nhc were subsequently used in marker-assisted breeding value estimation by applying random regression on these covariables. To evaluate the method, a population was simulated with one additive QTL and an additive polygenic genetic effect. The QTL was located in the middle of a haplotype based on SNP-markers. Results: The accuracy of predicted haplotype copies for ungenotyped animals ranged between 0.59 and 0.64 depending on haplotype length. Because powerful BLUP-software was used, the method was computationally very efficient. The accuracy of total EBV increased for genotyped animals when marker-assisted breeding value estimation was compared with conventional breeding value estimation, but for ungenotyped animals the increase was marginal unless the heritability was smaller than 0.1. Haplotypes based on four markers yielded the highest accuracies and when only the nearest left marker was used, it yielded the lowest accuracy. The accuracy increased with increasing marker density. Accuracy of the total EBV approached that of gene-assisted BLUP when 4-marker haplotypes were used with a distance of 0.1 cM between the markers. Conclusions: The proposed method is computationally very efficient and suitable for marker-assisted breeding value estimation in large livestock populations including effects of a number of known QTL. Marker-assisted breeding value estimation using predicted haplotypes increases accuracy especially for traits with low heritabilit
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
QTLMAS 2009: simulated dataset
No full textBackground - The simulation of the data for the QTLMAS 2009 Workshop is described. Objective was to simulate observations from a growth curve which was influenced by a number of QTL. Results - The data consisted of markers, phenotypes and pedigree. Genotypes of 453 markers, distributed over 5 chromosomes of 1 Morgan each, were simulated for 2,025 individuals. From those, 25 individuals were parents of the other 2,000 individuals. The 25 parents were genetically related. Phenotypes were simulated according to a logistic growth curve and were made available for 1,000 of the 2,000 offspring individuals. The logistic growth curve was specified by three parameters. Each parameter was influenced by six Quantitative Trait Loci (QTL), positioned at the five chromosomes. For each parameter, one QTL had a large effect and five QTL had small effects. Variance of large QTL was five times the variance of small QTL. Simulated data was made available at http://www.qtlmas2009.wur.nl/UK/Dataset
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
Estimating genetic diversity across the neutral genome with the use of dense marker maps
No full textAbstract Background With the advent of high throughput DNA typing, dense marker maps have become available to investigate genetic diversity on specific regions of the genome. The aim of this paper was to compare two marker based estimates of the genetic diversity in specific genomic regions lying in between markers: IBD-based genetic diversity and heterozygosity. Methods A computer simulated population was set up with individuals containing a single 1-Morgan chromosome and 1665 SNP markers and from this one, an additional population was produced with a lower marker density i.e. 166 SNP markers. For each marker interval based on adjacent markers, the genetic diversity was estimated either by IBD probabilities or heterozygosity. Estimates were compared to each other and to the true genetic diversity. The latter was calculated for a marker in the middle of each marker interval that was not used to estimate genetic diversity. Results The simulated population had an average minor allele frequency of 0.28 and an LD (r2) of 0.26, comparable to those of real livestock populations. Genetic diversities estimated by IBD probabilities and by heterozygosity were positively correlated, and correlations with the true genetic diversity were quite similar for the simulated population with a high marker density, both for specific regions (r = 0.19-0.20) and large regions (r = 0.61-0.64) over the genome. For the population with a lower marker density, the correlation with the true genetic diversity turned out to be higher for the IBD-based genetic diversity. Conclusions Genetic diversities of ungenotyped regions of the genome (i.e. between markers) estimated by IBD-based methods and heterozygosity give similar results for the simulated population with a high marker density. However, for a population with a lower marker density, the IBD-based method gives a better prediction, since variation and recombination between markers are missed with heterozygosity.</p
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