mbend: an R package for bending non-positive-definite symmetric matrices to positive-definite

Nilforooshan, Mohammad Ali

doi:10.1186/s12863-020-00881-z

Cited by 12 publications

(8 citation statements)

References 17 publications

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“…The across-country matrix was constructed by combining the genetic correlations between countries previously estimated by Interbeef using a series of bi-variate analyses. The resulting combined across-country matrix was not positive definite and a bending procedure was applied using the R package “mbend” [ 40 ] (method “hj” [ 41 ], unweighted, with a threshold value of 10 –4 ). The final across-country genetic correlation matrix and co-variance matrix are reported in Additional file 1 : Table S3.…”

Section: Methodsmentioning

confidence: 99%

International single-step SNPBLUP beef cattle evaluations for Limousin weaning weight

et al. 2022

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Background Compared to national evaluations, international collaboration projects further improve accuracies of estimated breeding values (EBV) by building larger reference populations or performing a joint evaluation using data (or proxy of them) from different countries. Genomic selection is increasingly adopted in beef cattle, but, to date, the benefits of including genomic information in international evaluations have not been explored. Our objective was to develop an international beef cattle single-step genomic evaluation and investigate its impact on the accuracy and bias of genomic evaluations compared to current pedigree-based evaluations. Methods Weaning weight records were available for 331,593 animals from seven European countries. The pedigree included 519,740 animals. After imputation and quality control, 17,607 genotypes at a density of 57,899 single nucleotide polymorphisms (SNPs) from four countries were available. We implemented two international scenarios where countries were modelled as different correlated traits: an international genomic single-step SNP best linear unbiased prediction (SNPBLUP) evaluation (ssSNPBLUPINT) and an international pedigree-based BLUP evaluation (PBLUPINT). Two national scenarios were implemented for pedigree and genomic evaluations using only nationally submitted phenotypes and genotypes. Accuracies, level and dispersion bias of EBV of animals born from 2014 onwards, and increases in population accuracies were estimated using the linear regression method. Results On average across countries, 39 and 17% of sires and maternal-grand-sires with recorded (grand-)offspring across two countries were genotyped. ssSNPBLUPINT showed the highest accuracies of EBV and, compared to PBLUPINT, led to increases in population accuracy of 13.7% for direct EBV, and 25.8% for maternal EBV, on average across countries. Increases in population accuracies when moving from national scenarios to ssSNPBLUPINT were observed for all countries. Overall, ssSNPBLUPINT level and dispersion bias remained similar or slightly reduced compared to PBLUPINT and national scenarios. Conclusions International single-step SNPBLUP evaluations are feasible and lead to higher population accuracies for both large and small countries compared to current international pedigree-based evaluations and national evaluations. These results are likely related to the larger multi-country reference population and the inclusion of phenotypes from relatives recorded in other countries via single-step international evaluations. The proposed international single-step approach can be applied to other traits and breeds.

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Section: Methodsmentioning

confidence: 99%

International single-step SNPBLUP beef cattle evaluations for Limousin weaning weight

et al. 2022

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“…It should be noted that the resulting genetic correlation matrix in scenario CUR was non-positive definite, and therefore, it was bended using the unweighted bending approach of Jorjani et al (2003) (using the R package “mbend” [ Nilforooshan, 2020 ] with a threshold of 10 −3 ). Initial analyses showed that the effects of bending on all the estimated r g were minimal with an unweighted bending approach and allowed to keep the r dm_BC close to 0.…”

Section: Methodsmentioning

confidence: 99%

The impact of direct-maternal genetic correlations on international beef cattle evaluations for Limousin weaning weight

Bonifazi

Vandenplas

Napel

et al. 2021

Journal of Animal Science

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In beef cattle maternally influenced traits, estimates of direct-maternal genetic correlations (rdm) are usually reported to be negative. In international evaluations, rdm can differ both within countries (rdm_WC) and between countries (rdm_BC). The rdm_BC are difficult to estimate and are assumed to be zero in the current model for international beef cattle evaluations (Interbeef). Our objective was to investigate re-ranking of international EBV (IEBV) in international beef cattle evaluations between models that either used estimated values for rdm or assumed them to be 0. Age-adjusted weaning weights and pedigree data were available for Limousin beef cattle from ten European countries. International EBV were obtained using a multi-trait animal model with countries modelled as different traits. We compared IEBV from a model that uses estimated rdm_BC (ranging between -0.14 and +0.14) and rdm_WC (between -0.33 and +0.40) with IEBV obtained either from the current model that assumes rdm_BC to be 0, or from an alternative model that assumes both rdm_BC and rdm_WC to be 0. Direct and maternal IEBV were compared across those three scenarios for different groups of animals. The ratio of population accuracies from the Linear Regression method was used to further investigate the impact of rdm on international evaluations, for both the whole set of animals in the evaluation and the domestic ones. Ignoring rdm_BC, i.e. replacing estimated values with 0, resulted in no (rank correlations > 0.99) or limited (between 0.98 and 0.99) re-ranking for direct and maternal IEBV, respectively. Both rdm_BC and rdm_WC had less impact on direct IEBV than on maternal IEBV. Re-ranking of maternal IEBV decreased with increasing reliability. Ignoring rdm_BC resulted in no re-ranking for sires with IEBV that might be exchanged across countries, and limited re-ranking for the top 100 sires. Using estimated rdm_BC values instead of considering them to be to 0, resulted in null to limited increases in population accuracy. Ignoring both rdm_BC and rdm_WC resulted in considerable re-ranking of animals’ IEBV in all groups of animals evaluated. This study showed the limited impact of the current practice of ignoring rdm_BC in international evaluations for Limousin weaning weight, most likely because the estimated rdm_BC were close to 0. We expect that these conclusions can be extended to other traits that have reported rdm values in the range of rdm_WC values for weaning weight in Limousin.

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“…When estimated r g are set to arbitrary values or when a series of r g estimated using multi-trait models are combined together, bending may be required to ensure that the final r g matrix across all countries is positive definite (Hill and Thompson 1978). In this thesis, I always used unweighted bending, but weighted bending can also be used (Jorjani et al 2003;Nilforooshan 2020). Weighted bending uses the measure of uncertainty of an estimated r g , such as the associated standard errors, as weights during the bending process: parameters with low weights change less at each bending iteration compared to those with high weights.…”

Section: A General Procedures To Estimate Across-country Rg In Interbeefmentioning

confidence: 99%

International genetic and genomic evaluations of beef cattle

Bonifazi¹

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. International genetic and genomic evaluations of beef cattle.PhD thesis, Wageningen University, the Netherlands.In cattle, advancements in reproductive technologies such as artificial insemination allowed breeders to access the genetic material of superior bulls from foreign countries. However, animals' estimated breeding values (EBV) computed from different national evaluations are not directly comparable across countries due to differences in scales and genetic bases, trait and model definitions, and the possible presence of genotype-by-environment interactions. International evaluations account for such differences by jointly analysing all national data and modelling the same trait recorded in different countries as different correlated traits. The resulting international EBV (EBV INT ) facilitate the comparison of domestic and foreign sires and worldwide trading of their genetic material. This thesis aimed to improve and further develop methodologies for international beef cattle evaluations (Interbeef) by addressing various challenges, mainly related to: i) the estimation of across-country genetic correlations (r g ) and their impact on the EBV INT ; ii) the inclusion of national genomic information; and iii) the development of an official procedure for participating countries to integrate the distributed EBV INT back into their national evaluations. First, I showed that both large and small participating countries benefit from current Interbeef pedigree-based evaluations. Second, I showed the feasibility of estimating across-country r g using a multi-trait approach that simultaneously fits data from all countries and proposed data sub-setting strategies to improve computational time. Third, I showed that the current practice of assuming across-country direct-maternal r g to be 0 has limited impact on the EBV INT of animals of interest such as publishable sires, i.e., sires that meet Interbeef publications rules. On the other hand, assuming zero within-country direct-maternal r g impacts the EBV INT of such animals. Fourth, I developed international genomic evaluations for beef cattle using a single-step SNPBLUP approach (ssSNPBLUP). International ssSNPBLUP evaluations lead to higher accuracies compared to both current international pedigree evaluations and either national pedigree or genomic evaluations, while keeping similar or slightly reduced level and dispersion bias. Finally, I developed a generalized procedure to integrate pedigree-based or singlestep EBV INT of publishable sires into national evaluations. The procedure can be easily implemented with current software. Compared to national evaluations without integration, the integration reduces level bias, gives similar dispersion, and increases accuracies of publishable sires' EBV INT . Overall, this thesis contributes to the development of international evaluations of beef cattle.

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mbend: an R package for bending non-positive-definite symmetric matrices to positive-definite

Cited by 12 publications

References 17 publications

International single-step SNPBLUP beef cattle evaluations for Limousin weaning weight

International single-step SNPBLUP beef cattle evaluations for Limousin weaning weight

The impact of direct-maternal genetic correlations on international beef cattle evaluations for Limousin weaning weight

International genetic and genomic evaluations of beef cattle

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