THE EFFECT OF DIFFERENT NUMERATOR RELATIONSHIP MATRICES ON BREEDING VALUES ESTIMATED FROM MULTIPLE TRAIT BLUP

1987 ◽  
Vol 67 (1) ◽  
pp. 201-204
Author(s):  
R. A. KEMP ◽  
J. W. WILTON
Keyword(s):  
Relationship Matrix ◽  
Genetic Progress ◽  
Multiple Trait ◽  
Breeding Values ◽  
Reduced Animal Model ◽  
Numerator Relationship Matrix ◽  
Best Linear Unbiased ◽  
The Mean ◽  
Estimated Breeding Values ◽  
Accuracy Of Prediction

A numerator relationship matrix (Ac) due to sires and dams was compared with a numerator relationship matrix (Ai) due to sires and maternal grandsires in a multiple-trait-reduced animal model (MT-RAM). Best linear unbiased predictors of estimated breeding values (EBV) for 200-d weight (WW) and postweaning gain (PG) (gain from 200 to 365 d of age) were estimated from data simulating a beef cattle population. As expected, mean EBV and bias (EBV-BV) for both traits were not significantly affected by different relationship matrices. The mean variances of EBV with Ac were larger than those with Ai for both traits. The mean EBV variances were closer to mean BV variances with Ac compared to Ai, which is consistent with increased precision of EBV. Product-moment correlations of EBV and BV (accuracy of prediction) were not equal (P < 0.01) for Ac compared to Ai with WW or PG. The EBV using Ac were more accurate than EBV using Ai. The increased precision and accuracy of EBV from a MT-RAM with Ac would result in greater genetic progress in the population. Key words: Relationship matrices, estimated breeding values, MT-RAM

scholarly journals Reduced Animal Models Fitting Only Equations for Phenotyped Animals

2021 ◽  
Vol 12 ◽  
Author(s):  
Mohammad Ali Nilforooshan ◽  
Dorian Garrick
Keyword(s):  
Animal Model ◽  
Animal Models ◽  
Mixed Model ◽  
Reduced Model ◽  
Relationship Matrix ◽  
Full Model ◽  
Breeding Values ◽  
Reduced Animal Model ◽  
Numerator Relationship Matrix ◽  
Model Equations

Reduced models are equivalent models to the full model that enable reduction in the computational demand for solving the problem, here, mixed model equations for estimating breeding values of selection candidates. Since phenotyped animals provide data to the model, the aim of this study was to reduce animal models to those equations corresponding to phenotyped animals. Non-phenotyped ancestral animals have normally been included in analyses as they facilitate formation of the inverse numerator relationship matrix. However, a reduced model can exclude those animals and obtain identical solutions for the breeding values of the animals of interest. Solutions corresponding to non-phenotyped animals can be back-solved from the solutions of phenotyped animals and specific blocks of the inverted relationship matrix. This idea was extended to other forms of animal model and the results from each reduced model (and back-solving) were identical to the results from the corresponding full model. Previous studies have been mainly focused on reduced animal models that absorb equations corresponding to non-parents and solve equations only for parents of phenotyped animals. These two types of reduced animal model can be combined to formulate only equations corresponding to phenotyped parents of phenotyped progeny.

Mixed model procedures for the Australian beef industry. 1. Multiple-trait model for estimation of breeding values for 200-day and final weights of cattle

1985 ◽  
Vol 36 (3) ◽  
pp. 527 ◽  
Author(s):  
H-U Graser ◽  
K Hammond
Keyword(s):  
Maternal Effects ◽  
Fixed Effects ◽  
Mixed Model ◽  
Growth Traits ◽  
Breeding Value ◽  
Relationship Matrix ◽  
Beef Industry ◽  
Multiple Trait ◽  
Breeding Values ◽  
Numerator Relationship Matrix

A multiple-trait mixed model is defined for regular use in the Australian beef industry for the estimation of breeding values for continuous traits of sires used non-randomly across a number of herds and/or years. Maternal grandsires, the numerator relationship matrix, appropriate fixed effects, and the capacity to partition direct and maternal effects are incorporated in this parent model. The model was fitted to the National Beef Recording Scheme's data bank for three growth traits of the Australian Simental breed, viz 200-, 365- and 550-day weights. Estimates are obtained for the effects of sex, dam age, grade of dam, age of calf and breed of base dam. The range in estimated breeding value is reported for each trait, with 200-day weight being partitioned into 'calves' and 'daughters' calves', for the Simmental sires commonly used in Australia. Estimates of the fixed effects were large, and dam age, grade of dam and breed of base dam had an important influence on growth to 365 days of age. The faster growth of higher percentage Simmental calves to 200 days continued to 550 days. Estimates of genetic variance for the traits were lower than reported for overseas populations of Simmental cattle, and the genetic covariance between direct and maternal effects for 200-day weight was slightly positive.

scholarly journals 63 A comparison of clustering methods for cross-validation of genomic predictors when training on phenotypes or deregressed Estimated Breeding Values

2019 ◽  
Vol 97 (Supplement_2) ◽  
pp. 34-35
Author(s):  
Johnna Baller ◽  
Jeremy T Howard ◽  
Stephen Kachman ◽  
Matthew L Spangler
Keyword(s):  
Cross Validation ◽  
Relationship Matrix ◽  
Clustering Methods ◽  
Bivariate Model ◽  
Breeding Values ◽  
Numerator Relationship Matrix ◽  
Red Angus ◽  
Estimated Breeding Values ◽  
The Impact ◽  
Selection Of

Abstract The objective of the study was to evaluate the impact of clustering methods for cross-validation on the accuracy of prediction of molecular breeding values (MBV) in Red Angus cattle (n = 9,763) and in simulation. Individuals were clustered using seven methods [k-means, k-medoids, principal component analysis on the numerator relationship matrix (A) and identical-by-state genomic matrix (G) as data and covariance matrices, and random] and two response variables [deregressed Estimated Breeding Values (DEBV) and adjusted phenotypes]. Genotypes were imputed to a 50K reference panel. Using cross-validation and a Bayes C model, MBV were estimated for traits including birth weight (BWT), marbling (MARB), rib-eye area (REA), and yearling weight (YWT) for DEBV and BWT, YWT, and ultrasonically measured intramuscular fat percentage and rib eye area for adjusted phenotypes. A bivariate animal model was used to estimate prediction accuracies calculated using the genetic correlation between estimated MBV and the associated response variable. To quantify the difference between true and estimated accuracies, a simulation mimicking a cattle population was replicated five times. The same clustering methods were used as with the Red Angus data with the addition of forward validation and two genotyping methods (random selection and selection of the top 25% of animals). Predicted accuracies were estimated similarly and true accuracies were estimated using the residual correlation of a bivariate model using MBV and true breeding values (TBV). The Rand index was used to quantify the similarity between clustering methods, showing relationship-based clusters were clearly different from random clusters. In simulation, random genotyping led to higher estimated accuracies than selection of top individuals; however, estimated accuracies over predicted true accuracies with random genotyping but under predicted true accuracies with the selection of top individuals. When forward validation was evaluated within simulation, results suggested DEBV led to less biased estimates of MBV accuracy.

Practical aspects of a genetic evaluation system using parentage assigned from genetic markers

2005 ◽  
Vol 45 (8) ◽  
pp. 935 ◽  
Author(s):  
K. G. Dodds ◽  
J. A. Sise ◽  
M. L. Tate
Keyword(s):  
Genetic Markers ◽  
Evaluation System ◽  
Fixed Effects ◽  
Genetic Evaluation ◽  
Diagnostic Systems ◽  
Breeding Values ◽  
Mating Group ◽  
Animal Management ◽  
The Mean ◽  
Estimated Breeding Values

Animal breeding values can be calculated when genetic markers have been used to help determine the parentage of some of the animals, but their parentage has been incompletely determined. The pedigree sampling method is 1 computing strategy for calculating these breeding values. This paper describes and discusses methods for dealing with a number of practical issues that arise when implementing such a system for industry use. In particular, diagnostic systems for detecting inadequacies or possible errors in the genotyping systems and the recording of animal management are developed. Also, characteristics of the best assigned pedigrees are calculated according to mating group and used to check for sires missing from these groups. The correlation between breeding values estimated from a single sampled pedigree (using parentage probabilities) and those estimated as the mean from many sampled pedigrees gives a diagnostic to indicate which estimated breeding values are more influenced by uncertainties in relationships. For the analysis of survival traits, a method to enumerate and assign likely parentage to dead offspring which have not been DNA sampled and genotyped is described. When embryo transfer technology is used, the genetic dam needs to be included as a possible dam when considering parentage. If some fixed effects which depend on the parent are missing, these can be sampled similarly to parentage, and this may improve the evaluation if certain assumptions are met. A method to provide a likely list of parents, the ‘fitted pedigree’, which is based on the most likely parents, but modified to reduce the occurrence of unlikely family sets (e.g. very large litters) is also presented. The use of these methods will enhance the practical application of DNA parenting when used in conjunction with genetic evaluation.

scholarly journals Prevalence and breeding values of elbow dysplasia in the Estrela mountain dog

2013 ◽  
Vol 58 (No. 9) ◽  
pp. 484-490 ◽  
Author(s):  
S. Alves-Pimenta ◽  
B. Colaco ◽  
AM Silvestre ◽  
MM Ginja
Keyword(s):  
Hip Dysplasia ◽  
Mass Selection ◽  
Genetic Trend ◽  
Genetic Progress ◽  
Breeding Values ◽  
Elbow Dysplasia ◽  
Low Mass ◽  
The Mean ◽  
Dog Breed ◽  
Genetic Trends

The aims of this study were to determine the prevalence and heritability of elbow dysplasia in the Estrela mountain dog breed, to investigate genetic trends over the last 20 years (1990&ndash;2009) and to evaluate the association of individual records with breeding values. The elbows of 351 Estrela mountain dogs were examined using the flexed mediolateral radiographic view and evaluated using the International Elbow Working Group scoring system. Heritability and breeding values were estimated using a linear model. Elbow Dysplasia was found in 16.5% (59/351) of the dogs; males (27%, 34/127) were more affected than females (11%, 24/224) (P &lt; 0.05). The heritability was very low (0.065) and the genetic trend showed a slight positive slope with an improvement in 2004 and 2005. The mean breeding values in elbow dysplasia grades were different but the overlap among grades was very pronounced. The prevalence and heritability of elbow dysplasia in the breed are thus low. Mass selection using individual phenotypes may not be effective. Elbow dysplasia genetic trends are similar to trends for hip dysplasia and passive hip laxity, so the use of selection against hip dysplasia may also result in genetic progress for elbow dysplasia. &nbsp;

scholarly journals Level-biases in estimated breeding values due to the use of different SNP panels over time in ssGBLUP

2019 ◽  
Vol 51 (1) ◽  
Author(s):  
Øyvind Nordbø ◽  
Arne B. Gjuvsland ◽  
Leiv Sigbjørn Eikje ◽  
Theo Meuwissen
Keyword(s):  
Value Added ◽  
Single Step ◽  
Fine Tuning ◽  
Genomic Relationship Matrix ◽  
Relationship Matrix ◽  
Optimal Selection ◽  
Breeding Values ◽  
Estimated Breeding Values ◽  
Snp Panels ◽  
Genomic Predictions

Abstract Background The main aim of single-step genomic predictions was to facilitate optimal selection in populations consisting of both genotyped and non-genotyped individuals. However, in spite of intensive research, biases still occur, which make it difficult to perform optimal selection across groups of animals. The objective of this study was to investigate whether incomplete genotype datasets with errors could be a potential source of level-bias between genotyped and non-genotyped animals and between animals genotyped on different single nucleotide polymorphism (SNP) panels in single-step genomic predictions. Results Incomplete and erroneous genotypes of young animals caused biases in breeding values between groups of animals. Systematic noise or missing data for less than 1% of the SNPs in the genotype data had substantial effects on the differences in breeding values between genotyped and non-genotyped animals, and between animals genotyped on different chips. The breeding values of young genotyped individuals were biased upward, and the magnitude was up to 0.8 genetic standard deviations, compared with breeding values of non-genotyped individuals. Similarly, the magnitude of a small value added to the diagonal of the genomic relationship matrix affected the level of average breeding values between groups of genotyped and non-genotyped animals. Cross-validation accuracies and regression coefficients were not sensitive to these factors. Conclusions Because, historically, different SNP chips have been used for genotyping different parts of a population, fine-tuning of imputation within and across SNP chips and handling of missing genotypes are crucial for reducing bias. Although all the SNPs used for estimating breeding values are present on the chip used for genotyping young animals, incompleteness and some genotype errors might lead to level-biases in breeding values.

Genetic changes generated within the Katanning Merino Resource flocks

2006 ◽  
Vol 46 (7) ◽  
pp. 803 ◽  
Author(s):  
J. C. Greeff ◽  
G. Cox
Keyword(s):  
Body Weight ◽  
Phase 1 ◽  
Fibre Diameter ◽  
Linear Unbiased Prediction ◽  
Genetic Changes ◽  
Breeding Values ◽  
Best Linear Unbiased ◽  
Fleece Weight ◽  
Estimated Breeding Values ◽  
Genetic Trends

Genetic changes for clean fleece weight, fibre diameter and hogget body weight were determined in the Katanning Merino Resource flocks from 1982 to 2004. From 1982 to 1992 genetic trends are presented for individual studs that used mainly subjective classing selection methods (Phase 1) and the genetic trends from 1997 to 2004 demonstrate the genetic changes that can be achieved from using estimated breeding values calculated from best linear unbiased prediction (BLUP) mixed methodology (Phase 2). The results during the first phase show that very few genetic changes occurred in most studs, except for the 4 studs of the Performance Sheep Breeding strain which showed genetic increases in hogget body weight. The genetic trends show that some studs generated change towards their breeding objective, while others show no changes or changes in the opposite direction. In contrast, the use of BLUP estimated breeding values resulted in positive changes in clean fleece weight, fibre diameter and body weight in accordance with the defined breeding objectives.

scholarly journals Core-dependent changes in genomic predictions using the Algorithm for Proven and Young in single-step genomic best linear unbiased prediction

2020 ◽  
Vol 98 (12) ◽  
Author(s):  
Ignacy Misztal ◽  
Shogo Tsuruta ◽  
Ivan Pocrnic ◽  
Daniela Lourenco
Keyword(s):  
Prediction Accuracy ◽  
Best Linear Unbiased Prediction ◽  
Single Step ◽  
Relationship Matrix ◽  
Linear Unbiased Prediction ◽  
Breeding Values ◽  
Best Linear Unbiased ◽  
The Impact ◽  
Genomic Predictions ◽  
Unbiased Prediction

Abstract Single-step genomic best linear unbiased prediction with the Algorithm for Proven and Young (APY) is a popular method for large-scale genomic evaluations. With the APY algorithm, animals are designated as core or noncore, and the computing resources to create the inverse of the genomic relationship matrix (GRM) are reduced by inverting only a portion of that matrix for core animals. However, using different core sets of the same size causes fluctuations in genomic estimated breeding values (GEBVs) up to one additive standard deviation without affecting prediction accuracy. About 2% of the variation in the GRM is noise. In the recursion formula for APY, the error term modeling the noise is different for every set of core animals, creating changes in breeding values. While average changes are small, and correlations between breeding values estimated with different core animals are close to 1.0, based on the normal distribution theory, outliers can be several times bigger than the average. Tests included commercial datasets from beef and dairy cattle and from pigs. Beyond a certain number of core animals, the prediction accuracy did not improve, but fluctuations decreased with more animals. Fluctuations were much smaller than the possible changes based on prediction error variance. GEBVs change over time even for animals with no new data as genomic relationships ties all the genotyped animals, causing reranking of top animals. In contrast, changes in nongenomic models without new data are small. Also, GEBV can change due to details in the model, such as redefinition of contemporary groups or unknown parent groups. In particular, increasing the fraction of blending of the GRM with a pedigree relationship matrix from 5% to 20% caused changes in GEBV up to 0.45 SD, with a correlation of GEBV &gt; 0.99. Fluctuations in genomic predictions are part of genomic evaluation models and are also present without the APY algorithm when genomic evaluations are computed with updated data. The best approach to reduce the impact of fluctuations in genomic evaluations is to make selection decisions not on individual animals with limited individual accuracy but on groups of animals with high average accuracy.

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