Predicting breeding values using an implicit representation of the mixed model equations for a multiple trait animal model

1991 ◽  
Vol 108 (1-6) ◽  
pp. 81-88 ◽  
Author(s):  
B. Tier ◽  
H.-U. Graser
Keyword(s):  
Animal Model ◽  
Mixed Model ◽  
Multiple Trait ◽  
Implicit Representation ◽  
Breeding Values ◽  
Model Equations

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 Genetic parameter of birth and weaning weights for Friesian calves by using an animal model

2005 ◽  
Vol 48 (3) ◽  
pp. 261-269 ◽  
Author(s):  
H. Atil ◽  
A. S. Khattab ◽  
L. Badawy
Keyword(s):  
Animal Model ◽  
Birth Weight ◽  
Fixed Effects ◽  
Genetic Parameter ◽  
Genetic Correlations ◽  
Likelihood Method ◽  
Multiple Trait ◽  
Breeding Values ◽  
Heritability Estimates ◽  
Maternal Heritability

Abstract. Birth and weaning weights of 556 Friesian calves by 41 sires out of 318 different dams over a 11 years period were obtained from a herd of Friesian in Sakha Experimental Farm, Ministry of Agriculture, Egypt were used. The records were analyzed by Multiple Trait Likelihood Method (MTDFREML) by using a repeatability animal model (BOLDMAN et al., 1995). Convergence was attained after 699 iterations. The fixed effects included in the model were season and year of calving, parity and sex and the random effects were direct and maternal genetic, permanent maternal environmental and error. Direct heritability estimates for birth weight (BW) and weaning weight (WW) are 0.28 and 0.13, respectively, while, maternal heritability estimates for the same traits are 0.14 and 0.06, respectively. Repeatability estimates are 0.75 and 0.15 for BW and WW, respectively. Phenotypic and genetic correlations are 0.89 and 0.80, respectively. Estimates of calve breeding values ranged from −3.12 to 4.11 kg for BW and ranged from −4.10 to 5.11 kg for WW. Sire breeding values ranged from −3.40 to 2.99 kg for BW and ranged from −2.50 to 4.47 kg for WW. Dam breeding values ranged from −6.80 to 5.54 kg for BW and ranged from -6.10 to 6.39 kg for WW.

scholarly journals Simplifications of marker-assisted genetic evaluation and accounting for non-additive interaction effects

2005 ◽  
Vol 48 (5) ◽  
pp. 460-474
Author(s):  
Y. Liu ◽  
P. K. Mathur
Keyword(s):  
Animal Model ◽  
Quantitative Traits ◽  
Mixed Model ◽  
Genetic Evaluation ◽  
Polygenic Effect ◽  
Additive Effects ◽  
Additive Interaction ◽  
Direct Inversion ◽  
Model Equations ◽  
Computing Method

Abstract. A computing simplification was applied to marker-assisted genetic evaluation of quantitative traits including additive and non-additive effects of QTL as well as residual polygenic effects. Different situations including QTL and the residual polygenic effect estimated as a sum or separately, and with or without non-additive effects integrated in models were evaluated. The computing simplification was used in combinations with different models and parameterizations. An example data was adopted to illustrate the simplified computing strategy and was compared with the computing method of direct inversion. Identical results were obtained from both computing strategies. The main advantage of the simplification is that it does not require inversion of non-additive relationship matrices and relationship matrices of QTL, and the number of random effects in mixed model equations is the same as any animal model with only additive effects.

Sparse Inverse of Covariance Matrix of QTL Effects with Incomplete Marker Data

2004 ◽  
Vol 3 (1) ◽  
pp. 1-21 ◽  
Author(s):  
R. Mark Thallman ◽  
Kathryn J Hanford ◽  
Stephen D Kachman ◽  
L. Dale Van Vleck
Keyword(s):  
Covariance Matrix ◽  
Random Effects ◽  
Mixed Model ◽  
Simple Algorithm ◽  
Equivalent Model ◽  
Breeding Values ◽  
Marker Data ◽  
Proposed Model ◽  
Model Equations ◽  
Outbred Populations

Gametic models for fitting breeding values at QTL as random effects in outbred populations have become popular because they require few assumptions about the number and distribution of QTL alleles segregating. The covariance matrix of the gametic effects has an inverse that is sparse and can be constructed rapidly by a simple algorithm, provided that all individuals have marker data, but not otherwise. An equivalent model, in which the joint distribution of QTL breeding values and marker genotypes is considered, was shown to generate a covariance matrix with a sparse inverse that can be constructed rapidly with a simple algorithm. This result makes more feasible including QTL as random effects in analyses of large pedigrees for QTL detection and marker assisted selection. Such analyses often use algorithms that rely upon sparseness of the mixed model equations and require the inverse of the covariance matrix, but not the covariance matrix itself. With the proposed model, each individual has two random effects for each possible unordered marker genotype for that individual. Therefore, individuals with marker data have two random effects, just as with the gametic model. To keep the notation and the derivation simple, the method is derived under the assumptions of a single linked marker and that the pedigree does not contain loops. The algorithm could be applied, as an approximate method, to pedigrees that contain loops.

Combining direct and correlated traits into an aggregate index for dairy cattle fertility

2007 ◽  
Vol 2007 ◽  
pp. 64-64
Author(s):  
Stefano Biffani ◽  
Fabiola Canavesi ◽  
Maurizio Marusi
Keyword(s):  
Animal Model ◽  
Dairy Cattle ◽  
Milk Yield ◽  
Genetic Evaluation ◽  
Conception Rate ◽  
Calving Interval ◽  
Multiple Trait ◽  
Breeding Values ◽  
Breeding Goal ◽  
Aggregate Index

In January 2006, ANAFI (Italian Holstein Breeders Association) introduced a genetic evaluation for fertility based on a multiple-trait animal model (Biffani et al., 2005), which included the following traits: days from calving to first insemination (DTFS), calving interval (CI), first-service non return rate to 56 d (NR56), angularity (ANG) and mature equivalent milk yield at 305 d (ME305). Breeding values have been subsequently combined in an aggregate index (T), with the breeding goal to increase conception rate (CR). This paper will show how the breeding values have been combined into an aggregate index. At the same time the efficiency of selecting on alternative aggregate indexes versus the official aggregate index is presented.

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