scholarly journals An Algorithm for Genetic Analysis of Full-Sib Datasets with Mixed-Model Software Lacking a Numerator Relationship Matrix Function, and a Comparison with Results from a Dedicated Genetic Software Package

Forests ◽  
2020 ◽  
Vol 11 (11) ◽  
pp. 1169
Author(s):  
Gary R. Hodge ◽  
Juan Jose Acosta
Keyword(s):  
Mixed Model ◽  
Genetic Parameter ◽  
Male Parent ◽  
Parameter Estimates ◽  
Relationship Matrix ◽  
Forest Tree Breeding ◽  
Tree Model ◽  
Individual Tree ◽  
Breeding Values ◽  
Numerator Relationship Matrix

Research Highlights: An algorithm is presented that allows for the analysis of full-sib genetic datasets using generalized mixed-model software programs. The algorithm produces variance component estimates, genetic parameter estimates, and Best Linear Unbiased Prediction (BLUP) solutions for genetic values that are, for all practical purposes, identical to those produced by dedicated genetic software packages. Background and Objectives: The objective of this manuscript is to demonstrate an approach with a simulated full-sib dataset representing a typical forest tree breeding population (40 parents, 80 full-sib crosses, 4 tests, and 6000 trees) using two widely available mixed-model packages. Materials and Methods: The algorithm involves artificially doubling the dataset, so that each observation is in the dataset twice, once with the original female and male parent identification, and once with the female and male parent identities switched. Five linear models were examined: two models using a dedicated genetic software program (ASREML) with the capacity to specify A or other pedigree-related functions, and three models with the doubled dataset and a parent (or sire) linear model (ASREML, SAS Proc Mixed, and R lme4). Results: The variance components, genetic parameters, and BLUPs of the parental breeding values, progeny breeding values, and full-sib family-specific combining abilities were compared. Genetic parameter estimates were essentially the same across all the analyses (e.g., the heritability ranged from h2 = 0.220 to 0.223, and the proportion of dominance variance ranged from d2 = 0.057 to 0.058). The correlations between the BLUPs from the baseline analysis (ASREML with an individual tree model) and the doubled-dataset/parent models using SAS Proc Mixed or R lme4 were never lower than R = 0.99997. Conclusions: The algorithm can be useful for analysts who need to analyze full-sib genetic datasets and who are familiar with general-purpose statistical packages, but less familiar with or lacking access to other software.

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.

scholarly journals Direct and Competition Additive Effects in Tree Breeding: Bayesian Estimation From an Individual Tree Mixed Model

2008 ◽  
Vol 57 (1-6) ◽  
pp. 45-56 ◽  
Author(s):  
E. P. Cappa ◽  
R. J. C. Cantet
Keyword(s):  
Environmental Effects ◽  
Fixed Effects ◽  
Mixed Model ◽  
Phenotypic Variance ◽  
Tree Model ◽  
Data Set ◽  
Additive Variance ◽  
Individual Tree ◽  
Breeding Values ◽  
Competition Effects

Abstract An individual tree model with additive direct and competition effects is introduced to account for competitive effects in forest genetics evaluation. The mixed linear model includes fixed effects as well as direct and competition breeding values plus permanent environmental effects. Competition effects, either additive or environmental, are identified in the phenotype of a competitor tree by means of ‘intensity of competition’ elements (IC), which are non-zero elements of the incidence matrix of the additive competition effects. The ICs are inverse function of the distance and the number of competing individuals, either row-column wise or diagonally. The ICs allow standardization of the variance of competition effects in the phenotypic variance of any individual tree, so that the model accounts for unequal number of neighbors. Expressions are obtained for the bias in estimating additive variance using the covariance between half-sibs, when ignoring competition effects for row-plot designs and for single-tree plot designs. A data set of loblolly pines on growth at breast height is used to estimate the additive variances of direct and competition effects, the covariance between both effects, and the variance of permanent environmental effects using a Bayesian method via Gibbs sampling and Restricted Maximum Likelihood procedures (REML) via the Expectation- Maximization (EM) algorithm. No problem of convergence was detected with the model and ICs used when compared to what has been reported in the animal breeding literature for such models. Posterior means (standard error) of the estimated parameters were σ̂2Ad = 12.553 (1.447), σ̂2Ac = 1.259 (0.259), σ̂AdAc = -3.126 (0.492), σ̂2 p = 1.186 (0.289), and σ̂2e = 5.819 (1.07). Leaving permanent environmental competition effects out of the model may bias the predictions of direct breeding values. Results suggest that selection for increasing direct growth while keeping a low level of competition is feasible.

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.

Genetic parameter estimates and principal component analysis of breeding values of reproduction and growth traits in female Canchim cattle

2013 ◽  
Vol 25 (5) ◽  
pp. 775 ◽  
Author(s):  
M. E. Buzanskas ◽  
R. P. Savegnago ◽  
D. A. Grossi ◽  
G. C. Venturini ◽  
S. A. Queiroz ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Mixed Model ◽  
Growth Traits ◽  
Genetic Parameter ◽  
Genetic Correlations ◽  
Principal Component ◽  
Component Analysis ◽  
Parameter Estimates ◽  
Breeding Values ◽  
Heritability Estimates

Phenotypic data from female Canchim beef cattle were used to obtain estimates of genetic parameters for reproduction and growth traits using a linear animal mixed model. In addition, relationships among animal estimated breeding values (EBVs) for these traits were explored using principal component analysis. The traits studied in female Canchim cattle were age at first calving (AFC), age at second calving (ASC), calving interval (CI), and bodyweight at 420 days of age (BW420). The heritability estimates for AFC, ASC, CI and BW420 were 0.03 ± 0.01, 0.07 ± 0.01, 0.06 ± 0.02, and 0.24 ± 0.02, respectively. The genetic correlations for AFC with ASC, AFC with CI, AFC with BW420, ASC with CI, ASC with BW420, and CI with BW420 were 0.87 ± 0.07, 0.23 ± 0.02, –0.15 ± 0.01, 0.67 ± 0.13, –0.07 ± 0.13, and 0.02 ± 0.14, respectively. Standardised EBVs for AFC, ASC and CI exhibited a high association with the first principal component, whereas the standardised EBV for BW420 was closely associated with the second principal component. The heritability estimates for AFC, ASC and CI suggest that these traits would respond slowly to selection. However, selection response could be enhanced by constructing selection indices based on the principal components.

Natural variation and genetic parameters in Fraser fir for growth and Christmas tree traits

1994 ◽  
Vol 24 (7) ◽  
pp. 1480-1486 ◽  
Author(s):  
R.J. Arnold ◽  
J.B. Jett ◽  
S.E. McKeand
Keyword(s):  
Growth Traits ◽  
Genetic Parameter ◽  
Genetic Correlations ◽  
Christmas Tree ◽  
Parameter Estimates ◽  
Early Age ◽  
Individual Tree ◽  
Fraser Fir ◽  
Seed Sources ◽  
Height Class

Open-pollinated progeny trials of Fraser fir (Abiesfraseri (Pursh) Poir.) assessed at 8 years provided genetic parameter estimates for growth, Christmas tree quality traits, and wholesale value at harvest age. Significant variation was found between and within nine different seed sources. Estimated individual tree heritabilities of important traits ranged from a low of 0.13 for USDA Christmas tree grade to a moderate value of 0.33 for crown diameter. Heritabilities within the better performing seed sources tended to be higher. Of the two traits that determine wholesale value, USDA grade and height class, the latter proved to have the greater influence, both phenotypically and genetically. Genetic correlations of early age height growth with 8-year total height, height class, USDA Christmas tree grade, and individual tree wholesale value proved favorable and strong (range of 0.57–0.96). In combination with moderate heritabilities for early growth traits, such correlations provide potential for effective early age selections in Fraser fir Christmas trees.

scholarly journals Effect of selection on bias and accuracy in genomic prediction of breeding values

2018 ◽  
Author(s):  
G. R. Gowane ◽  
Sang Hong Lee ◽  
Sam Clark ◽  
Nasir Moghaddar ◽  
Hawlader A Al-Mamun ◽  
...  
Keyword(s):  
Random Mating ◽  
Careful Consideration ◽  
Selective Genotyping ◽  
Genetic Models ◽  
Genomic Relationship Matrix ◽  
Relationship Matrix ◽  
Breeding Values ◽  
Numerator Relationship Matrix ◽  
Lower Accuracy ◽  
Frequency Changes

AbstractReference populations for genomic selection (GS) usually involve highly selected individuals, which may result in biased prediction of estimated genomic breeding values (GEBV). In the present study, bias and accuracy of GEBV were explored for various genetic models and prediction methods when using selected individuals for a reference. Data were simulated for an animal breeding program to compare Best Linear Unbiased Prediction of breeding values using pedigree based relationships (PBLUP), genomic relationships for genotyped animals only (GBLUP) and a Single Step approach (SSGBLUP), where information on genotyped individuals was used to infer a matrix H with relationships among all available genotyped and non-genotyped individuals that were linked through pedigree. In SSGBLUP, various weights (α=0.95, 0.80, 0.50) for the genomic relationship matrix (G) relative to the numerator relationship matrix (A) were applied to construct H and in another version (SSGBLUP_F), inbreeding was accounted for while computing A-1. With GBLUP, accuracy of GEBV prediction increased linearly with an increase in the number of animals selected in reference. For the scenario with no-selection and random mating (RR) prediction was unbiased. For GBLUP, lower accuracy and bias observed in the scenarios with selection and random mating (SR) or selection and positive assortative mating (SA), in which prediction bias increased when a smaller and highly selected proportion genotyped. Bias disappeared when all individuals were genotyped. SSGBLUP_F showed higher accuracy compared to GBLUP and bias of prediction was negligible even with selective genotyping. However, PBLUP and SSGBLUP showed bias in SA owing to not fully accounting for allele frequency changes because of selection of quantitative trait loci (QTL) with larger effects and also due to high inbreeding rate. In genetic models with fewer QTL but each with larger effect, predictions were less accurate and more biased for selection scenarios. Results suggest that prediction accuracy and bias is affected by the genetic architecture of the trait. Selective genotyping lead to significant bias in GEBV prediction. SSGBLUP with appropriate scaling of A and G matrices can provide accurate and less biased prediction but scaling requires careful consideration in populations under selection and with high levels of inbreeding.

Bayesian estimation of a surface to account for a spatial trend using penalized splines in an individual-tree mixed model

2007 ◽  
Vol 37 (12) ◽  
pp. 2677-2688 ◽  
Author(s):  
Eduardo P. Cappa ◽  
Rodolfo J.C. Cantet
Keyword(s):  
Spatial Variability ◽  
Large Scale ◽  
Mixed Model ◽  
Deviance Information Criterion ◽  
Covariance Structure ◽  
Information Criterion ◽  
Penalized Splines ◽  
Dispersion Parameters ◽  
Individual Tree ◽  
Breeding Values

Unaccounted for spatial variability leads to bias in estimating genetic parameters and predicting breeding values from forest genetic trials. Previous attempts to account for large-scale continuous spatial variation employed spatial coordinates in the direction of the rows (or columns). In this research, we use an individual-tree mixed model and the tensor product of B-spline bases with a proper covariance structure for the random knot effects to account for spatial variability. Dispersion parameters were estimated using Bayesian techniques via Gibbs sampling. The procedure is illustrated with data from a progeny trial of Eucalyptus globulus subsp. globulus Labill. Four different models were used in the sequel. The first model included block effects and the three other models included a surface on a grid of either 8 × 8, 12 × 12, or 18 × 18 knots. The three models with B-splines displayed a sizeable lower value of the deviance information criterion than the model with blocks. Also, the mixed models fitting a surface displayed a consistent reduction in the posterior mean of σ2e, an increase in the posterior means of σ2A and h2DBH, and an increase of 66% (for parents) or 60% (for offspring) in the accuracy of breeding values.

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