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1

Estimation of dominance components in noninbred populations by using additive animal model residuals

100%
Chalh A., El_ G. M.
Journal of Applied Genetics
|
2002
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vol. 43
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issue 4
471-488
EN
In the case of noninbred and unselected populations with linkage equilibrium, the additive and dominance genetic effects are uncorrelated and the variance-covariance matrix of the second component is simply a product of its variance by a matrix that can be computed from the numerator relationship matrix A. The aim of this study is to present a new approach to estimate the dominance part with a reduced set of equations and hence a lower computing cost. The method proposed is based on the processing of the residual terms resulting from the BLUP methodology applied to an additive animal model. Best linear unbiased prediction of the dominance component 'delta' is almost identical to the one given by the full mixed model equations. Based on this approach, an algorithm for restricted maximum likelihood (REML) estimation of the variance components is also presented. By way of illustration, two numerical examples are given and a comparison between the parameters estimated with the expectation maximization (EM) algorithm and those obtained by the proposed algorithm is made. The proposed algorithm is iterative and yields estimates that are close to those obtained by EM, which is also iterative.
2

Estimation of the dominance merit in noninbred populations without recourse to its inverted relationship matrix

100%
Chalh A., El_ G. M.
Journal of Applied Genetics
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2003
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vol. 44
|
issue 1
63-69
EN
This study presents a new approach to obtain dominance estimates without using the full Henderson?s mixed model equations (MMEs) related to an additive plus dominance animal model. This reduction could decrease substantially the computing time and hence its cost. In contrast to a procedure that we proposed before, the method developed in this paper does not require D?1 and provides best linear unbiased prediction (BLUP) of genetic values that is close to that given by processing the full MMEs. In the previous study, we also elaborated an algorithm (denoted ?-REML) in order to approximate restricted maximum likelihood estimation of variance components via the expectation maximization (EM) algorithm. The ?-REML algorithm has been modified to be adapted to our new resolution approach. Through a numerical example, we show that there is a good agreement between REML-(EM), ?-REML and modified ?-REML estimates and that the latter algorithm is more efficient than our first proposition in terms of computing time and memory conservation.
3

Bayesian estimation of dominance merits in noninbred populations by using Gibbs sampling with two reduced sets of mixed model equations

100%
Chalh A., El_ G. M.
Journal of Applied Genetics
|
2004
|
vol. 45
|
issue 3
331-339
EN
Henderson's mixed model equations system is generally required in a Gibbs sampling application. In two previous studies, we proposed two indirect solving approaches that give dominance values in an animal model context with no need to process all this system. The first one does not require D-1 and the second is based on processing the additive animal model residuals. In the present work, we show that these two methods can be handled iteratively. Since the Bayesian approach is now a widely used tool in estimation of genetic parameters, the main part of this work is devoted to a Gibbs sampling application that can be accelerated by means of the aforementioned indirect solving methods. Three replicates of a population data set are simulated in the paper to compare the applications and estimates. This shows effectively that the estimates given by implementing a Gibbs sampler with each of the two suggested solving methods are obtained with less computational time and are comparable to those given by considering the integral system, particularly when priors are more weighted.
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