Advances in Statistical Methods for Genetic Improvement of Livestock: A Review

Developments in statistics and computing as well as their application to genetic improvement of livestock gained momentum over the last 30 years. This paper reviews and consolidates the statistical methodology used in animal breeding. This paper will prove useful as a reference source for animal breeders, quantitative geneticists, and statisticians working in these areas. The estimates of genetic and phenotypic parameters viz. heritability, genetic and phenotypic correlation are used to determine the method of selection, the intensity of selection for different traits of interest, and prediction of selection response. The unbiased property of ANOVA estimators demands no distributional assumptions of the random effects and the residual error terms in a model but all sampling variance results have been developed based on assuming normality. The parameters are estimated by maximizing the logarithm of the likelihood function. The estimates of predictors of the random effects are expected to be more efficient. The drawbacks of ML are first, that it is downwardly biased because the loss of degrees of freedom due to estimating fixed effects is not taken into account. The estimates of predictors of the random effects are expected to be more efficient. The drawbacks of ML are first, that it is downwardly biased because the loss of degrees of freedom due to estimating fixed effects is not taken into account. Maximum likelihood (ML) restricted maximum likelihood and minimum norm quadratic unbiased estimations (MINQUE) are all preferred to ANOVA because they have built-in properties. MINQUE may considerably be better than the analysis of variance procedures. DFREML was the first public package to implement the derivative -free REML, and it became the standard in the field to which every other program is compared. Its unique feature is the likelihood ratio test for testing the significance of variance component estimates. The use of ML and REML in animal breedi ng has brought about a change in the random effects fitted in the infinitesimal additive genetic model. In traditional ANOVA and related methods, (co) variance is described in terms of random effect due to single parent (e.g., sire model) or both parents (sire dam model), uniquely partitioning the total sum of the squared deviations of the observations from the grand mean into the sum of squares contributed by each factor in the design. However, over the last decade, considerable research effort has concentrated on the development of specialized and efficient algorithms. This has been closely linked to advances in the genetic evaluation of animals by Best Linear Unbiased Prediction (BLUP). However, ML and REML allow the random effect of models to be expresse d in terms of the genetic merit or breeding value of animals. These models are called individual animal models (IAM) and incorporate information on the relationship between all animals. Animal Model (AM) has influenced the use of the mixed model methodology in the statistical analysis of animal breeding data considerably. The AM includes a random effect for the additive genetic merit of each animal, both for animals with records and animals which are parents only, incorporating all known relationship information in the analysis.