Developments in statistics and computing as well as their application to genetic improvement of livestock gained momentum over the last 20 years. This text reviews and consolidates the statistical foundations of animal breeding. This text will prove useful as a reference source to animal breeders, quantitative geneticists and statisticians working in these areas. It will also serve as a text in graduate courses in animal breeding methodology with prerequisite courses in linear models, statistical inference and quantitative genetics.

Inhalt

I: General.- 1 Statistical Methods in Animal Improvement: Historical Overview.- 1.1 Introduction.- 1.2 Pearson's Pioneering Work.- 1.3 Fisher's Work of the Late Teens and the Twenties.- 1.4 Wright's Work of the Teens and Twenties.- 1.5 Lush and Wright - Early Prediction Methods.- 1.6 Selection Index.- 1.7 Early Development of Linear Model Methods for Unbalanced Data.- 1.8 Derivation of Best Linear Unbiased Prediction.- 1.9 The Development of Methods for Estimation of Variances and Covariances.- 1.10 Some Recent Developments in Computing Strategies.- 1.11 Recent Work in Optimum Selection Criteria.- 2 Mixed Model Methodology and the Box-Cox Theory of Transformations: A Bayesian Approach.- 2.1 Introduction.- 2.2 Motivation: A Simple Sire Evaluation Model.- 2.3 Family of Transformations.- 2.3.1 Prior Distributions.- 2.4 Some Posterior Distributions.- 2.4.1 Joint Posterior Distribution of all Parameters.- 2.4.2 Posterior Distribution of the Variance Components and of ?.- 2.4.3 Posterior Distribution of Functions of the Variance Ratio and of ?.- 2.4.4 Posterior Distribution of ?.- 2.5 Estimation of the Transformation.- 2.5.1 From the Marginal Distribution of ?.- 2.5.2 From the Joint Distribution of ? and ?.- 2.5.3 From the Joint Distribution of ?e2, ?u2 and ?.- 2.6 Analysis of the Effects After Transformation.- 2.6.1 Analysis Conditional on ? and ?.- 2.6.2 Analysis Conditional on ?.- 2.7 Extensions and Conclusions.- 3 Models for Discrimination Between Alternative Modes of Inheritance.- 3.1 Introduction.- 3.2 Data on Inbred Lines, Their F1 and Backcrosses.- 3.2.1 One Locus.- 3.2.2 Polygenic Inheritance.- 3.2.3 Mixed Major Locus and Polygenic Inheritance.- 3.2.4 Two Loci.- 3.3 Pedigree Data from a Random Mating Population.- 3.3.1 One Locus.- 3.3.2 Polygenic Inheritance.- 3.3.3 Mixed Major Gene and Polygenic Inheritance.- 3.3.4 Regressive Models.- 3.4 Choice of Genetic Hypothesis.- Discussion Summary.- II: Design of Experiments and Breeding Programs.- 4 Considerations in the Design of Animal Breeding Experiments.- 4.1 Introduction.- 4.2 Formal Designs.- 4.2.1 Intra-Class Correlation of Sibs.- 4.2.2 Offspring-Parent Regression.- 4.2.3 Joint Sib and Offspring-Parent Analyses.- 4.2.4 Genetic Correlations.- 4.3 Selection Experiments.- 4.3.1 Single Generation Experiments.- 4.3.2 Multiple Generation Experiments.- 4.4 Field Experiments.- 4.5 Concluding Remarks.- 5 Use of Mixed Model Methodology in Analysis of Designed Experiments.- 5.1 Introduction.- 5.2 Mixed Model Methods.- 5.3 Selection of Breeding Animals.- 5.4 Estimation of Genetic Variances.- 5.5 Estimation of Selection Response.- 5.6 Design.- 5.7 Conclusions.- 6 Statistical Aspects of Design of Animal Breeding Programs: A Comparison Among Various Selection Strategies.- 6.1 Introduction.- 6.2 Full-Sib Structures.- 6.2.1 First Generation.- 6.2.2 Short-to Medium-Term Results.- 6.2.3 Long-Term Results.- 6.3 Discussion.- 7 Optimum Designs for Sire Evaluation Schemes.- 7.1 Introduction.- 7.2 Theory.- 7.3 Numerical Examples.- 7.3.1 Allocation of Progeny Testing Resources.- 7.3.2 Sampling New Candidates.- 7.3.3 Two-Stage Selection.- 7.4 Discussion.- Discussion Summary.- III: Estimation of Genetic Parameters.- 8 Computational Aspects of Likelihood-Based Inference for Variance Components.- 8.1 Introduction.- 8.2 Model.- 8.3 Analysis of Variance (ANOVA) and ANOVA-Related Notation.- 8.4 Likelihood Function.- 8.5 Extended Parameter Space.- 8.6 REML Estimation.- 8.7 Newton-Raphson Algorithms.- 8.8 Concentrated Log Likelihood Function.- 8.9 Linearization.- 8.10 Computation of Iterates.- 8.11 An Alternative Approach to the Computation of Iterates.- 8.12 Method of Scoring.- 8.13 EM Algorithm and the Method of Successive Approximations.- 8.14 Linearized Method of Successive Approximations.- 8.15 Confidence Intervals and Hypothesis Tests.- 8.16 Example.- 8.17 Extensions.- 8.17.1 More than One Set of Random Effects.- 8.17.2 Correlated or Heteroscedastic Random Effects.- 9 Parameter Estimation in Variance Component Models for Binary Response Data.- 9.1 Introduction.- 9.2 Review of the Linear Case.- 9.3 Mixed Model Analysis with Binary Response.- 9.3.1 Bayes Approach.- 9.3.2 Likelihood Approaches.- 10 Estimation of Genetic Parameters in Non-Linear Models.- 10.1 Introduction.- 10.2 Models.- 10.3 Linearization.- 10.3.1 Maximum Likelihood.- 10.3.2 Maximum a Posteriori.- 10.3.3 Foulley's Method.- 10.3.4 The Method of Harville and Mee.- 10.3.5 Gilmour's Method.- 10.3.6 Remarks.- 10.4 Numerical Methods.- 10.4.1 Preliminaiy Absorption.- 10.4.2 Accommodating Relationships.- 10.4.3 Tridiagonalization and the EM Algorithm.- 10.4.4 Remarks.- 10.5 A Preliminary Investigation.- 10.6 Conclusion.- Discussion Summary.- IV: Prediction and Estimation of Genetic Merit.- 11 A Framework for Prediction of Breeding Value.- 11.1 Introduction.- 11.2 The Mixed Linear Model.- 11.3 Joint Posterior Distribution.- 11.4 Known Variance Components.- 11.4.1 Posterior Distribution of ß with Known u.- 11.4.2 Posterior Distribution of u when ? is Known.- 11.5 Unknown Variance Components.- 11.5.1 Joint Inferences About Location Parameters and Variance Components.- 11.5.2 Marginal Inferences About Variance Components and Functions Thereof.- 11.5.3 Marginal Inferences About Location Parameters.- 11.6 Choosing a Predictor.- 11.7 Choosing a Model.- 11.8 Prediction of Future Records.- 12 BLUP (Best Linear Unbiased Prediction) and Beyond.- 12.1 Introduction.- 12.2 Formulation of the Prediction Problem.- 12.2.1 Mixed Model.- 12.2.2 Example.- 12.2.3 General Prediction Problem.- 12.3 State 1: Joint Distribution Known.- 12.3.1 Point Prediction.- 12.3.2 Interval Prediction.- 12.3.3 Special Case: Mixed Linear Model.- 12.4 State 2: Only First and Second Moments Known.- 12.4.1 Best Linear (Point) Prediction.- 12.4.2 Interval Prediction (Frequentist Approach).- 12.4.3 Bayesian Prediction.- 12.5 State 3: Only Variances and Covariances Known.- 12.5.1 Best Linear Unbiased (or Location-Equivariant) Prediction.- 12.5.2 Interval Prediction (Frequentist Approach).- 12.5.3 Special Case: Mixed Linear Model.- 12.5.4 Linear-Bayes Prediction.- 12.5.5 Bayesian Prediction.- 12.6 State 4: No Information.- 12.6.1 Estimation of ?.- 12.6.2 Point Prediction.- 12.6.3 MSE of Prediction.- 12.6.4 Approximating the MSE.- 12.6.5 Estimating the MSE.- 12.6.6 Interval Prediction (Frequentist Approach).- 12.6.7 Bayesian Prediction.- 13 Connectedness in Genetic Evaluation.- 13.1 Introduction.- 13.2 The Models.- 13.2.1 Classical Model.- 13.2.2 Certain Characteristics of the Males Known.- 13.3 The Unbiasedness Constraint.- 13.3.1 Models without Group Effects.- 13.3.2 Models with Group Effects.- 13.4 Minimum Mean Square Error.- 13.4.1 Models without Group Effects.- 13.4.2 Models with Group Effects.- 13.5 Other Objectives and Constraints.- 13.5.1 Relaxing the Unbiasedness Requirement for Group Effects.- 13.5.2 Maximum Genetic Progress.- 13.6 Discussion and Conclusions.- Discussion Summary.- V: Prediction and Estimation in Non-Linear Models.- 14 Generalized Linear Models and Applications to Animal Breeding.- 14.1 Introduction.- 14.2 Estimation of Heritability of Binary Traits by Offspring-Parent Regression.- 14.3 Estimation of Gene Frequencies.- 14.4 Variance Components for Normal Data.- 14.5 Variance Components with Generalized Linear Models.- 14.6 Discussion.- 15 Analysis of Linear and Non-Linear Growth Models with Random Parameters.- 15.1 Introduction.- 15.2 A …