Advances in Statistical Methods for Genetic Improvement of Livestock

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 Two-Stage Model for Linear Growth.- 15.3 Two-Step Methods for Linear Models.- 15.4 Methods for Non-Linear Growth Curves.- 16 Survival, Endurance and Censored Observations in Animal Breeding.- 16.1 Introduction.- 16.2 Characterization of Survival Times and Endurance Measures.- 16.2.1 Properties.- 16.2.2 Censoring.- 16.3 Models.- 16.3.1 Parametric Models.- 16.3.2 Semi-Parametric Models.- 16.4 Maximum a Posteriori.- 16.5 Numerical Methods.- 16.6 A Preliminary Investigation.- 16.7 Conclusion.- 17 Genetic Evaluation for Discrete Polygenic Traits in Animal Breeding.- 17.1 Introduction.- 17.2 Analysis of the Discontinuous Scale with Linear Models.- 17.2.1 Single Population Analysis.- 17.2.2 Multipopulation Analysis.- 17.3 Models Postulating an Underlying Scale.- 17.3.1 Binary Responses.- 17.3.2 Extension to Other Situations.- 17.4 Discussion and Conclusion.- Discussion Summary.- VI: Selection and Non-Random Mating.- 18 Accounting for Selection and Mating Biases in Genetic Evaluation.- 18.1 Introduction.- 18.2 Effect of Selection on u, e, G and R.- 18.3 Means and Covariances Conditional on Selection Functions.- 18.4 BLUE and BLUP in a Selection Model.- 18.5 Estimability and Predictability.- 18.6 Cow Culling.- 18.7 Translation Invariant Functions of Records Used in Selection Plus Other Unknown Selection Functions.- 18.8 Selection on Previous Records Not Available for Analysis.- 18.9 Mixed Model Equations to Estimate Genetic and Environmental Trends.- 18.10 The Problem of Association Between Sire Values and Herd Merits in Sire Evaluations.- 18.11 The Problem of Grouping in Sire Evaluations.- 18.12 The Problem of Differential Treatments.- 18.13 The Problem of Assortative Mating.- 18.14 Discussion.- 19 Statistical Inferences in Populations Undergoing Selection or Non-Random Mating.- 19.1 Introduction.- 19.2 Dynamics of a Breeding Population.- 19.2.1 Mathematical Representation of a Breeding Population.- 19.3 Making Inferences in a Population Undergoing Non-Random Mating and Selection.- 19.4 Making Inferences with Incomplete Information.- 19.5 Multivariate Normality.- 19.5.1 Maximum Likelihood Estimation.- 19.5.2 Best Linear Prediction.- 19.5.3 Best Linear Unbiased Prediction.- 20 Problems in the Use of the Relationship Matrix in Animal Breeding.- 20.1 Introduction.- 20.2 The Numerator Relationship Matrix.- 20.3 Additive Genetic Variance.- 20.4 Examples and Applications.- 20.4.1 Use of the NRM in a Simple Sire Evaluation.- 20.4.2 Use of the NRM when Sires of the Test Bulls are a Selected Group.- 20.5 The NRM and Unknown Parentage.- 20.5.1 Modification of the NRM to Handle Certain Kinds of Unknown Parentage.- 20.5.2 Example.- 20.5.3 Application.- 20.6 Shortcoming of the NRM.- 20.7 Conclusion.- Discussion Summary.- VII: Statistics and New Genetic Technology.- 21 Identification of Genes with Large Effects.- 21.1 Introduction and Motivation.- 21.1.1 Motivation.- 21.1.2 Prior Information - Number of Genes.- 21.2 Methods Using Population Differences.- 21.2.1 Segregation in Crosses and Backcrosses.- 21.2.2 Segregation Analysis.- 21.2.3 Repeated Backcrossing and Selection.- 21.2.4 Use of Linked Markers.- 21.2.5 Use of Physiological Markers.- 21.3 Within Population Analysis.- 21.3.1 Departures from Normality.- 21.3.2 Structured Exploratory Data Analysis.- 21.3.3 Complex Segregation Analysis.- 21.3.4 Miscellanea.- 21.4 Use of Selected Populations.- 21.5 Molecular Manipulation.- 21.5.1 Transposon Tagging.- 21.5.2 Transgenics.- 21.6 Discussion.- 22 A General Linkage Method for the Detection of Major Genes.- 22.1 Introduction.- 22.2 A Generalization of Haseman and Elston's (1972) Method.- 22.3 Transformations to Approximate Normality.- 22.4 Dichotomous Traits and Disease Traits with Variable Age of Onset.- 22.5 Discussion.- 23 Reproductive Technology and Genetic Evaluation.- 23.1 Introduction.- 23.2 Reproductive Technology and Evaluation for Additive Genetic Merit.- 23.2.1 Embryo Transfer.- 23.2.2 Embryo Splitting (Cloning).- 23.2.3 Embryo and Semen Sexing.- 23.2.4 Androgenous Matings and Self-Fertilization.- 23.2.5 Chimeras.- 23.2.6 Polyploidy.- 23.2.7 Gene Transfer.- 23.3 Evaluation for Non-Additive Genetic Merit.- 23.3.1 Cytoplasmic Inheritance.- 23.3.2 Dominance Effects.- 23.3.3 Preferential Treatment.- 23.4 Conclusions.- Discussion Summary.