Table Of ContentSelection Indices
•
Ill
Plant Breeding
Author
R. J. Baker, Ph.D.
Senior Research Scientist
Crop Development Centre
University of Saskatchewan
Saskatoon, Canada
Boca Raton London New York
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PREFACE
Chapter 1 provides a review of the strategy and methodology of selection indices, as well
as of some of the modifications that have been suggested. Recent literature on research
relating to the use of selection indices in plant species is reviewed in Chapter 2. This review
should provide the reader with insight into current thinking on the subject.
Basic principles of quantitative genetics are reviewed in Chapter 3. These principles are
considered in a context which applies particularly to the development of selection indices
for plant breeding. This is followed immediately by a detailed consideration in Chapter 4
of the methods that can be used to develop estimates of the genotypic and phenotypic
variances and covariances required for selection indices.
The first four chapters provide an overall review of topics which relate to the development
of selection indices. Readers who have studied the subject may wish to proceed directly to
Chapters 5 and 6 where there is a discussion of some of the issues related to the use of
selection indices, and of some related methods that have been recommended for evaluating
parental material for breeding programs. Chapter 7 includes an overall evaluation of various
modifications that have been proposed for selection indices and their use in plant breeding.
This chapter constitutes the author’s recommendations as to how selection indices should
be used for crop improvement.
Chapters 8 and 9 rely partly on the recommendations developed in Chapter 7 and partly
on the methods for estimating variances and covariances that were reviewed in Chapter 4.
Chapter 8 constitutes a recipe book for applying selection indices to single or multiple trait
improvement in plant breeding programs. In Chapter 9, methods for choosing parents for
plant breeding programs are presented.
Chapter 10 and the appendices provide a guide to computer techniques for carrying out
the calculations required to develop and apply selection indices.
THE AUTHOR
Dr. R. J. Baker has conducted significant theoretical and applied research on subjects
relating to crop improvement for nearly two decades. While employed as a quantitative
geneticist at the Agriculture Canada Research Station in Winnipeg, Canada, he worked
closely with cereal breeders and pathologists on a range of problems related to the devel-
opment of superior methods of crop improvement. He currently directs a wheat improvement
program at the University of Saskatchewan.
Dr. Baker has published more than 60 papers on selection indices, genotype-environment
interaction, breeding methodology in self-pollinated species, methods of genetic analysis,
methods of statistical analysis, and on the inheritance and heritability of agronomic and
quality traits in cereal crops. He has served as a research advisor in East Africa and is often
called upon for statistical advice and advice on computer methodology. He has contributed
significantly to graduate student training and to the research efforts of his colleagues.
He received his B.S.A. and M.Sc. from the University of Saskatchewan and his Ph.D.
in plant genetics from the University of Minnesota. He spent one year as a Visiting Research
Fellow in the Department of Genetics at the University of Birmingham, United Kingdom.
Dr. Baker has been awarded fellowships in the American Society of Agronomy and in
the Crop Science Society of America for his research contributions.
ACKNOWLEDGMENTS
Helpful suggestions on content and presentation were contributed by Drs. A. R. Hallauer,
R. R. Hill, Jr., D. R. Knott, W. R. Meredith, Jr., and A. E. Slinkard. The author sincerely
appreciates the efforts of these scientists who took time from their busy schedules to read
parts or all of the draft manuscript. The efforts of Ms. Lori Werdal in typing and proofreading
the many equations is also gratefully acknowledged.
The author wishes to acknowledge the encouragement of his wife, Joan, and to thank her
for her patience while this book was being written.
To my parents
TABLE OF CONTENTS
Chapter 1
History of Selection Index Methodology................................................................................. 1
I. Introduction....................................................................................................................... 1
II. The Basic Strategy of Optimum Selection Indices..................................................... 1
III. Optimum Selection Indices.............................................................................................2
IV. Relative Efficiency of Index Selection, Independent Culling, and Tandem
Selection..............................................................................................................................7
V. Restricted Selection Indices............................................................................................10
VI. General Selection Indices...............................................................................................10
VII. Other Modified Selection Indices.................................................................................11
VIII. Summary..........................................................................................................................11
References......................................................................................................................................12
Chapter 2
The Application of Selection Indices in Crop Improvement.................................................13
I. Introduction.......................................................................................................................13
II. Applications Involving Improvement of a Single Quantitative Trait........................13
III. Applications Involving the Simultaneous Improvement of Two or More
Traits.................................................................................................................................16
IV. Summary..........................................................................................................................18
References......................................................................................................................................19
Chapter 3
Basic Concepts in Quantitative Genetics.................................................................................23
I. Introduction.......................................................................................................................23
II. Estimation of Genotypic Values...................................................................................23
III. Comparison of Various Definitions of Heritability....................................................28
IV. Estimation of Genotypic Correlations..........................................................................29
V. Summary..........................................................................................................................32
References......................................................................................................................................33
Chapter 4
Methods for Estimating and Evaluating Genotypic and Phenotypic Variances and
Covariances..................................................................................................................................35
I. Introduction......................................................................................................................35
II. Measures of Precision of Estimates..............................................................................35
III. Estimation of Variances and Covariances from Parent-Offspring
Relationships.....................................................................................................................36
IV. Estimation of Variances and Covariances from Biparental Progeny........................37
V. Estimation of Variances and Covariances from Design I Experiments...................39
VI. Estimation of Variances and Covariances from Design II Experiments.................41
VII. Estimation of Variances and Covariances from Inbred or Partially
Inbred Lines.....................................................................................................................47
VIII. Estimation of Variances and Covariances from Comparison of Heterogeneous
and Homogeneous Populations......................................................................................53
IX. Inspection of Estimated Genotypic and Phenotypic Covariance Matrices.............57
X. Maximum Likelihood Estimation of Variance Components.....................................59
XI. Summary..........................................................................................................................60
References......................................................................................................................................60
Chapter 5
Issues in the Use of Selection Indices......................................................................................63
I. Introduction.......................................................................................................................63
II. Normality of Genotypic and Phenotypic Distributions..............................................63
III. Nonlinear Worth Functions...........................................................................................67
IV. Sample Sizes Required for Estimating Population Parameters..................................67
V. Summary..........................................................................................................................73
References......................................................................................................................................73
Chapter 6
Use of Selection Indices and Related Techniques for Evaluating Parental Material........75
I. Introduction.......................................................................................................................75
II. Methods for Choosing Parents to Produce Populations with Desirable
Means.................................................................................................................................76
A. Vector Analysis..................................................................................................76
B. Least-Squares Analysis......................................................................................78
C. Canonical Analysis.............................................................................................78
III. Methods for Choosing Parents Having Greater Genetic Diversity.............................80
IV. Summary..........................................................................................................................81
References......................................................................................................................................81
Chapter 7
Recommendations for Using Selection Indices in Plant Breeding........................................83
I. Introduction.......................................................................................................................83
II. General Considerations..................................................................................................83
A. Are Selection Indices Necessary in Plant Breeding?.......................................83
B. How Should One Choose Traits to be Included in a Selection
Index?...................................................................................................................83
C. Should a Weight-Free Index be Used Instead of an Estimated
Optimum Index?................................................................................................85
D. Should a Restricted Selection Index be Used?.................................................91
III. Use of Selection Indices................................................................................................91
A. Nonrecurrent Selection Programs.....................................................................91
B. Recurrent Selection.............................................................................................92
IV. Parental Evaluation in Self-Pollinated Species...........................................................92
V. Determining Relative Economic Weights....................................................................93
VI. Summary..........................................................................................................................94
References......................................................................................................................................94
Chapter 8
Development and Use of Selection Indices..............................................................................97
I. Introduction.......................................................................................................................97
II. Single Trait Selection.....................................................................................................97
A. Using Data from Correlated Traits to Enhance Response to Selection
for a Single Trait................................................................................................97
B. Multistage Selection for a Single Trait.........................................................103
C. Information from Relatives..............................................................................110
III. Multiple Trait Selection................................................................................................112
A. Weight-Free Index for Ranking Genotypes...................................................112
B. Base Indices.......................................................................................................114
C. Modified Base Index........................................................................................114
D. Optimum Selection Indices..............................................................................115
E. Restricted Selection Indices............................................................................116
IV. Summary..........................................................................................................................118
References..................................................................................................................................118
Chapter 9
Parental Evaluation....................................................................................................................121
I. Introduction.....................................................................................................................121
II. Methods for Assigning Relative Importance to Traits in a Breeding Program... 121
A. Proposal by Grafius..........................................................................................121
B. Proposal by Pederson........................................................................................123
III. Specifying an Ideal Genotype......................................................................................124
IV. Least-Squares Approach to Choosing Parents for a Breeding Program.................124
V. Choosing Parents to Give Maximum Genotypic Variability...................................127
VI. Summary........................................................................................................................129
References....................................................................................................................................130
Chapter 10
Computer Programs for the Study and Application of Selection Indices...........................131
I. Introduction....................................................................................................................131
II. Simulation of Genetic and Multivariate Data...........................................................131
III. Estimating Variances and Covariances from Balanced Designs.............................133
IV. Calculating Selection Indices......................................................................................137
V. Summary.......................................................................................................................138
References....................................................................................................................................139
Appendix 1: Program for Testing Random Number Generator........................................141
Appendix 2: Program for Genetic Simulation of Populations.........................................145
Appendix 3: Program for Multinormal Genotypic and Phenotypic Values...................151
Appendix 4: Program for Calculating Mean Squares and Mean Cross-Products in
Balanced Factorial Designs..............................................................................157
Appendix 5: Program for Calculating Specified Mean Squares
and Mean Cross-Products...............................................................................163
Appendix 6: Program for Calculating Mean Squares and Mean Cross-Products
for Balanced Designs........................................................................................169
Appendix 7: Program for Calculating Expectations of Mean Squares............................177
Appendix 8: Program for Calculating Genotypic and Phenotypic Covariances.............181
Appendix 9: Program for Calculating Hayes-Hill Transformation of
Genotypic and Phenotypic Covariance Matrices..........................................185
Appendix 10: Program for Estimating Coefficients for an Optimum
Selection Index..................................................................................................193
Appendix 11: Program for Calculation of, and Ranking According to,
Index Scores.....................................................................................................199
Appendix 12: Program for Weight-Free Ranking of Genotypes........................................203
Appendix 13: Program for Evaluating Potential Parents......................................................207
Index............................................................................................................................................213
