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Introduction to Quantitative Genetics in Forestry J)e^ ,3 INTRODUCTION TO QUANTITATIVE GENETICS IN FORESTRY r^-i Gene Namkoong U.S. DEPARTMENT OF AGRICULTURE FOREST SERVICE Technical Bulletin No. 1588 INTRODUCTION TO QUANTITATIVE GENETICS IN FORESTRY by Gene Namkoong, Principal Plant Geneticist Southeastern Forest Experiment Station Technical Bulletin No. 1588 Forest Service United States Department of Agriculture Washington, D. C. February 1979 For sale by the Superintendent of Documents, U.S. Government Printing Office For saie oy me o P^g^j^j^^^^ ^^ 20402 (Paper Cover) Stock Number 001-000-03773-1 Namkoong, Gene. ^Tech"Bun"No"l588?T42*pí^"^^ ^^"'*''' '" ^"'■''*''^- ^^ ^^ ^"P" ^^"'=- «tftLT"*^ information forest geneticists need about applied mathematics, ™ ^ ^' P°P"lat>7 biology, and genetics in order to design breeding pro- grams College-level training in mathematics, statistics, and genetics is re- quired to understand most of the book. ' s SJn?eÎS?J' '^"*""*''*^''^ genetics, tree breeding, genetic selection, popu- OXFORD NO.'165.3—015.5 m ACKNOWLEDGMENTS AND DEDICATION A diversity of people and skills is required to publish a book like this, but the distribution of credit is highly restricted. While quite inadequate for a just distribution, recognition must be given to the scientific critiques given by P. C. Burrows, W. J. Libby, J. H. Roberds, E. B. Snyder, J. P. Van Buijtenen, J. W. Wright, and the students in forest genetics at North Carolina State University. Their efforts have enhanced the quality of presentation and have reduced the multitude of errors which I had perpetrated to their present level. , .,^, ^ x In addition, this work rests on the foundation built by foresters and geneticists who pioneered in developing forest genetics, often in isolated pursuit and with meager recognition. In particular, the joyous dedication to forest genetics and to scientific truth and the gentle ethics of Philip C. Wakeley have been both directly useful and a continuing source of inspiration for more of us than he can know. It is to his great humanity that I am personally indebted, and to him that I dedicate this book. IV CONTENTS Page INTRODUCTION vii CHAPTER 1. MODELS OF GENE ACTION 1 Descriptive Statistics 1 Genetic Sources of Variation 3 Multiple-Gene Locus Models 6 Estimating Genetic Sources of Variation 9 Coefficients of Relationship 10 Designs for Estimation 12 Population Genetic Basis ' 13 CHAPTER 2. SELECTION THEORY !!.'!'.!'.*. 17 Single-Locus Models 17 Two-Locus Models 26 Nonselective Factors* 28 Single-Locus Selection With Phenotypic Variance Around Genotypic Means ^ 30 Griffing's Expected-Gain Formula 32 Heritability ....!!!. 34 Selection Differential 35 Gain WWW 36 Population Size 37 Diffusion Models for Selection 39 Other Probability Models for Selection* .!.!..'.*..!!..* 45 Selection Models 49 Selection Experiments 52 Initial Selection Consideration in Forestry 60 CHAPTER 3. BREEDING THEORY !.'.*.'.'.*!!.* ^Z Single-Population Breeding 65 Inbreeding Systems 66 Hybridizing Inbreds 66 Mass and Simple Recurrent Selection , W. 67 Family Selection !!.*..!. 70 Heritability Concepts .'.*!!.*.' 73 The Numerator 74 The Denominator ' 76 Expected Progress From Some Recurrent Selection and Breeding Systems 79 Mating Patterns .!.!...... 88 Recurrent Mating Systems Without Family Selection ......... 90 Recurrent Mating Systems With Family Selection 93 Partially Controlled Mating Systems , 95 Hybrid Breeding Systems .' ]. 96 Hybrids of Inbred Lines .....!.!.! 99 Hybrids of Population i ...]!.! 100 Mixed Breeding Programs ....!!!....! 105 Considerations in Choosing Breeding Methods .*.!!! 106 Seed Source Selection ' * log CHAPTER 4. TESTING AND ESTIMATING VALUE ÏN FOREST TREE BREEDING II7 Index on Relatives * II7 VI Page Index on Traits j|^ Correlated Response y^^ Nonlinear Relations j^^ Genotype X Environment Interaction l^^ Competition t^'r CHAPTER 5. TREE BREEDING PROGRAMS 145 Breeding Programs \^ CHAPTER 6. MODELS OF POPULATION GROWTH 153 The Simplest Model Y^l Density-Dependent and Competition Models* J-00 Age-Dependent Models* |^^ Effects of Variations* |^^ Populations V^ith Gene Differences * ' ' •;,*^r;o X^" " ^^^ CHAPTER 7. REGRESSION AND REGRESSION EFFECTS OF GENOTYPIC DIFFERENCES Yl} Linear Statistical Models Yl± Heterogeneous and Correlated Errors* |^^ Nonlinear Regression* |¿° Multivariate Regression* j°^ Linear Genetic Models ^^5 Extension* ;^f Genetic Variances in Tree Species ^^^ Covariances of Relatives j^^ Multivariate Variances* • • • ^1¿ CHAPTER 8. ESTIMATING GENETIC PARAMETERS 217 Estimating Variance Components in Analyses of Variance 222 Unbalanced Design Analyses* 225 Distributions of Variance Components* ^^ Designing Genetics Experiments ^^^ Errors of Estimating Genetic Variances ^44 Other Estimators 252 Higher-Order Relatives* ^^^ Special Forestry Problems j^^ CHAPTER 9. POPULATION GENETICS 263 Mutation „-»j. Migration • • • • * * * * ••;*;. OCQ The Special Restrictions of Sampling Errors in Small Populations .. ^by Inbreeding 270 Correlations Among Relatives ^^^ Predicting Inbreeding* ^¿^ Selection f^. Multiple Environment Selection ^o^ Multiple-Locus Selection* 288 Selection-Induced Polymorphism 2yd Stochastic Variation 294 Analysis of Stochastic Processes* 2y5 Stochastic Genetic Processes* 298 Mutation, Migration, Selection, and Stochastic Variations 303 Migration, Inbreeding, and Stochastic Variations 306 Neighborhood Inbreeding Models* 308 Geographic Variation in Forest Trees 309 CHAPTER 10. THE VIEW AHEAD FOR FOREST GENETICS .... 315 LITERATURE CITED 321 *Graduate-level statistical training required for thorough understanding. INTRODUCTION Man's explosive intrusion into forest ecosystems has not only affected the present character of our forests but in a more pro- foundly disturbing way has also affected the evolution of our future forests. Not only are the trees growing today different from those of past decades, but we have often lost the resilient capacity of this renewable resource to respond to the changing demands of nature and man. When whole forests are lost, the genes are lost, and replanting the land cannot recover the potential of any extinct genes. Even during breeding, the genetic resource may often be so reduced that future evolution is halted. Today, forests are being more intensively exploited and the forester has an obligation to safeguard the future of his resource. He can con- structively direct the evolution of forests toward increased pro- ductivity within a genetic system that is capable of cumulative improvement and of meeting the varying and uncertain demands of the future. If the genetic resource is to be effectively used and forest composition extensively controlled, we must look for ways to optimally control the evolutionary system of the whole species, and not just the transient status of any one generation. The forest scientist is thus obliged to understand the forces which have con- trolled or can control the evolving forest and to predict the conse- quences of directed or accidental changes in both the genetic and ecological systems. The potential benefits of tree breeding are widely recognized, and forest tree breeders will undoubtedly have at least partial control of the genetic basis of future forests. The forest geneticist must therefore understand the genetic materials and the manipulative techniques available. Quantitative genetics can help him to rationalize his tactics and strategies. It provides a means to construct unifying and explicit theoretical structures and testable hypotheses of alternate theories and practices. During the past two decades, forest geneticists have devoted most attention to observing inheritance patterns, correlations among traits, and developmental relations among traits and be- tween juvenile and mature tree performances. Much work has also been devoted to estimating the apportionment of genetic differences between and wi'thin seed sources, the utility of hybrids, and the economic and biological constraints of forest trees which affect breeding operations. Thus, the forest geneticist has begun to develop a greater understanding of the organisms handled and vii vin a pool of materials for starting a process of controlled evolution. However, the past two decades have also produced major develop- ments in the science of genetics and the theoretical foundations of evolutionary and breeding theory. Thus, the tree breeder often finds that his initial efforts have provided him with a good basis for directing the evolution of future forests but that there now exists a vast array of new selection theories. This book is a guide for forest geneticists to the more useful techniques and theories of that collection of applied mathematics, statistics, population biology, and genetics which is collectively called quantitative genetics. Those parts of the theoretical and analytical techniques which can be useful in forestry are reviewed. However, there is no general review of the forest genetics litera- ture. No detailed instructions on breeding mechanics or seed pro- duction are given, nor are many specific population or provenance studies reviewed excent to illustrate how the basic principles and theories are applied. Within most chanters, a skeletal guide to the necessary concepts is given with applications to forestry. Often, topics which are not immediately applicable to forestry are dis- cussed because of their potential future importance as our scien- tific knowledge increases. For the most part, the book requires undergraduate college-level mathematics, statistics, and genetics. Several
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