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9780878934812

Genetics and Analysis of Quantitative Traits

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  • ISBN13:

    9780878934812

  • ISBN10:

    0878934812

  • Format: Hardcover
  • Copyright: 1998-01-06
  • Publisher: Sinauer Associates is an imprint of Oxford University Press

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Summary

With the emerging recognition that the expression of most characters is influenced by multiple genes and multiple environmental factors, quantitative genetics has become the central paradigm for the analysis of phenotypic variation and evolution.

Genetics and Analysis of Quantitative Traits brings together the diverse array of theoretical and empirical applications of quantitative genetics under one cover, in a way that is both comprehensive and accessible to anyone with a rudimentary understanding of statistics and genetics. What was originally envisioned as a single text has now become two, with the focus of this first book being on the basic biology and methods of analysis of quantitative characters.

Three major features of Genetics and Analysis of Quantitative Traits distinguish it from earlier work. First, it reflects the explosive influx over the past few years of quantitative-genetic thinking into evolutionary biology. Second, in animal breeding, enormous strides have been made in the development of new techniques for estimating breeding values (for the purposes of identifying elite individuals in selection programs) and for estimating variance components from samples of complex pedigrees. In this text's last two chapters, the authors outline the basic principles of complex pedigree analysis, without getting bogged down in technical details. Third, Genetics and Analysis of Quantitative Traits provides a broad overview of the newly emerging array of techniques for quantitative-trait loci (QTL) analysis, currently one of the most active fields of quantitative-genetic research.

Genetics and Analysis of Quantitative Traits contains numerous fully-worked examples and illustrations of theoretical concepts, as well as over 2,000 references with indices by subject, author, and organism. In addition, the authors maintain a World Wide Web site featuring up-to-date lists of computer programs and on-line resources, and added information on various topics presented in the text.

Author Biography


Michael Lynch is Distinguished Professor of Biology at Indiana University.

Bruce Walsh is a Professor in the Department of Ecology and Evolutionary Biology at the University of Arizona.

Table of Contents

CONTENTS i(12)
PREFACE xiii
I. FOUNDATIONS OF QUANTITATIVE GENETICS 1(318)
1. AN OVERVIEW OF QUANTITATIVE GENETICS
3(16)
The Adaptationist Approach to Phenotypic Evolution
3(1)
Quantitative Genetics and Phenotypic Evolution
4(3)
Historical Background
7(6)
The Major Goals of Quantitative Genetics
13(3)
The nature of quantitative-trait variation
13(1)
The consequences of inbreeding and outcrossing
14(1)
The constraints on the evolutionary process
15(1)
The estimation of breeding values
15(1)
The development of predictive models for evolutionary change
16(1)
Mathematics in Biology
16(3)
2. PROPERTIES OF DISTRIBUTIONS
19(16)
Parameters of Univariate Distributions
19(7)
The Normal Distribution
26(6)
The truncated normal distribution
29(3)
Confidence Intervals
32(3)
3. COVARIANCE, REGRESSION, AND CORRELATION
35(16)
Jointly Distributed Random Variables
35(1)
Expectations of jointly distributed variables
36(1)
Covariance
36(3)
Useful identities for variances and covariances
38(1)
Regression
39(4)
Derivation of the least-squares linear regression
39(2)
Properties of least-squares regressions
41(2)
Correlation
43(2)
A Taste of Quantitative-Genetic Theory
45(6)
Directional selection differentials and the Robertson-Price identity
45(2)
The correlation between genotypic and phenotypic values
47(1)
Regression of offspring phenotype on parental phenotype
48(3)
4. PROPERTIES OF SINGLE LOCI
51(30)
Allele and Genotype Frequencies
52(2)
The Transmission of Genetic Information
54(7)
The Hardy-Weinberg principle
54(2)
Sex-linked loci
56(1)
Polyploidy
57(3)
Age structure
60(1)
Testing for Hardy-Weinberg Proportions
60(1)
Characterizing the Influence of a Locus on the Phenotype
61(2)
The Basis of Dominance
63(2)
Fisher's Decomposition of the Genotypic Value
65(4)
Partitioning the Genetic Variance
69(2)
Additive Effects, Average Excesses, and Breeding Values
71(3)
Extensions to Multiple Alleles and Nonrandom Mating
74(7)
Average excess
74(1)
Additive effects
75(1)
Additive genetic variance
76(5)
5. SOURCES OF GENETIC VARIATION FOR MULTILOCUS TRAITS
81(26)
Epistasis
82(3)
A General Least-Squares Model for Genetic Effects
85(9)
Extension to haploids and polyploids
92(2)
Linkage
94(6)
Estimation of gametic phase disequilibrium
97(3)
Effect of Disequilibrium on the Genetic Variance
100(7)
The evidence
103(4)
6. COMPONENTS OF ENVIRONMENTAL VARIATION
107(24)
Extension of the Linear Model to Phenotypes
108(3)
Special Environmental Effects
111(12)
Within-individual variation
112(4)
Developmental homeostasis and homozygosity
116(5)
Repeatability
121(2)
General Environmental Effects of Maternal Influence
123(4)
Genotype x Environmental Interaction
127(4)
7. RESEMBLANCE BETWEEN RELATIVES
131(46)
Measures of Relatedness
132(9)
Coefficients of identity
133(2)
Coefficients of coancestry and inbreeding
135(5)
The coefficient of fraternity
140(1)
The Genetic Covariance Between Relatives
141(5)
The Effects of Linkage and Gametic Phase Disequilibrium
146(7)
Linkage
146(4)
Gametic phase disequilibrium
150(3)
Assortative Mating
153(8)
Polyploidy
161(1)
Environmental Sources of Covariance Between Relatives
162(8)
The Heritability Concept
170(7)
Evolvability
175(2)
8. INTRODUCTION OF MATRIX ALGEBRA AND LINEAR MODELS
177(28)
Multiple Regression
177(5)
An application to multivariate selection
180(2)
Elementary Matrix Algebra
182(10)
Basic notation
182(1)
Partitioned matrices
183(1)
Addition and subtraction
183(1)
Multiplication
184(2)
Transposition
186(1)
Inverses and solutions to systems of equations
187(2)
Determinants and minors
189(1)
Computing inverses
190(2)
Expectations of Random Vectors and Matrices
192(1)
Covariance Matrices of Transformed Vectors
193(1)
The Multivariate Normal Distribution
194(4)
Properties of the MVN
195(3)
Overview of Linear Models
198(7)
Ordinary least squares
200(2)
Generalized least squares
202(3)
9. ANALYSIS OF LINE CROSSES
205(46)
Expectations for Line-cross Means
206(7)
Estimation of Composite Effects
213(9)
Hypothesis testing
215(4)
Line crosses in Nicotiana rustica
219(2)
Additional data
221(1)
The Genetic Interpretation of Heterosis and Outbreeding Depression
222(4)
Variance of Line-cross Derivatives
226(5)
Biometrical Approaches to the Estimation of Gene Number
231(13)
The Castle-Wright estimator
233(5)
Effect of the leading factor
238(3)
Extensions to haploids
241(3)
Other Biometrical Approaches to Gene Number Estimation
244(7)
The inbred-backcross technique
244(2)
Genotype assay
246(5)
10. INBREEDING DEPRESSION
251(42)
The Genetic Basis of Inbreeding Depression
252(7)
A more general model
256(3)
Methodological Considerations
259(10)
Single-generation analysis
260(2)
Multigenerational analyses
262(4)
Ritland's method
266(1)
Epistasis and inbreeding depression
267(1)
Variance in inbreeding depression
268(1)
The Evidence
269(5)
Purging Inbreeding Depression
274(2)
Number of Lethal Equivalents
276(7)
Results from vertebrates
278(1)
Results from Drosophila
279(2)
Results from plants
281(2)
Partial Recessives vs. Overdominance
283(10)
The (A+B)/A ratio
283(1)
Estimating the average degree of dominance
284(3)
Inferences from molecular markers
287(6)
11. MATTERS OF SCALE
293(26)
Transformations to Achieve Normality
293(7)
Log-normal distributions and the log transform
294(1)
Tests for normality
295(5)
Stabilizing the Variance
300(5)
Kleckowski's transformation
300(1)
General variance stabilizing-transformations
301(1)
The Roginskii-Yablokov effect
302(3)
The Kluge-Kerfoot phenomenon
305(1)
Allometry: the Scaling Implications of Body Size
305(2)
Removing Interaction Effects
307(2)
Developmental Maps, Canalization, and Genetic Assimilation
309(10)
Estimating developmental maps
310(4)
Selection and canalization
314(2)
Genetic assimilation
316(3)
II. QUANTITATIVE TRAIT LOCI 319(216)
12. POLYGENES AND POLYGENIC MUTATION
321(32)
The Genetic Basis of Quantitative-Genetic Variation
322(6)
Major genes and isoalleles
322(1)
The molecular nature of QTL variation
323(5)
The Mutational Rate of Production of Quantitative Variation
328(12)
Estimation from divergence experiments
330(3)
Bristle numbers in Drosophila
333(2)
Additional data
335(5)
The Deleterious Effects of New Mutations
340(13)
The Bateman-Mukai technique
341(2)
Results from flies, plants, and bacteria
343(5)
Analysis of natural populations
348(3)
The persistence of new mutations
351(2)
13. DETECTING MAJOR GENES
353(26)
Elementary Tests
354(5)
Departures from normality
354(1)
Tests based on sibship variances
355(2)
Major-gene indices (MGI)
357(1)
Nonparametric line-cross tests
358(1)
Mixture Models
359(5)
The distribution under a mixture model
360(1)
Parameter estimation
360(1)
Hypothesis testing
361(3)
Complex Segregation Analysis
364(11)
Likelihood functions assuming a single major gene
366(4)
Common-family effects
370(1)
Polygenic background
371(2)
Other extensions
373(1)
Ascertainment bias
374(1)
Estimating individual genotypes
374(1)
Analysis of Discrete Characters
375(4)
Single-locus penetrance model
376(1)
Major gene plus a polygenic background
377(2)
14. PRINCIPLES OF MARKER-BASED ANALYSIS
379(52)
Classical Approaches
379(11)
Chromosomal assays
380(1)
Thoday's method
381(4)
Genetics of Drosophila bristle number
385(2)
Genetics of Drosophila speciation
387(3)
Molecular Markers
390(3)
Genetic Maps
393(5)
Map distance vs. recombination frequencies
394(3)
How many markers are needed?
397(1)
Marker-trait Associations
398(7)
Selective genotyping and progeny testing
401(1)
Recombinant inbred lines (RILs)
401(1)
Bulked segregant analysis
402(2)
QTL mapping by marker changes in populations under selection
404(1)
Marker-based Analysis Using Nearly Isogenic Lines (NILs)
405(8)
Marker-based introgressions
407(6)
Fine Mapping of Major Genes Using Population-level Disequilibrium
413(5)
LD mapping in expanding populations
414(4)
Candidate Loci
418(7)
The transmission/disequilibrium test
419(3)
Estimating effects of candidate loci
422(2)
Templeton and Sing's method: Using the historical information in haplotypes
424(1)
Cloning QTLs
425(6)
Transposon tagging
426(1)
Positional cloning and comparative mapping
426(5)
15. MAPPING AND CHARACTERIZING QTLS: INBRED LINE CROSSES
431(60)
Foundations of Line-Cross Mapping
431(11)
Experimental designs
432(1)
Conditional probabilities of QTL genotypes
433(4)
Expected marker-class means
437(2)
Marker variance and higher-order moments
439(2)
Overall significance level with multiple tests
441(1)
QTL Detection and Estimation Using Linear Models
442(3)
QTL Detection and Estimation via Maximum Likelihood
445(12)
Likelihood maps
446(2)
Precision of ML estimates of QTL position
448(2)
ML interval mapping
450(3)
Approximating ML interval mapping by Haley-Knott regressions
453(4)
Dealing with Multiple QTLs
457(12)
Marker-difference regression
459(4)
Interval mapping with marker cofactors
463(4)
Detecting multiple linked QTLs using standard marker-trait regressions
467(2)
Sample Size Required for QTL Detection
469(8)
Power under selective genotyping
474(1)
Power and repeatability of mapping experiments
474(3)
Selected Applications
477(14)
The nature of transgressive segregation
477(1)
QTLs involved in reproductive isolation in Mimulus
478(1)
QTLs involved in protein regulation
478(1)
QTLs in the Illinois long-term selection maize lines
479(2)
QTLs involved in the differences between maize and teosinte
481(3)
QTLs for age-specific growth in mice
484(1)
Summary of QTL mapping experiments
484(7)
16. MAPPING AND CHARACTERIZING QTLS: OUTBRED POPULATIONS
491(44)
Measures of Informativeness
492(3)
Sib Analysis: Linear Models
495(6)
A single half-sib family
496(2)
Several half-sib families
498(3)
Power of Nested ANOVA Designs
501(4)
A single full-sib family
502(2)
Several full-sib families
504(1)
Sib Analysis: Maximum Likelihood
505(5)
Constructing likelihood functions
507(3)
Maximum Likelihood over General Pedigrees: Variance Components
510(3)
Estimating QTL position
512(1)
The Haseman-Elston Regression
513(8)
Derivation of the Haseman-Elston regression
513(3)
Estimating the number of marker genes ibd
516(1)
Power and improvements
517(1)
Interval mapping by a modified Haseman-Elston regression
518(3)
Mapping Dichotomous Characters
521(14)
Recurrent and relative risks of pairs of relatives
523(2)
Affected sib-pair tests
525(2)
Power of ASP tests and related issues
527(2)
Genomic scanning
529(1)
Exclusion mapping and information content mapping
530(2)
Affected pedigree member tests
532(3)
III. ESTIMATION PROCEDURES 535(270)
17. PARENT-OFFSPRING REGRESSION
537(16)
Estimation Procedures
538(4)
Balanced data
538(1)
Unequal family sizes
539(3)
Standardization of data from the different sexes
542(1)
Precision of Estimates
542(1)
Optimum Experimental Designs
543(5)
Assortative mating
547(1)
Estimation of Heritability in Natural Populations
548(2)
Linearity of the Parent-Offspring Regression
550(3)
18. SIB ANALYSIS
553(28)
Half-sib Analysis
554(16)
One-way analysis of variance
556(4)
Hypothesis testing
560(1)
Sampling variance and standard errors
561(1)
Confidence intervals
562(1)
Negative estimates of heritability
563(1)
Optimal experimental design
564(2)
Unbalanced data
566(3)
Resampling procedures
569(1)
Full-sib Analysis
570(11)
Nested analysis of variance
573(1)
Hypothesis testing
574(2)
Sampling error
576(1)
Optimal design
577(4)
19. TWINS AND CLONES
581(16)
The Classical Approach
582(5)
Heritability estimation
584(3)
The Monozygotic-Twin Half-sib Method
587(5)
Clonal Analysis
592(5)
20. CROSS-CLASSIFIED DESIGNS
597(32)
North Carolina Design II
598(12)
The average degree of dominance
603(2)
The Cockerham-Weir model
605(5)
Diallels
610(9)
Pooled reciprocals, no self crosses
611(3)
Reciprocals, no self crosses
614(4)
Complete diallels
618(1)
Partial diallels
618(1)
Hayman-Jinks analysis
619(6)
North Carolina Design III and the Triple Test Cross
625(2)
Some Closing Statistical Considerations
627(2)
21. CORRELATIONS BETWEEN CHARACTERS
629(28)
Theoretical Composition of the Genetic Covariance
630(2)
Estimation of the Genetic Covariance
632(5)
Pairwise comparison of relatives
632(1)
Nested analysis of variance and covariance
633(3)
Regression of family means
636(1)
Components of Phenotypic Correlation
637(2)
Phenotypic correlations as surrogate estimates of genetic correlations
639(1)
Statistical Issues
639(9)
Hypothesis tests
641(1)
Standard errors
642(2)
Bias due to selection
644(4)
Applications
648(1)
Genetic basis of population differentiation
648(2)
The homogeneity of genetic covariance matrices among species
650(3)
Evolutionary allometry
653(2)
Evolution of life-history characters
655(2)
22. GENOTYPE x ENVIRONMENT INTERACTION
657(30)
Genetic Correlation Across Two Environments
660(6)
Estimation procedures
663(3)
Two-way Analysis of Variance
666(6)
Relationship to Falconer's correlation across environments
671(1)
Further Characterization of Interaction Effects
672(6)
Joint-regression analysis
672(6)
Testing for Cross-over Interaction
678(2)
Concepts of Stability and Plasticity
680(3)
Additional issues
682(1)
The Quantitative Genetics of Genotype x Environment Interaction
683(4)
23. MATERNAL EFFECTS
687(28)
Components of Variance and Covariance
689(7)
Cytoplasmic transmission
693(2)
Postpollination reproductive traits in plants
695(1)
Cross-fostering experiments
696(7)
Body weight in mice
700(3)
Eisen's Approach
703(3)
Bondari's experiment
703(3)
Falconer's Approach
706(5)
Extension to Other Types of Relatives
711(4)
24. SEX LINKAGE AND SEXUAL DIMORPHISM
715(12)
Sex-linked Loci and Dosage Compensation
715(3)
Sex-modified Expression of an Autosomal Locus
718(1)
Gametic imprinting
718(1)
Extension to Multiple Loci and the Covariance Between Relatives
719(5)
Variation for Sexual Dimorphism
724(3)
25. THRESHOLD CHARACTERS
727(18)
Heritability on the Underlying Scale
730(6)
Multiple Thresholds
736(3)
Genetic Correlation Among Threshold Traits
739(2)
Heritability on the Observed Scale
741(4)
26. ESTIMATION OF BREEDING VALUES
745(34)
The General Mixed Model
746(2)
Estimating Fixed Factors and Predicting Random Effects
748(7)
Estimability of fixed factors
753(1)
Standard errors
754(1)
Models for the Estimation of Breeding Values
755(7)
The animal model
755(3)
The gametic model
758(1)
The reduced animal model
759(3)
Simple Rules for Computing A and A(-1)
762(5)
Allowing for mutation when computing A
766(1)
Joint Estimation of Several Vectors of Random Effects
767(12)
BLUP estimates of dominance values
767(2)
Repeated records
769(4)
Maternal effects
773(1)
Multiple traits
774(5)
27. VARIANCE-COMPONENT ESTIMATION WITH COMPLEX PEDIGREES
779(26)
ML versus REML Estimates of Variance Components
780(4)
A simple example of ML versus REML
781(3)
ML Estimates of Variance Components in the General Mixed Model
784(5)
Standard errors of ML estimates
788(1)
Restricted Maximum Likelihood
789(4)
Multivariate analysis
792(1)
ML/REML estimation in populations under selection
792(1)
Solving ML/REML Equations
793(7)
Derivative-based methods
794(3)
EM methods
797(2)
Additional approaches
799(1)
A Molecular-marker Based Method for Inferring Variance Components
800(5)
IV. APPENDICES 805(86)
A1. EXPECTATIONS, VARIANCES, AND COVARIANCES OF COMPOUND VARIABLES
807(16)
The Delta Method
807(6)
Expectations of complex variables
808(2)
Variances of complex variables
810(3)
Covariances of complex variables
813(1)
Variance of Variances and Covariances
813(4)
Expectations and Variances of Products
817(1)
Expectations and Variances of Ratios
818(5)
Sampling variance of regression and correlations coefficients
818(1)
Sampling variance of a coefficient of variation
819(4)
A2. PATH ANALYSIS
823(12)
Univariate Analysis
823(3)
Bivariate Analysis
826(1)
Applications
826(9)
Phenotypic correlation between parents and offspring
827(2)
Correlations between characters
829(2)
Growth analysis
831(4)
A3. FURTHER TOPICS IN MATRIX ALGEBRA AND LINEAR MODELS
835(18)
Generalized Inverses and Solutions to Singular Systems of Equations
835(6)
Generalized inverses
836(1)
Consistency and solutions to consistent systems
836(3)
Estimability of fixed factors
839(2)
The Square Root of a Matrix
841(1)
Derivation of the GLS Estimators
842(1)
Quadratic Forms and Sums of Squares
843(5)
Moments of quadratic forms
843(1)
The sample variance as a quadratic form
844(2)
Sums of squares expressed as a quadratic form
846(2)
Testing Hypotheses About Linear Models
848(1)
Equivalent Linear Models
849(2)
Derivatives of Vectors and Matrices
851(2)
A4. MAXIMUM LIKELIHOOD ESTIMATION AND LIKELIHOOD-RATIO TESTS
853(16)
Likelihood, Support, and Score Functions
853(4)
Large-sample properties of MLEs
854(1)
The Fisher information matrix
855(2)
Likelihood-ratio tests
857(4)
The G-test
859(1)
Likelihood-ratio tests for the general linear model
860(1)
Iterative Methods for Solving ML Equations
861(8)
Newton-Raphson methods
861(2)
Expectation-maximization methods
863(1)
EM for mixture model likelihoods
863(2)
EM modifications for QTL mapping
865(4)
A5. COMPUTING THE POWER OF STATISTICAL TESTS
869(22)
Power of Normally Distributed Test Statistics
870(7)
One-sided tests
870(2)
Two-sided tests
872(2)
Applications: Parent-offspring regressions
874(2)
Applications: QTL detection tests using doubly affected sib pairs
876(1)
Power of F-ratio Tests
877(14)
Central and noncentral X(2) distributions
878(1)
Central and noncentral F distributions
879(1)
Power of fixed-effects ANOVA designs
880(3)
Application: Power of QTL mapping in half-sib families
883(2)
Power of random-effects ANOVA designs
885(2)
Application: Power of the half-sib design for variance estimation
887(4)
LITERATURE CITED 891(58)
AUTHOR INDEX 949(12)
ORGANISM AND TRAIT INDEX 961(10)
SUBJECT INDEX 971

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