Genetics and Analysis of Quantitative Traits

- Contents
- Preface
I. FOUNDATIONS OF QUANTITATIVE GENETICS
1. AN OVERVIEW OF QUANTITATIVE GENETICS
The Adaptationist Approach to Phenotypic Evolution
Quantitative Genetics and Phenotypic Evolution
Historical Background
The Major Goals of Quantitative Genetics
The nature of quantitative-trait variation
The consequences of inbreeding and outcrossing
The constraints on the evolutionary process
The estimation of breeding values
The development of predictive models for evolutionary change
Mathematics in Biology
2. PROPERTIES OF DISTRIBUTIONS
Parameters of Univariate Distributions
The Normal Distribution
The truncated normal distribution
Confidence Intervals
3. COVARIANCE, REGRESSION, AND CORRELATION
Jointly Distributed Random Variables
Expectations of jointly distributed variables
Covariance
Useful identities for variances and covariances
Regression
Derivation of the least-squares linear regression
Properties of least-squares regressions
Correlation
A Taste of Quantitative-Genetic Theory
Directional selection differentials and the Robertson-Price identity
The correlation between genotypic and phenotypic values
Regression of offspring phenotype on parental phenotype
4. PROPERTIES OF SINGLE LOCI
Allele and Genotype Frequencies
The Transmission of Genetic Information
The Hardy-Weinberg principle
Sex-linked loci
Polyploidy
Age structure
Testing for Hardy-Weinberg proportions
Characterizing the Influence of a Locus on the Phenotype
The Basis of Dominance
Fisher's Decomposition of the Genotypic Value
Partitioning the Genetic Variance
Additive Effects, Average Excesses, and Breeding Values
Extensions to Multiple Alleles and Nonrandom Mating
Average excess
Additive effects
Additive genetic variance
5. SOURCES OF GENETIC VARIATION FOR MULTI-LOCUS TRAITS
Epistasis
A General Least-Squares Model for Genetic Effects
Extension to haploids and polyploids
Linkage
Estimation of gametic phase disequilibrium
Effect of Disequilibrium on the Genetic Variance
The evidence
6. COMPONENTS OF ENVIRONMENTAL VARIATION
Extension of the Linear Model to Phenotypes
Special Environmental Effects
Within-individual variation
Developmental homeostasis and homozygosity . . .'
Repeatability
General Environmental Effects of Maternal Influence
Genotype >< Environment Interaction
7. RESEMBLANCE BETWEEN RELATIVES 131
Measures of Relatedness
Coefficients of identity
Coefficients of coancestry and inbreeding
The coefficient of fraternity
The Genetic Covariance Between Relatives
The Effects of Linkage and Gametic Phase Disequilibrium
Linkage
Gametic phase disequilibrium
Assortative Mating
Polyploidy
Environmental Sources of Covariance Between Relatives
The Heritability Concept
Evolvability
8. INTRODUCTION OF MATRIX ALGEBRA AND LINEAR MODELS 177
Multiple Regression . '
An application to multivariate selection
Elementary Matrix Algebra
Basic notation
Partitioned matrices
Addition and subtraction
Multiplication . .,
Transposition
Inverses and solutions to systems of equations
Determinants and minors ;
Computing inverses
Expectations of Random Vectors and Matrices
Covariance Matrices of Transformed Vectors
The Multivariate Normal Distribution
Properties of the MVN
Overview of Linear Models
Ordinary least squares .
Generalized least squares
9. ANALYSIS OF LINE CROSSES
Expectations for Line-cross Means
Estimation of Composite Effects
Hypothesis testing
Line crosses in Nicotiana rustica
Additional data
The Genetic Interpretation of Heterosis and Outbreeding Depression
Variance of Line-cross Derivatives
Biometrical Approaches to the Estimation of Gene Number
The Castle-Wright estimator
Effect of the leading factor
Extensions to haploids
Other Biometrical Approaches to Gene Number Estimation
The inbred-backcross technique
Genotype assay
10. INBREEDING DEPRESSION
The Genetic Basis of Inbreeding Depression
A more general model
Methodological Considerations
Single-generation analysis
Multigenerational analyses
Ritland's method
Epistasis and inbreeding depression
Variance in inbreeding depression
The Evidence
Purging Inbreeding Depression
Number of Lethal Equivalents
Results from vertebrates
Results from Drosophila
Results from plants
Partial Recessives vs. Overdominance
The (A+B)/ A ratio
Estimating the average degree of dominance
Inferences from molecular markers
11. MATTERS OF SCALE
Transformations to Achieve Normality
Log-normal distributions and the log transform
Tests for normality
Stabilizing the Variance
Kleckowski's transformation
General variance stabilizing-transformations
The Roginskii-Yablokov effect
The Kluge-Kerfoot phenomenon
Allometry: the Scaling Implications of Body Size
Removing Interaction Effects
Developmental Maps, Canalization, and Genetic Assimilation
Estimating developmental maps
Selection and canalization
Genetic assimilation
II. QUANTITATIVE TRAIT LOCI
12. POLYGENES AND POLYGENIC MUTATION
The Genetic Basis of Quantitative-Genetic Variation
Major genes and isoalleles
The molecular nature of QTL variation
The Mutational Rate of Production of Quantitative Variation
Estimation from divergence experiments
Bristle numbers in Drosophila
Additional data
The Deleterious Effects of New Mutations
The Bateman-Mukai technique
Results from flies, plants, and bacteria
Analysis of natural populations
The persistence of new mutations
13. DETECTING MAJOR GENES
Elementary Tests
Departures from normality
Tests based on sibship variances
Major-gene indices (MGI)
Nonparametric line-cross tests
Mixture Models
The distribution under a mixture model
Parameter estimation
Hypothesis testing
Complex Segregation Analysis
Likelihood functions assuming a single major gene
Common-family effects
Polygenic background
Other extensions
Ascertainment bias
Estimating individual genotypes
Analysis of Discrete Characters
Single-locus penetrance model
Major gene plus a polygenic background
14. PRINCIPLES OF MARKER-BASED ANALYSIS
Classical Approaches
Chromosomal assays
Thoday's method
Genetics of Drosophila bristle number
Genetics of Drosophila speciation
Molecular Markers
Genetic Maps
Map distance vs. recombination frequencies
How many markers are needed?
Marker-trait Associations
Selective genotyping and progeny testing
Recombinant inbred lines (RILs)
Bulked segregant analysis
QTL mapping by marker changes in populations under selection
Marker-based Analysis Using Nearly Isogenic Lines (NILs)
Marker-based introgressions
Fine Mapping of Major Genes Using Population-level Disequilibrium
LD mapping in expanding populations
Candidate Loci
The transmission/ disequilibrium test
Estimating effects of candidate loci
Templeton and Sing's method: Using the historical
information in haplotypes
Cloning QTLs
Transposon tagging
Positional cloning and comparative mapping
15. MAPPING AND CHARACTERIZING QTLS: INBRED LINE CROSSES
Foundations of Line-Cross Mapping
Experimental designs
Conditional probabilities of QTL genotypes
Expected marker-class means
Marker variance and higher-order moments
Overall significance level with multiple tests
QTL Detection and Estimation Using Linear Models
QTL Detection and Estimation Via Maximum Likelihood . . .'
Likelihood maps
Precision of ML estimates of QTL position
ML interval mapping
Approximating ML interval mapping by Haley-Knott regressions
Dealing with Multiple QTLs
Marker-difference regression
Interval mapping with marker cofactors
Detecting multiple linked QTLs using standard marker-trait regressions . . 467
Sample Size Required for QTL Detection
Power under selective genotyping
Power and repeatabilty of mapping experiments
Selected Applications
The nature of transgressive segregation
QTLs involved in reproductive isolation in Mimulus
QTLs involved in protein regulation
QTLs in the Illinois long-term selection maize lines
QTLS involved in the differences between maize and teosinte
QTLs for age-specific growth in mice
Summary of QTL mapping experiments
16. MAPPING AND CHARACTERIZING QTLS: OUTBRED POPULATIONs
Measures of Informativeness
Sib Analysis: Linear Models
A single half-Sib family
Several half-Sib families
Power of Nested ANOVA Designs
A single full-Sib family . . . . . . . . . . . . . . .'
Several full-Sib families
Sib Analysis: Maximum Likelihood
Constructing likelihood functions
Maximum Likelihood over General Pedigrees: Variance Components
Estimating QTL position
The Haseman-Elston Regression
Derivation of the Haseman-Elston regression
Estimating the number of marker genes IBD
Power and improvements
Interval mapping by a modified Haseman-Elston regression
Mapping Dichotomous Characters
Recurrent and relative risks of pairs of relatives
Affected Sib-pair tests
Power of ASP tests and related issues
Genomic scanning
Exclusion mapping and information content mapping
Affected pedigree member tests
III. ESTIMATION PROCEDURES
17. PARENT-OFFSPRING REGRESSION
Estimation Procedures
Balanced data
Unequal family sizes
Standardization of data from the different sexes
Precision of Estimates
Optimum Experimental Designs
Assortative mating
Estimation of Heritability in Natural Populations
Linearity of the Parent-Offspring Regression
18. SIB ANALYSIS
Half-Sib Analysis
One-way analysis of variance
Hypothesis testing
Sampling variance and standard errors . . . . . ,
Confidence intervals
Negative estimates of heritability
Optimal experimental design
Unbalanced data
Resampling procedures
Full-sib Analysis
Nested analysis of variance
Hypothesis testing
Sampling error
Optimal design
19. TWINS AND CLONES
The Classical Approach
Heritability estimation
The Monozygotic-Twin Half-sib Method
Clonal Analysis
20. CROSS-CLASSIFIED DESIGNS
North Carolina Design
The average degree of dominance
The Cockerham-Weir model
Diallels
Pooled reciprocals, no self crosses
Reciprocals, no self crosses
Complete diallels
Partial diallels
Hayman-Jinks analysis
North Carolina Design III and the Triple Test Cross
Some Closing Statistical Considerations
21. CORRELATIONS BETWEEN CHARACTERS
Theoretical Composition of the Genetic Covariance
Estimation of the Genetic Covariance
Pairwise comparison of relatives
Nested analysis of variance and covariance
Regression of family means
Components of Phenotypic Correlation
Phenotypic correlations as surrogate estimates of genetic correlations . . . 639
Statistical Issues
Hypothesis tests
Standard errors
Bias due to selection
Applications
Evolutionary allometry
Evolution of life-history characters
Joint-regression analysis
Testing for Cross-over Interaction
Concepts of Stability and Plasticity
Additional issues
The Quantitative Genetics of Genotype X Environment Interaction
23. MATERNAL EFFECTS
Components of Variance and Covariance
Cytoplasmic transmission
Postpollination reproductive traits in plants
Cross-fostering experiments
Body weight in mice
Eisen's Approach
Falconer's Approach
Extension to Other Types of Relatives
24. SEX LINKAGE AND SEXUAL DIMORPHISM
Sex-linked Loci and Dosage Compensation
Sex-modified Expression of an Autosomal Locus
Gametic imprinting
Extension to Multiple Loci and the Covariance Between Relatives
Variation for Sexual Dimorphism
25. THRESHOLD CHARACTERS
Heritability on the Underlying Scale
Multiple Thresholds
Genetic Correlation Among Threshold Traits
Heritability on the Observed Scale
The General Mixed Model
Estimating Fixed Factors and Predicting Random Effects
Estimability of fixed factors
Standard errors
Models for the Estimation of Breeding Values
The animal model
The gametic model
The reduced animal model
Simple Rules for Computing A and Ae-1
Allowing for mutation When computing A
Joint Estimation of Several Vectors of Random Effects
BLUP estimates of dominance values
Repeated records
Maternal effects
Multiple traits
27. VARIANCE-COMPONENT ESTIMATION WITH COMPLEX PEDIGREES
ML versus REML Estimates of Variance Components
A simple example of ML versus REML
ML Estimates of Variance Components in the General Mixed Model
Standard errors of ML estimates .,
Restricted Maximum Likelihood
Multivariate analysis
ML / REML estimation in populations under selection .'
Solving ML/ REML Equations
Derivative-based methods
EM methods
Additional approaches
A Molecular-marker Based Method for Inferring Variance Components . . . . 800
IV. APPENDICES
A1. EXPECTATIONS, VARIANCES, AND COVARIANCES OF COMPOUND VARIABLES
The Delta Method
Expectations of complex variables
Variances of complex variables
Covariances of complex variables
Variance of Variances and Covariances
Expectations and Variances of Products
Expectations and Variances of Ratios
Sampling variance of regression and correlations coefficients
Sampling variance of a coefficient of variatio
A2. PATH ANALYSIS
Univariate Analysis
Bivariate Analysis
Applications
Phenotypic correlation between parents and offspring
Correlations between characters
Growth analysis
A3. FURTHER TOPICS IN MATRIX ALGEBRA AND LINEAR MODELS
Generalized Inverses and Solutions to Singular Systems of Equations
Generalized inverses
Consistency and solutions to consistent systems
Estimability of fixed factors
The Square Root of a Matrix
Derivation of the GLS Estimators
Quadratic Forms and Sums of Squares
Moments of quadratic forms
The sample variance as a quadratic form
Sums of squares expressed as a quadratic form
Testing Hypotheses About Linear Models
Equivalent Linear Models
Derivatives of Vectors and Matrices
A4. MAXIMUM LIKELIHOOD ESTIMATION AND LIKELIHOOD-RATIO TESTS
Likelihood, Support, and Score Functions
Large-sample properties of MLEs
The Fisher information matrix
Likelihood-ratio tests
The G-test
Likelihood-ratio tests for the general linear model
Iterative Methods for Solving ML Equations
Newton-Raphson methods
Expectation-maximization methods
EM for mixture model likelihoods
EM modifications for QTL mapping ................................. 865
A5. COMPUTING THE POWER OF STATISTICAL TESTS
Power of Normally Distributed Test Statistics
One-sided tests
Two-sided tests
Applications: QTL detection tests using doubly affected sib pairs
Power. of F-ratio Tests
Central and noncentral X2 distributions
Central and noncentral F distributions
Power of fixed-effects ANOVA designs
Application: Power of QTL mapping in half-sib families
Power of random-effects ANOVA designs
Application: Power of the half-sib design for variance estimation
- LITERATURE CITED
- AUTHOR INDEX
- ORGANISM AND TRAIT INDEX
- SUBJECT INDEX