Over the past several decades an enormous body of quantitative-genetic theory and empirical work has accumulated, nearly independently, in the fields of evolutionary biology, plant and animal breeding, and human genetics. The first of a two-volume set, this book attempts to integrate this diverse body of literature, focusing primarily on the basic biological properties of quantitative traits and on the statistical approaches to analyzing such characters. Starting from first principles, the book is accessible to the reader with only a rudimentary knowledge of genetics and/or statistics. Substantial coverage is given to the rapidly expanding area of QTL mapping and characterization. Volume 2, the writing of which is well underway, will focus on the evolutionary dynamics of quantitative characters under natural and/or artificial selection and random genetic drift.

1. An Overview of Quantitative Genetics

• The Adaptationist Approach to Phenotypic Evolution
• The Quantitative-genetic Approach to Phenotypic Evolution
• Historical Background
• The Major Goals of Quantitative Genetics
• 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 value
  • Regression of offspring phenotype on mid-parent 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
• Fisher's Decomposition of the Genotypic Value
• Partitioning the Genetic Variance
• Additive Effects, Average Excesses, and Breeding Values
• Generalization of the Linear Model
• The Basis of Dominance

5. Sources of Genetic Variation for Multilocus Traits

• Epistasis
• A General Least-squares Model for Genetic Effects
  • Extension to haploids and polyploids
• Linkage
  • Estimation of gametic-phase disequilibrium
• Effect of Gametic-phase Disequilibrium on the Genetic Variance
  • The evidence

6. Sources 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 Origin
• Genotype X Environment Interaction

7. Resemblance Between Relatives

• 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 to Matrix Algebra and Linear Models

• Multiple Regression
  • An application to multivariate selection
• Elementary Matrix Algebra
  • Basic notation
  • Partitioned matrices
  • Addition and subtraction
  • Scalar multiplication
  • Matrix multiplication
  • Transposition
  • Inverses and solutions to systems of equations
  • Determinants and minors
  • Computing inverses
• Expectations of Random Vectors and Matrices
  • Quadratic and bilinear forms
  • Variance-covariance matrices of transformed vectors
  • Expectations of quadratic products
• The Multivariate Normal Distribution
  • Properties of the MVN
• Overview of Linear Models
  • Polynomial regressions and interaction effects
  • Fixed vs . random effects
  • Ordinary least squares
  • Generalized least squares
  • Chi-square and F-distributions
  • Sums of squares
  • Hypothesis testing

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 line-cross method
  • Effect of the leading factor
  • Extension to haploids
• Other Biometrical Approaches Gene Number Estimation
  • The inbred-backcross technique
  • Genotype assay
  • Panse's technique

10. Inbreeding Depression

• The Genetic Basis of Inbreeding Depression
  • A more general model
• Methodological Considerations
  • Single-generation analysis
  • Multigenerational analysis
  • Ritland's method
  • Epistasis and inbreeding depression
  • Variance in inbreeding depression
• The Evidence
  • Purging inbreeding depression
• The 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
• Removal of Interaction Effects
• Developmental Maps, Canalization, and Genetic Assimilation
  • Estimating developmental maps
  • Selection and canalization
• Genetic assimilation

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
• Segregation Analysis Likelihood Functions for Full-sib Families
  • Single major gene
  • Common-family effects
  • Polygenic background
  • Other extensions
  • Ascertainment bias
  • Estimating individual genotypes
• Dichotomous and Polychotomous Traits
  • Single-locus penetrance model
  • Major gene plus a polygenic background

14. Basic Concepts of Marker-based Analysis

• Classical Approaches
  • Chromosomal assays
  • Thoday's method
  • Genetics of bristle number
  • Genetics of Drosophila speciation
• Molecular Markers
• Genetic Maps
  • Map distances vs. recombination frequencies
  • How many markers are needed?
• Marker-trait associations
  • Selective genotyping and progeny testing
  • Recombinant inbred lines
  • 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 Disease 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
• 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, given marker genotypes
  • Conditional probabilities for common designs
  • Expected marker class means
  • Overall significance level with multiple tests
• QTL Detection and Estimation Using Linear Models
  • Other single-marker moment estimators
• Detection and Estimation via Maximum Likelihood
  • Hypothesis testing and estimation
  • ML interval mapping
  • Tests of significance for ML interval mapping
  • Precision of ML estimates of QTL position
  • Haley-Knott regressions
• Dealing with Multiple QTLs
  • Marker-difference regression
  • Interval mapping with marker cofactors
  • Detecting multiple linked QTLs
• Sample Sizes Required for QTL Detection
  • Power under selective genotyping
  • Power and repeatability 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 lines of maize
  • 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
  • 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
  • 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 for 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

17. Parent-offspring Regression

• Estimation Procedures
  • Balanced data
  • Unequal family sizes
  • Standardization of data from the different sexes
• Precision of Estimates
• Optimum Experimental Design
  • 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 II
  • The average degree of dominance
  • The Cockerham-Weir model
• Diallels
  • Pooled reciprocals, no self crosses
  • Reciprocals, no pure lines
  • 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 Correlation
  • Pairwise comparison of relatives
  • Nested analysis of variance and covariance
  • Regression of family means
• Components of the Phenotypic Correlation
  • Phenotypic correlations as surrogates of genetic correlations
• Statistical Issues
  • Hypothesis tests
  • Standard errors
  • Bias due to selection
• Applications
  • Genetic basis of population differentiation
  • The homogeneity of genetic covariance matrices among species
  • Evolutionary allometry
  • Evolution of life-history characters

22. Genotype X Environment Interaction

• Genetic Correlation Across Two Environments
  • Estimation procedures
• Two-way Analysis of Variance
  • Relationship to Falconer's correlation across environments
• Further Characterization of Interaction Effects
  • Joint-regression analysis
  • Testing for cross-over interaction
  • Concepts of stability and plasticity
  • Additional issues
• 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
  • Bondari's experiment
• 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 Correlations Among Threshold Traits
• Heritability on the Observed Scale

26. Estimation of Breeding Values

• The General Mixed Model
• Estimating Fixed Effects and Predicting Random Effects
  • Estimability of fixed effects
  • 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 A^(-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 the ML/REML Equations
  • Derivative-based methods
  • EM methods
  • Additional approaches
• A Molecular-marker Based Method for Inferring Variance Components

A1. Expectations, Variances and Covariances of Compound Variables

• The Delta Method
  • Expectations of complex variables
  • Variances of complex variables
  • Covariances of complex variables
• Variances of Variances and Covariances
• Expectations and Variances of Products
• Expectations and Variances of Ratios
  • Sampling variance of regression and correlation coefficients
  • Sampling variance of a coefficient of variation

A2. Path Analysis

• Univariate Analysis
• Bivariate Analysis
• Applications
  • Phenotypic correlation between parents and offspring
• Correlations between characters
  • Growth analysis

A3. Generalized Inverses and Singular Systems of Equations

• Estimability of fixed factors

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
• Likelihood-ratio tests for the general linear model
• Iternative methods for solving ML equations
  • Newton-Raphson methods
  • The EM algorithm
  • EM algorithm for mixture models
  • EM modifications for QTL mapping

A5. Computing the Power of Statistical Tests

• Power of normally-distributed tests
  • One-sided tests
  • Two-sided tests
  • Applications: Parent-Offspring regressions
  • Applications: QTL-detection tests using doubly-affected sib-pairs
• Power of F-ratio tests
  • Noncentral chi^2 Distributions
  • Noncentral F Distributions
  • Power of fixed effects ANOVA
  • Power of random effects ANOVA
  • Applications: power of QTL mapping in full-sib families

Created 13 November 1996, last updated 19 November 1996.

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Working table of contents for Volume 2 (still in progress)