Expanded table of Contents:
Genetics and Analysis of Quantitative Characters
You are visitor number 

since 14 November 1996 
Over the past several decades an enormous body of quantitativegenetic 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 twovolume 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.
PART I: THE GENETIC BASIS OF QUANTITATIVE VARIATION
1. An Overview of Quantitative Genetics

The Adaptationist Approach to Phenotypic Evolution

The Quantitativegenetic 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 leastsquares linear regression

Properties of leastsquares regressions

Correlation

A Taste of Quantitativegenetic Theory

Directional selection differentials and the RobertsonPrice identity

The correlation between genotypic and phenotypic value

Regression of offspring phenotype on midparent phenotype
4. Properties of Single Loci

Allele and Genotype Frequencies

The Transmission of Genetic Information

The HardyWeinberg principle

Sexlinked loci

Polyploidy

Age structure

Testing for HardyWeinberg 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 Leastsquares Model for Genetic Effects

Extension to haploids and polyploids

Linkage

Estimation of gameticphase disequilibrium

Effect of Gameticphase Disequilibrium on the Genetic Variance
6. Sources of Environmental Variation

Extension of the Linear Model to Phenotypes

Special Environmental Effects

Withinindividual 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 Gameticphase Disequilibrium

Linkage

Gameticphase disequilibrium

Assortative Mating

Polyploidy

Environmental Sources of Covariance Between Relatives

The Heritability Concept
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

Variancecovariance matrices of transformed vectors

Expectations of quadratic products

The Multivariate Normal Distribution

Overview of Linear Models

Polynomial regressions and interaction effects

Fixed vs . random effects

Ordinary least squares

Generalized least squares

Chisquare and Fdistributions

Sums of squares

Hypothesis testing
9. Analysis of Line Crosses

Expectations for Linecross Means

Estimation of Composite Effects

Hypothesis testing

Line crosses in Nicotiana rustica

Additional data

The Genetic Interpretation of Heterosis and Outbreeding Depression

Variance of Linecross Derivatives

Biometrical Approaches to the Estimation of Gene Number

The CastleWright linecross method

Effect of the leading factor

Extension to haploids

Other Biometrical Approaches Gene Number Estimation

The inbredbackcross technique

Genotype assay

Panse's technique
10. Inbreeding Depression

The Genetic Basis of Inbreeding Depression

Methodological Considerations

Singlegeneration 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

Lognormal distributions and the log transform

Tests for normality

Stabilizing the Variance

Kleckowski's transformation

General variancestabilizing transformations

The RoginskiiYablokov effect

The KlugeKerfoot 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
PART II. QUANTITATIVETRAIT LOCI
12. Polygenes and Polygenic Mutation

The Genetic Basis of Quantitativegenetic 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 BatemanMukai 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

Majorgene indices (MGI)

Nonparametric linecross tests

Mixture Models

The distribution under a mixture model

Parameter estimation

Hypothesis testing

Complex segregation analysis

Segregation Analysis Likelihood Functions for Fullsib Families

Single major gene

Commonfamily effects

Polygenic background

Other extensions

Ascertainment bias

Estimating individual genotypes

Dichotomous and Polychotomous Traits

Singlelocus penetrance model

Major gene plus a polygenic background
14. Basic Concepts of Markerbased 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?

Markertrait associations

Selective genotyping and progeny testing

Recombinant inbred lines

Bulked segregant analysis

QTL mapping by marker changes in populations under selection

Markerbased Analysis Using Nearly Isogenic Lines (NILs)

Markerbased introgressions

Fine Mapping of Disease Genes Using Populationlevel 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: Inbredline Crosses

Foundations of Linecross 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 singlemarker 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

HaleyKnott regressions

Dealing with Multiple QTLs

Markerdifference 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 longterm selection lines of maize

QTLs involved in the differences between maize and teosinte

QTLs for agespecific growth in mice

Summary of QTL mapping experiments
16. Mapping and Characterizing QTLs: Outbred Populations

Measures of Informativeness

Sib Analysis: Linear Models

A single halfsib family

Several halfsib families

Power

A single fullsib family

Several fullsib families

Sib Analysis: Maximum Likelihood

Constructing likelihood functions

Maximum Likelihood over General Pedigrees: Variance Components

The HasemanElston Regression

Estimating the number of marker genes ibd

Power and improvements

Interval mapping by a modified HasemanElston regression

Mapping Dichotomous Characters

Recurrent and relative risks for pairs of relatives

Affected sibpair tests

Power of ASP tests and related issues

Genomic scanning

Exclusion mapping and information content mapping

Affectedpedigree member tests
PART III. ESTIMATION PROCEDURES
17. Parentoffspring Regression

Estimation Procedures

Balanced data

Unequal family sizes

Standardization of data from the different sexes

Precision of Estimates

Optimum Experimental Design

Estimation of heritability in natural populations

Linearity of the Parentoffspring Regression
18. Sib Analysis

Halfsib Analysis

Oneway analysis of variance

Hypothesis testing

Sampling variance and standard errors

Confidence intervals

Negative estimates of heritability

Optimal experimental design

Unbalanced data

Resampling procedures

Fullsib analysis

Nested analysis of variance

Hypothesis testing

Sampling error

Optimal design
19. Twins and Clones

The Classical Approach

The Monozygotictwin Halfsib Method

Clonal Analysis
20. Crossclassified Designs

North Carolina Design II

The average degree of dominance

The CockerhamWeir model

Diallels

Pooled reciprocals, no self crosses

Reciprocals, no pure lines

Complete diallels

Partial diallels

HaymanJinks 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 lifehistory characters
22. Genotype X Environment Interaction

Genetic Correlation Across Two Environments

Twoway Analysis of Variance

Relationship to Falconer's correlation across environments

Further Characterization of Interaction Effects

Jointregression analysis

Testing for crossover 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

Crossfostering Experiments

Eisen's Approach

Falconer's Approach

Extension to Other Types of Relatives
24. Sex Linkage and Sexual Dimorphism

Sexlinked Loci and Dosage Compensation

Sexmodified Expression of an Autosomal Locus

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. Variancecomponent 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

Derivativebased methods

EM methods

Additional approaches

A Molecularmarker Based Method for Inferring Variance Components
APPENDICES
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
A3. Generalized Inverses and Singular Systems of Equations

Estimability of fixed factors
A4. Maximum Likelihood Estimation and Likelihoodratio Tests

Likelihood, support, and score functions

Largesample properties of MLEs

The Fisher information matrix

Likelihoodratio tests

Likelihoodratio tests for the general linear model

Iternative methods for solving ML equations

NewtonRaphson methods

The EM algorithm

EM algorithm for mixture models

EM modifications for QTL mapping
A5. Computing the Power of Statistical Tests

Power of normallydistributed tests
 Onesided tests
 Twosided tests

Applications: ParentOffspring regressions

Applications: QTLdetection tests using doublyaffected sibpairs

Power of Fratio tests

Noncentral chi^2 Distributions

Noncentral F Distributions

Power of fixed effects ANOVA

Power of random effects ANOVA

Applications: power of QTL mapping in fullsib families
Created 13 November 1996, last updated 19 November 1996.
RETURN to
Book Home page
Working
table of contents for Volume 2 (still in progress)