Notebook for GAQT
1
Preface
2
An Overview of Quantitative Genetics
2.1
The Adaptationist Approach to Phenotypic Evolution
2.2
Quantitative Genetics and Phenotypic Evolution
2.3
Historical Background
2.4
The Major Goals of Quantitative Genetics
2.4.1
The nature of quantitative-trait variation
2.4.2
The consequences of inbreeding and outcrossing
2.4.3
The constraints on the evolutionary process
2.4.4
The estimation of breeding values
2.4.5
The development of predictive models for evolutionary change
2.5
Mathematics in Biology
3
Properties of Distributions
3.1
Parameters of Univariate Distributions
3.2
The Normal Distribution
3.2.1
The truncated normal distribution
3.3
Confidence Intervals
4
Covariance, Regression, and Correlation
4.1
Jointly Distributed Random Variables
4.1.1
Expectations of jointly distributed variables
4.2
Covariance
4.2.1
Useful identities for variances and covariances
4.3
Regression
4.3.1
Derivation of the least-squares linear regression
4.4
Correlation
4.5
A Taste of Quantitative-Genetic Theory
4.5.1
Directional selection differentials and the Robertson-Price identity
4.5.2
The correlation between genotypic and phenotypic values
4.5.3
Regression of offspring pheotype on parental phenotype
5
Properties of Single Loci
5.1
Allele and Genotype Frequencies
5.2
The Transmission of Genetic Information
5.2.1
The Hardy-Weinberg principle
5.2.2
Sex-linked loci
5.2.3
Polyploidy
5.2.4
Age structure
5.2.5
Testing for Hardy-Weinberg propertions
5.3
Characterizzing the influence of a Locus on the Phenotype
5.4
The Basis of Dominance
5.5
Fisher’s Decomposition of the Genetypic Value
5.6
Partitioning the Genetic Variance
5.7
Additive Effects, Average Excesses, and Breeding Values
5.8
Extensions to Multiple Alleles and Nonrandom Mating
5.8.1
Average excess
5.8.2
Additive effects
5.8.3
Additive genetic variance
6
Sources of Genetic Variation for Multilocus Traits
6.1
Epistasis
6.2
A General Least-Squares Model for Genetic Effects
6.2.1
Extension to haploids and polyploids
6.3
Linkage
6.3.1
Estimation of gametic phase disequilibrium
6.4
Effect of Diseequilibrium on the Genetic Variance
6.4.1
The evidence
7
Components of Environmental Variation
7.1
Extension of the Linear Models to Phenotypes
7.2
Special Environmental Effects
7.2.1
Within-individual variations
7.2.2
Developmental homeostasis and homozygosity
7.2.3
Repeatability
7.3
General Environmental Effects of Maternal Influence
7.4
Genotype * Environment Interaction
8
Resemblance between Realtives
8.1
Measures of Relatedness
8.1.1
Coefficients of identity
8.1.2
Coefficients of coancestry and inbreeding
8.1.3
The coefficient of fraternity
8.2
The Genetic Covariance between Relatives
8.3
The effects of Linkage and Gametic Phase Disequilibrium
8.3.1
Linkage
8.3.2
Gametic phase disequilibrium
8.4
Assortative Mating
8.5
Polyploidy
8.6
Environmental Sources of Covariance Between Relatives
8.7
The Heritability Concept
8.7.1
Evolvability
9
Introduction of Matrix Algebra and Linear Models
9.1
Multiple Regression
9.1.1
An application to multivariate selection
9.2
Elementary Matrix Algebra
9.2.1
Basic notation
9.2.2
Partitioned matrices
9.2.3
Addition and subtraction
9.2.4
Multiplication
9.2.5
Transposition
9.2.6
Inverses and solutions to systems of equations
9.2.7
Determinants and minors
9.2.8
Computing inverses
9.3
Expectations of Random Vectors and Matrices
9.4
Covariance Matrices of Transformed Vectors
9.5
The Multivariate Normal Distribution
9.5.1
Properties of the MVN
9.6
Overview of Linear Models
9.6.1
Ordinary Least squares
9.6.2
Generalized least squares
10
Estimation of Breeding Values
10.1
The General Mixed Model
10.1.1
Estimating Fixed Effects and Predicting Random Effects
10.1.2
Estimability of fixed factors
10.1.3
Standard Errors
10.2
Models for the Estimation of Breeding Values
10.2.1
The animal model
10.2.2
The gametic model
10.2.3
The reduced animal model
10.3
Sample Rules for Computing
\(A\)
and
\(A^{-1}\)
10.3.1
Allowing for mutation when computing A
10.4
Joint Estimation of Several Vectors of Random Effects
10.4.1
BLUP estimates of dominance values
10.4.2
Repeated records
10.4.3
Maternal effects
10.4.4
Multiple traits
11
Variance-component estimation with complex pedigrees
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8
Resemblance between Realtives
8.1
Measures of Relatedness
8.1.1
Coefficients of identity
8.1.2
Coefficients of coancestry and inbreeding
8.1.3
The coefficient of fraternity
8.2
The Genetic Covariance between Relatives
8.3
The effects of Linkage and Gametic Phase Disequilibrium
8.3.1
Linkage
8.3.2
Gametic phase disequilibrium
8.4
Assortative Mating
8.5
Polyploidy
8.6
Environmental Sources of Covariance Between Relatives
8.7
The Heritability Concept
8.7.1
Evolvability