Computer Simulation and Computer Algebra - Lectures for Beginners

Part I Genetic Linkage Map
1 Map Functions
1.1 Physical map and genetic map
1.2 Derivation of map functions
1.3 Haldane map function
1.4 Kosambi map function
2 Recombination Fraction
2.1 Mating designs
2.2 Maximum likelihood estimation of recombination fraction
2.3 Standard error and significance test
2.4 Fisher's scoring algorithm for estimating
2.5 EM algorithm for estimating
3 Genetic Map Construction
3.1 Criteria of optimality
3.2 Search algorithms
3.2.1 Exhaustive search
3.2.2 Heuristic search
3.2.3 Simulated annealing
3.2.4 Branch and bound
3.3 Bootstrap confidence of a map
4 Multipoint Analysis of Mendelian Loci
4.1 Joint distribution of multiple locus genotype
4.1.1 BC design
4.1.2 F2 design
4.1.3 Four-way cross design
4.2 Incomplete genotype information
4.2.1 Partially informative genotype
4.2.2 BC and F2 are special cases of FW
4.2.3 Dominance and missing markers
4.3 Conditional probability of a missing marker genotype
4.4 Joint estimation of recombination fractions
4.5 Multipoint analysis for m markers
4.6 Map construction with unknown recombination fractions
Part II Analysis of Quantitative Traits
5 Basic Concepts of Quantitative Genetics
5.1 Gene frequency and genotype frequency
5.2 Genetic effects and genetic variance
5.3 Average effect of allelic substitution
5.4 Genetic variance components
5.5 Heritability
5.6 An F2 family is in Hardy-Weinberg equilibrium
6 Major Gene Detection
6.1 Estimation of major gene effect
6.1.1 BC design
6.1.2 F2 design
6.2 Hypothesis tests
6.2.1 BC design
6.2.2 F2 design
6.3 Scale of the genotype indicator variable
6.4 Statistical power
6.4.1 Type I error and statistical power
6.4.2 Wald-test statistic
6.4.3 Size of a major gene
6.4.4 Relationship between W-test and Z-test
6.4.5 Extension to dominance effect
7 Segregation Analysis
7.1 Gaussian mixture distribution
7.2 EM algorithm
7.2.1 Closed form solution
7.2.2 EM steps
7.2.3 Derivation of the EM algorithm
7.2.4 Proof of the EM algorithm
7.3 Hypothesis tests
7.4 Variances of estimated parameters
7.5 Estimation of the mixing proportions
8 Genome Scanning for Quantitative Trait Loci
8.1 The mouse data
8.2 Genome scanning
8.3 Missing genotypes
8.4 Test statistics
8.5 Bonferroni correction
8.6 Permutation test
8.7 Piepho's approximate critical value
8.8 Theoretical consideration
9 Interval Mapping
9.1 Least squares method
9.2 Weighted least squares
9.3 Fisher scoring
9.4 Maximum likelihood method
9.4.1 EM algorithm
9.4.2 Variance-covariance matrix of ˆθ
9.4.3 Hypothesis test
9.5 Remarks on the four methods of interval mapping
10 Interval Mapping for Ordinal Traits
10.1 Generalized linear model
10.2 ML under homogeneous variance
10.3 ML under heterogeneous variance
10.4 ML under mixture distribution
10.5 ML via the EM algorithm
10.6 Logistic analysis
10.7 Example
11 Mapping Segregation Distortion Loci
11.1 Probabilistic model
11.1.1 The EM Algorithm
11.1.2 Hypothesis test
11.1.3 Variance matrix of the estimated parameters
11.1.4 Selection coefficient and dominance
11.2 Liability model
11.2.1 EM algorithm
11.2.2 Variance matrix of estimated parameters
11.2.3 Hypothesis test
11.3 Mapping QTL under segregation distortion
11.3.1 Joint likelihood function
11.3.2 EM algorithm
11.3.3 Variance-covariance matrix of estimated parameters
11.3.4 Hypothesis tests
11.3.5 Example
12 QTL Mapping in Other Populations
12.1 Recombinant inbred lines
12.2 Double haploids
12.3 Four-way crosses
12.4 Full-sib family
12.5 F2 population derived from outbreds
12.6 Example
13 Random Model Approach to QTL Mapping
13.1 Identity-by-descent (IB