Page 15 - Applied Probability

8.4
8.5
Left and Right-Hand Finger Ridge Counts . . . . . . . . . . 149
8.6
. . . . . . . . . . . . . . . . . . . . . . . . . 150
QTL Mapping
8.7
Factor Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 151
A QTL Example . . . . . . . . . . . . . . . . . . . . . . . . 152
8.8
8.9 Multivariate Traits . . . . . . . . . . . . . . . . . . . . . . . 147
The Hypergeometric Polygenic Model . . . . . . . . . . . . 154
8.10 Application to Risk Prediction . . . . . . . . . . . . . . . . 157
8.11 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
8.12 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
9 Descent Graph Methods 169
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
9.2 Review of Discrete-Time Markov Chains . . . . . . . . . . . 170
9.3 The Hastings-Metropolis Algorithm and Simulated Annealing173
9.4 Descent States and Descent Graphs . . . . . . . . . . . . . . 175
9.5 Descent Trees and the Founder Tree Graph . . . . . . . . . 177
9.6 The Descent Graph Markov Chain . . . . . . . . . . . . . . 181
9.7 Computing Location Scores . . . . . . . . . . . . . . . . . . 184
9.8 Finding a Legal Descent Graph . . . . . . . . . . . . . . . . 185
9.9 Haplotyping . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
9.10 Application to Episodic Ataxia . . . . . . . . . . . . . . . . 187
9.11 The Lander-Green-Kruglyak Algorithm . . . . . . . . . . . 188
9.12 Genotyping Errors . . . . . . . . . . . . . . . . . . . . . . . 191
9.13 Marker Sharing Statistics . . . . . . . . . . . . . . . . . . . 192
9.14 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
9.15 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

10 Molecular Phylogeny 203
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
10.2 Evolutionary Trees . . . . . . . . . . . . . . . . . . . . . . . 203
10.3 Maximum Parsimony . . . . . . . . . . . . . . . . . . . . . . 205
10.4 Review of Continuous-Time Markov Chains . . . . . . . . . 209
10.5 A Nucleotide Substitution Model . . . . . . . . . . . . . . . 211
10.6 Maximum Likelihood Reconstruction . . . . . . . . . . . . . 214
10.7 Origin of the Eukaryotes . . . . . . . . . . . . . . . . . . . . 215
10.8Codon Models ... .. .. ... .. .. ... .. ... .. . 218
10.9 Variation in the Rate of Evolution . . . . . . . . . . . . . . 219
10.10Illustration of the Codon and Rate Models . . . . . . . . . . 221
10.11Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
10.12References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
11 Radiation Hybrid Mapping 231
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
11.2 Models for Radiation Hybrids . . . . . . . . . . . . . . . . . 232
11.3 Minimum Obligate Breaks Criterion . . . . . . . . . . . . . 233