1 Haplotype Inference

Fresh Pond Research Institute 1.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1 1.2 Introduction to Variation, SNPs, Genotypes, and Haplotypes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2 The Biological Problem • The Computational Problems • The Need for a Genetic Model • Two Major Approaches 1.3 Clark’s Algorithm and Other Rule-Based Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3 Introduction to Clark’s Algorithm • What is the Genetic Model in Clark’s Method? • The Maximum Resolution Problem • Improving Clark’s Method 1.4 The Pure Parsimony Criterion . . . . . . . . . . . . . . . . . . . . . . 1-7 Introduction to Pure Parsimony • A Conceptual Integer Programming Formulation • A More Practical Formulation • Computational Results • Further Work on Pure Parsimony 1.5 Perfect Phylogeny Haplotyping . . . . . . . . . . . . . . . . . . . . . 1-12 Introduction to Perfect Phylogeny Haplotyping • Algorithms and Programs for the PPH Problem • Uniqueness of the Solution: A Phase Transition • Related Models, Results, and Algorithms • Near-Perfect Phylogeny 1.6 Population-Genetic and Statistical Methods . . . . . . 1-19 1.7 Going Forward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-21 1.8 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-21