Methods for Inferring Block-Wise Ancestral History from Haploid Sequences The Haplotype Coloring Problem

Recent evidence for a “blocky” haplotype structure to the human genome and for its importance to disease inference studies has created a pressing need for tools that identify patterns of past recombination in sequences of samples of human genes and gene regions. We present two new approaches to the reconstruction of likely recombination patterns from a set of haploid sequences which each combine combinatorial optimization techniques with statistically motivated recombination models. The first breaks the problem into two discrete steps: finding recombination sites then coloring sequences to signify the likely ancestry of each segment. The second poses the problem as optimizing a single probability function for parsing a sequence in terms of ancestral haplotypes. We explain the motivation for each method, present algorithms, show their correctness, and analyze their complexity. We illustrate and analyze the methods with results on real, contrived, and simulated datasets.