Reconstructing Ancestral Haplotypes with a Dictionary Model

Abstract

Running head Dictionary Model for HaplotypesKeywords linkage disequilibrium; haplotype blocks; minimum description length; forward and backwards algorithms; EM algorithm. Corresponding author ABSTRACTWe propose a dictionary model for haplotypes. According to the model, a haplotype is constructed by randomly concatenating haplotype segments from a given dictionary of segments.A haplotype block is defined as a set of haplotype segments that begin and end with the same pair of markers. In this framework, haplotype blocks can overlap, and the model provides a setting for testing the accuracy of simpler models invoking only nonoverlapping blocks. Each haplotype segment in a dictionary has an assigned probability and alternate spellings that account for genotyping errors and mutation. The model also allows for missing data, unphased genotypes, and prior distribution of parameters. Likelihood evaluations rely on forward and backward recurrences similar to the ones encountered in hidden Markov models. Parameter estimation is carried out with an EM algorithm. The search for the optimal dictionary is a particularly difficult because of the variable dimension of the model space. We define a minimum description length criteria to evaluate each dictionary and use a combination of greedy search and careful initialization to select a best dictionary for a given data set. Application of the model to simulated data gives encouraging results. In a real data set, we are able to reconstruct a parsimonious dictionary that captures patterns of linkage disequilibrium well.1

Whole population, genome-wide mapping of hidden relatedness

“…Inspired by the quintessential matching algorithms for noisily homologous sequences (Altschul et al 1990;Kent 2002) GERMLINE is based on a two-stage process: First, GERMLINE detects completely identical match-seeds of potentially shared segments by creating a dictionary (Ayers et al 2006) of allele combination words across the population observed at different slices along the genome. The second stage involves extending these candidate matches to resolve likelihood of IBD by a dynamic programming algorithm along different slices.…”

A dictionary model for haplotyping, genotype calling, and association testing

“…Our recent paper [Ayers et al, 2006] adapts the dictionary model of Bussemaker et al [2000] to the description of haplotypes. The dictionary model proposed by Bussemaker et al [2000] is motivated by the problem of motif finding in DNA sequence data.…”

“…As explained in Ayers et al [2006], the intrinsic ambiguity of hidden boundary does not pose an insurmountable barrier to statistical analysis. Likelihood evaluation is efficiently accomplished using forward and backward algorithms adapted from the theory of hidden Markov chains.…”

“…In Ayers et al [2006], we describe an EM algorithm for estimating the parameters q, r and e of a dictionary. With trivial changes, the EM algorithm extends to maximum a posteriori estimation with independent Dirichlet priors on the parameters.…”

“…In Ayers et al [2006], we introduced a dictionary model that describes each haplotype as a concate-nation of conserved haplotype segments; we also showed how the model combines parsimony and accuracy in capturing linkage disequilibrium patterns. We now illustrate how this framework is helpful in haplotyping and association testing.…”