Minimum Parent-Offspring Recombination Haplotype Inference in Pedigrees

Abstract

Abstract. The problem of haplotype inference under the Mendelian law of inheritance on pedigree genotype data is studied. The minimum recombination principle states that genetic recombinations are rare and haplotypes with fewer recombinations are more likely to exist. Given genotype data on a pedigree, the problem of Minimum Recombination Haplotype Inference (MRHI) is to find a set of haplotype configurations consistent with the genotype data having the minimum number of recombinations. In this paper, we focus on a variation of the MRHI problem that gives more realistic solutions, namely the k-MRHI problem, which has the additional constraint that the number of recombinations in each parent-offspring pair is at most k. Although the k-MRHI problem is NPhard even for k = 1, the k-MRHI problem with k > 1 can be solved efficiently by dynamic programming in O(nm 3k+1 0 2 m 0 ) time by adopting an approach similar to the one used by Doi, Li and Jiang [4] on pedigrees with n nodes and at most m0 heterozygous loci in each node. In particular, the 1-MRHI problem can be solved in O(nm 4 0 2 m 0 ) time. We propose an O(n 2 m0) algorithm to find a node as the root of the pedigree tree so as to further reduce the time complexity to O(m0min(tR)), where tR is the number of feasible haplotype configuration combinations in all trios in the pedigree tree when R is the root. If the pedigree has few generations, the 1-MRHI problem can be solved in O(min{nmwhere µR is the number of heterozygous loci in the root, and l is the maximum path length from the root to the leaves in the pedigree tree. Experiments on both real and simulated data confirm the out-performance of our algorithm when compared with other popular algorithms. In most real cases, our algorithm gives the same haplotyping results but runs much faster. In some real cases, other algorithms give an answer which has the least number of recombinations, while our algorithm gives a more credible solution and runs faster.

Estimate haplotype frequencies in pedigrees

“…Several different tree pedigree structures are used in the simulation, the first pedigree is Figure 1 in [15], which is a tree with 13 nodes. The second one is Figure 8 in [9], which is a tree with 29 nodes.…”

“…The second one is Figure 8 in [9], which is a tree with 29 nodes. The third one is a 21 node pedigree from Figure 5 of [15]. The results are given in Figure 2.…”

“…Excoffier's EM algorithm was widely applied in haplotype analysis [14,15]. Unfortunately, it should calculate the frequencies of all possible haplotype pairs consistent to each given genotype, which is unbearable in storage when the haplotype length grows to more than 20 [16].…”

An overview of the haplotype problems and algorithms

“…Recently, Chin et al [6,28] developed a new problem called k-recombinant haplotype inference by adding a constraint to the number of recombinant events in a parentoffspring inheritance, which could get a more reasonable solution. This problem was also proved to be NP-hard.…”

“…Many researchers conducted an investigation into the haplotype problem [2][3][4][5], and we also did some research work in this area [6][7][8][9]. In general, four categories of haplotype problems are widely studied: the haplotype assembly problem, the haplotype inference problem, the haplotype block partition problem and the haplotype tagging SNP selection problem.…”