Efficient haplotype block recognition of very long and dense genetic sequences

Abstract

BackgroundThe new sequencing technologies enable to scan very long and dense genetic sequences, obtaining datasets of genetic markers that are an order of magnitude larger than previously available. Such genetic sequences are characterized by common alleles interspersed with multiple rarer alleles. This situation has renewed the interest for the identification of haplotypes carrying the rare risk alleles. However, large scale explorations of the linkage-disequilibrium (LD) pattern to identify haplotype blocks are not easy to perform, because traditional algorithms have at least Θ(n2) time and memory complexity.ResultsWe derived three incremental optimizations of the widely used haplotype block recognition algorithm proposed by Gabriel et al. in 2002. Our most efficient solution, called MIG ++, has only Θ(n) memory complexity and, on a genome-wide scale, it omits >80% of the calculations, which makes it an order of magnitude faster than the original algorithm. Differently from the existing software, the MIG ++ analyzes the LD between SNPs at any distance, avoiding restrictions on the maximal block length. The haplotype block partition of the entire HapMap II CEPH dataset was obtained in 457 hours. By replacing the standard likelihood-based D′ variance estimator with an approximated estimator, the runtime was further improved. While producing a coarser partition, the approximate method allowed to obtain the full-genome haplotype block partition of the entire 1000 Genomes Project CEPH dataset in 44 hours, with no restrictions on allele frequency or long-range correlations. These experiments showed that LD-based haplotype blocks can span more than one million base-pairs in both HapMap II and 1000 Genomes datasets. An application to the North American Rheumatoid Arthritis Consortium (NARAC) dataset shows how the MIG ++ can support genome-wide haplotype association studies.ConclusionsThe MIG ++ enables to perform LD-based haplotype block recognition on genetic sequences of any length and density. In the new generation sequencing era, this can help identify haplotypes that carry rare variants of interest. The low computational requirements open the possibility to include the haplotype block structure into genome-wide association scans, downstream analyses, and visual interfaces for online genome browsers.

Second-generation PLINK: rising to the challenge of larger and richer datasets

“…The PLINK 1.9 implementation combines optimizations recently developed by Taliun et al [26] with additional laziness and bit-level parallelism.…”

On the use of dense SNP marker data for the identification of distant relative pairs

“…LD models based on confidence bounds for D are also recommended [21] and implemented in popular software such as Haploview [4]. For comparison, we used a fast version of this algorithm [52] on the MICROS data using the standard thresholds. There were 69, 280 LD blocks covering 245, 341 SNPs Table 5: 101 relative pairs from the 8-generation MICROS pedigree whose most recent relationship is second cousin tested against a suite of extended cousin relationships and 'unrelated'.…”

Fast Sampling-Based Whole-Genome Haplotype Block Recognition

“…In previous work [14], we presented the MIG ++ algorithm which improves the first step of the Haploview algorithm both in terms of memory and runtime. Firstly, the use of an incremental approach avoids the need to store the LD coefficients for all SNP pairs, which reduces memory complexity to O(n).…”

“…problem, we have recently proposed a memory-efficient implementation of the Gabriel et al [3] method, termed MIG ++ [14], implemented in the LDExplorer software package in R. MIG ++ reduces the memory complexity of the Gabriel et al [3] method from quadratic to linear and improves the runtime by more than 80% using sophisticated search space pruning. With such improvement and by adopting an approximation method to estimate the LD variance [15], we were able to obtain a complete haplotype block partitioning of the 1000 Genomes Project (phase 1 release 3, see [16]), comprising 11 million SNPs, in approximately 44 hours.…”