Finding all maximal perfect haplotype blocks in linear time

Recent large-scale community sequencing efforts allow at an unprecedented level of detail the identification of genomic regions that show signatures of natural selection. Traditional methods for identifying such regions from individuals' haplotype data, however, require excessive computing times and therefore are not applicable to current datasets. In 2019, Cunha et al. (Advances in bioinformatics and computational biology: 11th Brazilian symposium on bioinformatics, BSB 2018, Niteroi, Brazil, October 30 - November 1, 2018, Proceedings, 2018. 10.1007/978-3-030-01722-4_3) suggested the maximal perfect haplotype block as a very simple combinatorial pattern, forming the basis of a new method to perform rapid genome-wide selection scans. The algorithm they presented for identifying these blocks, however, had a worst-case running time quadratic in the genome length. It was posed as an open problem whether an optimal, linear-time algorithm exists. In this paper we give two algorithms that achieve this time bound, one conceptually very simple one using suffix trees and a second one using the positional Burrows-Wheeler Transform, that is very efficient also in practice.Peer reviewe

Efficient Haplotype Block Matching in Bi-Directional PBWT

Efficient haplotype matching search is of great interest when large genotyped cohorts are becoming available. Positional Burrows-Wheeler Transform (PBWT) enables efficient searching for blocks of haplotype matches. However, existing efficient PBWT algorithms sweep across the haplotype panel from left to right, capturing all exact matches. As a result, PBWT does not account for mismatches. It is also not easy to investigate the patterns of changes between the matching blocks. Here, we present an extension to PBWT, called bi-directional PBWT that allows the information about the blocks of matches to be present at both sides of each site. We also present a set of algorithms to efficiently merge the matching blocks or examine the patterns of changes on both sides of each site. The time complexity of the algorithms to find and merge matching blocks using bi-directional PBWT is linear to the input size. Using real data from the UK Biobank, we demonstrate the run time and memory efficiency of our algorithms. More importantly, our algorithms can identify more blocks by enabling tolerance of mismatches. Moreover, by using mutual information (MI) between the forward and the reverse PBWT matching block sets as a measure of haplotype consistency, we found the MI derived from European samples in the 1000 Genomes Project is highly correlated (Spearman correlation r=0.87) with the deCODE recombination map

Populations in statistical genetic modelling and inference

What is a population? This review considers how a population may be defined in terms of understanding the structure of the underlying genetics of the individuals involved. The main approach is to consider statistically identifiable groups of randomly mating individuals, which is well defined in theory for any type of (sexual) organism. We discuss generative models using drift, admixture and spatial structure, and the ancestral recombination graph. These are contrasted with statistical models for inference, principle component analysis and other `non-parametric' methods. The relationships between these approaches are explored with both simulated and real-data examples. The state-of-the-art practical software tools are discussed and contrasted. We conclude that populations are a useful theoretical construct that can be well defined in theory and often approximately exist in practice

Analysis and Visualization of Local Phylogenetic Structure within Species

While it is interesting to examine the evolutionary history and phylogenetic relationship between species, for example, in a sort of tree of life, there is also a great deal to be learned from examining population structure and relationships within species. A careful description of phylogenetic relationships within species provides insights into causes of phenotypic variation, including disease susceptibility. The better we are able to understand the patterns of genotypic variation within species, the better these populations may be used as models to identify causative variants and possible therapies, for example through targeted genome-wide association studies (GWAS). My thesis describes a model of local phylogenetic structure, how it can be effectively derived under various circumstances, and useful applications and visualizations of this model to aid genetic studies. I introduce a method for discovering phylogenetic structure among individuals of a population by partitioning the genome into a minimal set of intervals within which there is no evidence of recombination. I describe two extensions of this basic method. The first allows it to be applied to heterozygous, in addition to homozygous, genotypes and the second makes it more robust to errors in the source genotypes. I demonstrate the predictive power of my local phylogeny model using a novel method for genome-wide genotype imputation. This imputation method achieves very high accuracy - on the order of the accuracy rate in the sequencing technology - by imputing genotypes in regions of shared inheritance based on my local phylogenies. Comparative genomic analysis within species can be greatly aided by appropriate visualization and analysis tools. I developed a framework for web-based visualization and analysis of multiple individuals within a species, with my model of local phylogeny providing the underlying structure. I will describe the utility of these tools and the applications for which they have found widespread use.Doctor of Philosoph

Minimum Mosaic Inference of a Set of Recombinants

International audienceIn this paper, we investigate the central problem of finding recombination events (Kececioglu & Gusfield 1998, Ukkonen 2002, Schwartz et al. 2002, Koivisto et al. 2004, Rastas & Ukkonen 2007, Wu & Gusfield 2007). It is commonly assumed that a present population is a descendent of a small number of specific sequences called founders. Due to recombination, a present sequence (called a recombinant ) is thus composed of blocks from the founders. A major question related to founder sequences is the so-called Minimum Mosaic problem: using the natural parsimony criterion for the number of recombinations, find the best founders. In this article, we prove that the Minimum Mosaic problem given haplotype recombinants with no missing values is hard for an unbounded number of founders and propose some exact exponential-time algorithms for the problem. Notice that, in (Rastas & Ukkonen 2007), Rastas et al. proved that the Minimum Mosaic problem is hard using a somewhat unrealistic mutation cost function (details provided afterwards). The aim of this paper is to provide a better complexity insight of the problem