A simple and rapid method for calculating identity-by-descent matrices using multiple markers

A fast, partly recursive deterministic method for calculating Identity-by-Descent (IBD) probabilities was developed with the objective of using IBD in Quantitative Trait Locus (QTL) mapping. The method combined a recursive method for a single marker locus with a method to estimate IBD between sibs using multiple markers. Simulated data was used to compare the deterministic method developed in the present paper with a stochastic method (LOKI) for precision in estimating IBD probabilities and performance in the task of QTL detection with the variance component approach. This comparison was made in a variety of situations by varying family size and degree of polymorphism among marker loci. The following were observed for the deterministic method relative to MCMC: (i) it was an order of magnitude faster; (ii) its estimates of IBD probabilities were found to agree closely, even though it does not extract information when haplotypes are not known with certainty; (iii) the shape of the profile for the QTL test statistic as a function of location was similar, although the magnitude of the test statistic was slightly smaller; and (iv) the estimates of QTL variance was similar. It was concluded that the method proposed provided a rapid means of calculating the IBD matrix with only a small loss in precision, making it an attractive alternative to the use of stochastic MCMC methods. Furthermore, developments in marker technology providing denser maps would enhance the relative advantage of this method

Crossover interference and sex-specific genetic maps shape identical by descent sharing in close relatives

Simulations of close relatives and identical by descent (IBD) segments are common in genetic studies, yet most past efforts have utilized sex averaged genetic maps and ignored crossover interference, thus omitting features known to affect the breakpoints of IBD segments. We developed Ped-sim, a method for simulating relatives that can utilize either sex-specific or sex averaged genetic maps and also either a model of crossover interference or the traditional Poisson model for inter-crossover distances. To characterize the impact of previously ignored mechanisms, we simulated data for all four combinations of these factors. We found that modeling crossover interference decreases the standard deviation of pairwise IBD proportions by 10.4% on average in full siblings through second cousins. By contrast, sex-specific maps increase this standard deviation by 4.2% on average, and also impact the number of segments relatives share. Most notably, using sex-specific maps, the number of segments half-siblings share is bimodal; and when combined with interference modeling, the probability that sixth cousins have non-zero IBD sharing ranges from 9.0 to 13.1%, depending on the sexes of the individuals through which they are related. We present new analytical results for the distributions of IBD segments under these models and show they match results from simulations. Finally, we compared IBD sharing rates between simulated and real relatives and find that the combination of sex-specific maps and interference modeling most accurately captures IBD rates in real data. Ped-sim is open source and available from https://github.com/williamslab/ped-sim

A combined long-range phasing and long haplotype imputation method to impute phase for SNP genotypes

<p>Abstract</p> <p>Background</p> <p>Knowing the phase of marker genotype data can be useful in genome-wide association studies, because it makes it possible to use analysis frameworks that account for identity by descent or parent of origin of alleles and it can lead to a large increase in data quantities via genotype or sequence imputation. Long-range phasing and haplotype library imputation constitute a fast and accurate method to impute phase for SNP data.</p> <p>Methods</p> <p>A long-range phasing and haplotype library imputation algorithm was developed. It combines information from surrogate parents and long haplotypes to resolve phase in a manner that is not dependent on the family structure of a dataset or on the presence of pedigree information.</p> <p>Results</p> <p>The algorithm performed well in both simulated and real livestock and human datasets in terms of both phasing accuracy and computation efficiency. The percentage of alleles that could be phased in both simulated and real datasets of varying size generally exceeded 98% while the percentage of alleles incorrectly phased in simulated data was generally less than 0.5%. The accuracy of phasing was affected by dataset size, with lower accuracy for dataset sizes less than 1000, but was not affected by effective population size, family data structure, presence or absence of pedigree information, and SNP density. The method was computationally fast. In comparison to a commonly used statistical method (fastPHASE), the current method made about 8% less phasing mistakes and ran about 26 times faster for a small dataset. For larger datasets, the differences in computational time are expected to be even greater. A computer program implementing these methods has been made available.</p> <p>Conclusions</p> <p>The algorithm and software developed in this study make feasible the routine phasing of high-density SNP chips in large datasets.</p

Statistics on continuous IBD data: Exact distribution evaluation for a pair of full(half)-sibs and a pair of a (great-) grandchild with a (great-) grandparent

BACKGROUND: Pairs of related individuals are widely used in linkage analysis. Most of the tests for linkage analysis are based on statistics associated with identity by descent (IBD) data. The current biotechnology provides data on very densely packed loci, and therefore, it may provide almost continuous IBD data for pairs of closely related individuals. Therefore, the distribution theory for statistics on continuous IBD data is of interest. In particular, distributional results which allow the evaluation of p-values for relevant tests are of importance. RESULTS: A technology is provided for numerical evaluation, with any given accuracy, of the cumulative probabilities of some statistics on continuous genome data for pairs of closely related individuals. In the case of a pair of full-sibs, the following statistics are considered: (i) the proportion of genome with 2 (at least 1) haplotypes shared identical-by-descent (IBD) on a chromosomal segment, (ii) the number of distinct pieces (subsegments) of a chromosomal segment, on each of which exactly 2 (at least 1) haplotypes are shared IBD. The natural counterparts of these statistics for the other relationships are also considered. Relevant Maple codes are provided for a rapid evaluation of the cumulative probabilities of such statistics. The genomic continuum model, with Haldane's model for the crossover process, is assumed. CONCLUSIONS: A technology, together with relevant software codes for its automated implementation, are provided for exact evaluation of the distributions of relevant statistics associated with continuous genome data on closely related individuals

Locations and patterns of meiotic recombination in two-generation pedigrees

<p>Abstract</p> <p>Background</p> <p>Meiotic crossovers are the major mechanism by which haplotypes are shuffled to generate genetic diversity. Previously available methods for the genome-wide, high-resolution identification of meiotic crossover sites are limited by the laborious nature of the assay (as in sperm typing).</p> <p>Methods</p> <p>Several methods have been introduced to identify crossovers using high density single nucleotide polymorphism (SNP) array technologies, although programs are not widely available to implement such analyses.</p> <p>Results</p> <p>Here we present a two-generation "reverse pedigree analysis" method (analyzing the genotypes of two children relative to each parent) and a web-accessible tool to determine and visualize inheritance differences among siblings and crossover locations on each parental gamete. This approach is complementary to existing methods and uses informative markers which provide high resolution for locating meiotic crossover sites. We introduce a segmentation algorithm to identify crossover sites, and used a synthetic data set to determine that the segmentation algorithm specificity was 92% and sensitivity was 89%. The use of reverse pedigrees allows the inference of crossover locations on the X chromosome in a maternal gamete through analysis of two sons and their father. We further analyzed genotypes from eight multiplex autism families, observing a 1.462 maternal to paternal recombination ratio and no significant differences between affected and unaffected children. Meiotic recombination results from pediSNP can also be used to identify haplotypes that are shared by probands within a pedigree, as we demonstrated with a multiplex autism family.</p> <p>Conclusion</p> <p>Using "reverse pedigrees" and defining unique sets of genotype markers within pedigree data, we introduce a method that identifies inherited allelic differences and meiotic crossovers. We implemented the method in the pediSNP software program, and we applied it to several data sets. This approach uses data from two generations to identify crossover sites, facilitating studies of recombination in disease. pediSNP is available online at <url>http://pevsnerlab.kennedykrieger.org/pediSNP</url>.</p

A phasing and imputation method for pedigreed populations that results in a single-stage genomic evaluation

<p>Abstract</p> <p>Background</p> <p>Efficient, robust, and accurate genotype imputation algorithms make large-scale application of genomic selection cost effective. An algorithm that imputes alleles or allele probabilities for all animals in the pedigree and for all genotyped single nucleotide polymorphisms (SNP) provides a framework to combine all pedigree, genomic, and phenotypic information into a single-stage genomic evaluation.</p> <p>Methods</p> <p>An algorithm was developed for imputation of genotypes in pedigreed populations that allows imputation for completely ungenotyped animals and for low-density genotyped animals, accommodates a wide variety of pedigree structures for genotyped animals, imputes unmapped SNP, and works for large datasets. The method involves simple phasing rules, long-range phasing and haplotype library imputation and segregation analysis.</p> <p>Results</p> <p>Imputation accuracy was high and computational cost was feasible for datasets with pedigrees of up to 25 000 animals. The resulting single-stage genomic evaluation increased the accuracy of estimated genomic breeding values compared to a scenario in which phenotypes on relatives that were not genotyped were ignored.</p> <p>Conclusions</p> <p>The developed imputation algorithm and software and the resulting single-stage genomic evaluation method provide powerful new ways to exploit imputation and to obtain more accurate genetic evaluations.</p

Recent identity by descent in human genetic data - methods and applications

The thesis describes algorithms for detecting regions of recent identity by descent (IBD) from human genetic data and its applications in optimising resequencing studies, genomic predictions and detecting Mendelian subtypes of diseases. Firstly, we describe the algorithm ANCHAP, which scans pairs of multi-point SNP genotypes for sharing IBD of long haplotypes. A comparison with other methods shows that ANCHAP outperforms them in terms of speed or accuracy. We demonstrate the algorithm on data from population isolates - from Orcades, Croatian islands, and from a population of unrelated individuals. We compare the abundance of IBD segments between cohorts, and identify genetic regions where IBD is most common. Secondly, we verify the IBD regions detected from array data against exome sequence data. We estimate that where sharing IBD between a pair of individuals is inferred, this is confirmed by exome data in 98% of cases. Correctness of IBD detection varies with settings of ANCHAP, length of IBD segments, and position with respect to segment endpoints. We find that with sample sizes of 1000 individuals from an isolated population genotyped using a dense SNP array, and with 20% of these individuals sequenced, 65% of sequences of the un-sequenced subjects can be partially inferred. Implementation of such resequencing strategies requires an IBD-based imputation algorithm, which is outlined. Thirdly, we use recent IBD to detect carriers of Mendelian subtypes of colon cancer. We show this with the example of Lynch syndrome, which accounts for about 3% of colon cancer patients. We detect IBD sharing between known and unknown carriers around DNA mismatch-repair genes. Using the IBD relationship, we build and evaluate a model that predicts presence of Lynch Syndrome mutations. Finally, we discuss whether regions of identity by descent can be used for genomic predictions. We conclude that the utility of the inferred IBD regions depends on accuracy of detection, time to most recent common ancestors and mutation rates since

Genetic analysis of a major international collection of cultivated apple varieties reveals previously unknown historic heteroploid and inbred relationships

Domesticated apple (Malus x domestica Borkh.) is a major global crop and the genetic diversity held within the pool of cultivated varieties is important for the development of future cultivars. The aim of this study was to investigate the diversity held within the domesticated form, through the analysis of a major international germplasm collection of cultivated varieties, the UK National Fruit Collection, consisting of over 2,000 selections of named cultivars and seedling varieties. We utilised Diversity Array Technology (DArT) markers to assess the genetic diversity within the collection. Clustering attempts, using the software STRUCTURE revealed that the accessions formed a complex and historically admixed group for which clear clustering was challenging. Comparison of accessions using the Jaccard similarity coefficient allowed us to identify clonal and duplicate material as well as revealing pairs and groups that appeared more closely related than a standard parent-offspring or full-sibling relations. From further investigation, we were able to propose a number of new pedigrees, which revealed that some historically important cultivars were more closely related than previously documented and that some of them were partially inbred. We were also able to elucidate a number of parent-offspring relationships that had resulted in a number of important polyploid cultivars. This included reuniting polyploid cultivars that in some cases dated as far back as the 18th century, with diploid parents that potentially date back as far as the 13th century

Linear models for joint association and linkage QTL mapping

<p>Abstract</p> <p>Background</p> <p>Populational linkage disequilibrium and within-family linkage are commonly used for QTL mapping and marker assisted selection. The combination of both results in more robust and accurate locations of the QTL, but models proposed so far have been either single marker, complex in practice or well fit to a particular family structure.</p> <p>Results</p> <p>We herein present linear model theory to come up with additive effects of the QTL alleles in any member of a general pedigree, conditional to observed markers and pedigree, accounting for possible linkage disequilibrium among QTLs and markers. The model is based on association analysis in the founders; further, the additive effect of the QTLs transmitted to the descendants is a weighted (by the probabilities of transmission) average of the substitution effects of founders' haplotypes. The model allows for non-complete linkage disequilibrium QTL-markers in the founders. Two submodels are presented: a simple and easy to implement Haley-Knott type regression for half-sib families, and a general mixed (variance component) model for general pedigrees. The model can use information from all markers. The performance of the regression method is compared by simulation with a more complex IBD method by Meuwissen and Goddard. Numerical examples are provided.</p> <p>Conclusion</p> <p>The linear model theory provides a useful framework for QTL mapping with dense marker maps. Results show similar accuracies but a bias of the IBD method towards the center of the region. Computations for the linear regression model are extremely simple, in contrast with IBD methods. Extensions of the model to genomic selection and multi-QTL mapping are straightforward.</p