Proportion of Genes Survived in Offspring Conditional on Inheritance of Flanking Markers

In mammalian genetics and perhaps in human genetics as well, it is an interesting question as to how many offspring are needed in order to have a desired chance of preserving part or the entire genome of an individual. A more practical and perhaps more important question is: given k children and DNA marker data on a particular region of interest, what proportion of one's genes has been actually passed on to his children? To answer this question, I define the concept of identity by descent proportion, or IBDP for short. The IBDP is defined to be the proportion of genetic material shared identical by descent by a group of relatives in a specified chromosomal region. I provide a novel approach to computing the mean and variance of IBDP for k (>/=2) half-sibs based on marker data, thus providing a means to compute the mean and variance of proportion of genes survived. I first show that each chromosome in an offspring can be represented by a two-state Markov chain, with the time parameter being the map distance along the chromosome. On this basis, I will show that IBDP can be written as a stochastic integral and that the computation of the EIBDP can be reduced to evaluating an integral of some elementary functions. Numerical examples are provided to illustrate the calculation.     

Gametogenesis processes and multilocus gene identity by descent.

With few exceptions, the determination of unconditional probability of genes shared identical by descent (IBD) by relatives can be very difficult, especially if the relationship is complex or if multiple loci are involved. It is particularly difficult if one needs the IBD probability in a explicit form, expressed in terms of interlocus recombination fractions. In this paper, I will further extend the concept of gametogenesis process introduced elsewhere and indicate that it completely determines the gene IBD events of interest in pedigrees. I will demonstrate that the gametogenesis process not only serves as a convenient conceptual framework in considering IBD events in pedigrees but also provides a simple yet powerful tool to solve a wide range of seemingly difficult problems. In particular, I consider the problem of multilocus IBD probability for relative pairs, k siblings, and a group of pedigree members. In addition, I consider the problem of multilocus autozygosity probability and the problem of gene preservation in close relatives.     

Distribution of genome shared identical by descent by two individuals in grandparent-type relationship

A methodology is introduced for numerical evaluation, with any given accuracy, of the cumulative probabilities of the proportion of genome shared identical by descent (IBD) on chromosome segments by two individuals in a grandparent-type relationship. Programs are provided in the popular software package Maple for rapidly implementing such evaluations in the cases of grandchild-grandparent and great-grandchild-great-grandparent relationships. Our results can be used to identify chromosomal segments that may contain disease genes. Also, exact P values in significance testing for resemblance of either a grandparent with a grandchild or a great-grandparent with a great-grandchild can be calculated. The genomic continuum model, with Haldane's model for the crossover process, is assumed. This is the model that has been used recently in the genetics literature devoted to IBD calculations. Our methodology is based on viewing the model as a special exponential family and elaborating on recent research results for such families.     

Carrier rate of APC I1307K is not increased in inflammatory bowel disease patients of Ashkenazi Jewish origin

Colorectal cancer (CRC) occurs with an increased incidence in individuals with chronic inflammatory bowel disease (IBD) of the colon. Recent data suggest that a family history of colorectal cancer is an independent risk factor for CRC in IBD, an observation that implies that genetic factors are relevant to the development of CRC in this context. Among the genetic defects associated with CRC, the APC I1307K mutation has been detected nearly exclusively in individuals of Ashkenazi Jewish (AJ) origin, occurring in 6%-7% of the AJ general population and in 10%-28% of AJ with a either a personal or family history of CRC or adenomatous polyps. These findings, together with the increased incidence of IBD in AJ, prompted the current analysis of the contribution of the APC I1307K variant of CRC in AJ IBD patients. APC I1307K carrier frequencies were determined in 306 AJ individuals affected with IBD and 308 of their unaffected relatives ascertained from a family collection obtained for the identification of IBD susceptibility genes. Prevalence of the I1307K variant was not significantly different among individuals with IBD, Crohn's disease, ulcerative colitis, and unaffected relatives (6.9%, 7.6%, 4.7%, and 6.2%, respectively), and the mutation was detected in only one of five IBD-affected individuals with a diagnosis of CRC. These results reveal that IBD patients of AJ origin carry the APC I1307K variant at the same rate as individuals within the general AJ population. Lack of an increased APC I1307K carrier rate suggests that this mutation does not account for the increased CRC susceptibility associated with IBD.     

A Random Model Approach to Interval Mapping of Quantitative Trait Loci

Mapping quantitative trait loci in outbred populations is important because many populations of organisms are noninbred. Unfortunately, information about the genetic architecture of the trait may not be available in outbred populations. Thus, the allelic effects of genes can not be estimated with ease. In addition, under linkage equilibrium, marker genotypes provide no information about the genotype of a QTL (our terminology for a single quantitative trait locus is QTL while multiple loci are referred to as QTLs). To circumvent this problem, an interval mapping procedure based on a random model approach is described. Under a random model, instead of estimating the effects, segregating variances of QTLs are estimated by a maximum likelihood method. Estimation of the variance component of a QTL depends on the proportion of genes identical-by-descent (IBD) shared by relatives at the locus, which is predicted by the IBD of two markers flanking the QTL. The marker IBD shared by two relatives are inferred from the observed marker genotypes. The procedure offers an advantage over the regression interval mapping in terms of high power and small estimation errors and provides flexibility for large sibships, irregular pedigree relationships and incorporation of common environmental and fixed effects.     

Computation of identity-by-descent proportions shared by two siblings.

I provide a novel approach to computing the mean and variance of the proportion of genetic material shared identical by descent (IBD) by sibling pairs in a specified chromosomal region, conditional on observed marker data. I first show that each chromosome in an offspring can be represented by a two-state Markov chain, with the time parameter being the map distance along the chromosome. On this basis, I show that IBD proportion can be written as a stochastic integral and that the computation of its mean and variance can be reduced to evaluation of an integral of some elementary functions. In addition, I show how Goldgar's model can be extended to include dominance effects. Several examples are provided to illustrate the calculation.     

A Monte Carlo algorithm for computing the IBD matrices using incomplete marker information

Identity-By-Descent (IBD) is a general measurement of the relationship between two groups of genes. If the two groups consist of two homologous genes, one from each individual, the IBD is called the coancestry between the two individuals. Coancestry is an important concept in both population and quantitative genetics. It is the probability that both genes are copies of the same gene in the genealogy. The average coancestry value at a random locus in a population reflects the level of population diversity, effective population size, the level of inbreeding and other attributes. Coancestry is also the building block for the covariance structure used to estimate the additive genetic variance component for a quantitative trait. There are many other types of IBD matrices, depending on the natures of the genes included in each group, and these IBD matrices vary from locus to locus. Molecular markers distributed along the genome provide information that can be used to infer these locus-specific IBD matrices. As a result, we can estimate and test the variance components of a quantitative trait contributed by these loci using the inferred IBD matrices. In this study, we develop the concept of locus-specific epistatic IBD matrices and a Monte Carlo method to infer these IBD matrices. The method is suitable for large pedigrees with arbitrary complexity and various levels of missing marker information. With these locus-specific IBD matrices, we are ready to search for quantitative trait loci along the genome in complicated pedigrees.     

Detecting Identity by Descent and Homozygosity Mapping in Whole-Exome Sequencing Data

The detection of genetic segments of Identical by Descent (IBD) in Genome-Wide Association Studies has proven successful in pinpointing genetic relatedness between reportedly unrelated individuals and leveraging such regions to shortlist candidate genes. These techniques depend on high-density genotyping arrays and their effectiveness in diverse sequence data is largely unknown. Due to decreasing costs and increasing effectiveness of high throughput techniques for whole-exome sequencing, an influx of exome sequencing data has become available. Studies using exomes and IBD-detection methods within known pedigrees have shown that IBD can be useful in finding hidden genetic candidates where known relatives are available. We set out to examine the viability of using IBD-detection in whole exome sequencing data in population-wide studies. In doing so, we extend GERMLINE, a method to detect IBD from exome sequencing data by finding small slices of matching alleles between pairs of individuals and extending them into full IBD segments. This algorithm allows for efficient population-wide detection in dense data. We apply this algorithm to a cohort of Crohn''s Disease cases where whole-exome and GWAS array data is available. We confirm that GWAS-based detected segments are highly accurate and predictive of underlying shared variation. Where segments inferred from GWAS are expected to be of high accuracy, we compare exome-based detection accuracy of multiple detection strategies. We find detection accuracy to be prohibitively low in all assessments, both in terms of segment sensitivity and specificity. Even after isolating relatively long segments beyond 10cM, exome-based detection continued to offer poor specificity/sensitivity tradeoffs. We hypothesize that the variable coverage and platform biases of exome capture account for this decreased accuracy and look toward whole genome sequencing data as a higher quality source for detecting population-wide IBD.     

Computation of identity by descent probabilities conditional on DNA markers via a Monte Carlo Markov Chain method

The accurate estimation of the probability of identity by descent (IBD) at loci or genome positions of interest is paramount to the genetic study of quantitative and disease resistance traits. We present a Monte Carlo Markov Chain method to compute IBD probabilities between individuals conditional on DNA markers and on pedigree information. The IBDs can be obtained in a completely general pedigree at any genome position of interest, and all marker and pedigree information available is used. The method can be split into two steps at each iteration. First, phases are sampled using current genotypic configurations of relatives and second, crossover events are simulated conditional on phases. Internal track is kept of all founder origins and crossovers such that the IBD probabilities averaged over replicates are rapidly obtained. We illustrate the method with some examples. First, we show that all pedigree information should be used to obtain line origin probabilities in F2 crosses. Second, the distribution of genetic relationships between half and full sibs is analysed in both simulated data and in real data from an F2 cross in pigs.     

Computation of the Full Likelihood Function for Estimating Variance at a Quantitative Trait Locus

The proportion of alleles identical by descent (IBD) determines the genetic covariance between relatives, and thus is crucial in estimating genetic variances of quantitative trait loci (QTL). However, IBD proportions at QTL are unobservable and must be inferred from marker information. The conventional method of QTL variance analysis maximizes the likelihood function by replacing the missing IBDs by their conditional expectations (the expectation method), while in fact the full likelihood function should take into account the conditional distribution of IBDs (the distribution method). The distribution method for families of more than two sibs has not been obvious because there are n(n - 1)/2 IBD variables in a family of size n, forming an n X n symmetrical matrix. In this paper, I use four binary variables, where each indicates the event that an allele from one of the four grandparents has passed to the individual. The IBD proportion between any two sibs is then expressed as a function of the indicators. Subsequently, the joint distribution of the IBD matrix is derived from the distribution of the indicator variables. Given the joint distribution of the unknown IBDs, a method to compute the full likelihood function is developed for families of arbitrary sizes.     

The architecture of long-range haplotypes shared within and across populations

Homologous long segments along the genomes of close or remote relatives that are identical by descent (IBD) from a common ancestor provide clues for recent events in human genetics. We set out to extensively map such IBD segments in large cohorts and investigate their distribution within and across different populations. We report analysis of several data sets, demonstrating that IBD is more common than expected by na?ve models of population genetics. We show that the frequency of IBD pairs is population dependent and can be used to cluster individuals into populations, detect a homogeneous subpopulation within a larger cohort, and infer bottleneck events in such a subpopulation. Specifically, we show that Ashkenazi Jewish individuals are all connected through transitive remote family ties evident by sharing of 50 cM IBD to a publicly available data set of less than 400 individuals. We further expose regions where long-range haplotypes are shared significantly more often than elsewhere in the genome, observed across multiple populations, and enriched for common long structural variation. These are inconsistent with recent relatedness and suggest ancient common ancestry, with limited recombination between haplotypes.     

基于高密度单核苷酸多态性的共祖远亲缘关系预测算法准确性研究

目的 研究构建基于共祖（identity-by-descent，IBD）片段算法预测远亲缘关系分析流程并评估预测准确性。方法 采用高密度单核苷酸多态性（single nucleotide polymorphism，SNP）芯片对253份家系样本进行检测，研究基于IBD片段算法的分析流程进行两两个体间亲缘关系预测，评估预测准确性。随机减少SNP位点，评估位点数对算法预测准确性的影响。结果 IBD片段算法预测1~7级亲缘关系平均置信区间准确率为94.72%，预测可信度为99.77%，6级及以上亲缘关系预测时出现假阴性。随着SNP数量减少，预测准确性会出现一定程度的下降。结论 IBD片段算法可用于7级以内亲缘关系的预测，该算法在群体遗传学、法医遗传学等领域有重要应用价值。     

The trouble with isolation by distance

The genetic population structure of many species is characterised by a pattern of isolation by distance (IBD): due to limited dispersal, individuals that are geographically close tend to be genetically more similar than individuals that are far apart. Despite the ubiquity of IBD in nature, many commonly used statistical tests are based on a null model that is completely non-spatial, the Island model. Here, I argue that patterns of spatial autocorrelation deriving from IBD present a problem for such tests as it can severely bias their outcome. I use simulated data to illustrate this problem for two widely used types of tests: tests of hierarchical population structure and the detection of loci under selection. My results show that for both types of tests the presence of IBD can indeed lead to a large number of false positives. I therefore argue that all analyses in a study should take the spatial dependence in the data into account, unless it can be shown that there is no spatial autocorrelation in the allele frequency distribution that is under investigation. Thus, it is urgent to develop additional statistical approaches that are based on a spatially explicit null model instead of the non-spatial Island model.     

Evolutionary dynamics of n-player games played by relatives

One of the core concepts in social evolution theory is kin selection. Kin selection provides a perspective to understand how natural selection operates when genetically similar individuals are likely to interact. A family-structured population is an excellent example of this, where relatives are engaged in social interactions. Consequences of such social interactions are often described in game-theoretical frameworks, but there is a growing consensus that a naive inclusive fitness accounting with dyadic relatedness coefficients are of limited use when non-additive fitness effects are essential in those situations. Here, I provide a general framework to analyse multiplayer interactions among relatives. Two important results follow from my analysis. First, it is generally necessary to know the n-tuple genetic association of family members when n individuals are engaged in social interactions. However, as a second result, I found that, for a special class of games, we need only measures of lower-order genetic association to fully describe its evolutionary dynamics. I introduce the concept of degree of the game and show how this degree is related to the degree of genetic association.     

Identity-by-descent approach to gene localisation in eight individuals affected by keratoconus from north-west Tasmania,Australia

The minimum physical distance surrounding a candidate gene has been determined in founder populations by studying allele sharing and then mapping historical recombination events. In this study, we developed a novel minimalistic approach by using the genetically isolated population of Tasmania, Australia, to identify candidate gene loci in a small number of individuals of unknown genetic relationship affected by a dominant disorder. Keratoconus, an inheritable non-inflammatory progressive degeneration of the cornea, is present at a five-fold increased incidence in Burnie, a coastal town on the island of Tasmania. Based on the fundamental assumption that individuals with keratoconus from this town are likely to be related through a founder effect, a 10-cM interval genome scan was conducted on six patients of undefined genetic relationship and one affected sib-pair to identify commonly shared chromosomal segments for the elucidation of candidate gene loci. Analysis of allele sharing revealed four markers on three chromosomes where all eight individuals shared a common allele on at least one chromosome, and thirteen markers where all but one patient shared common alleles. No excess of allele sharing was observed at any marker tested on chromosome 21, a suggested candidate chromosome for keratoconus. Further analysis of positive loci revealed suggestive association at 20q12, where significant deviation in allele frequency D20S119 ( P=2.1 x 10(-5)) is observed when additional Tasmanian keratoconus samples are genotyped. Identification of a conserved minimal chromosomal haplotype around D20S119 in related Tasmanian patients suggests association with this locus, however association with the nearby candidate gene MMP-9 has been excluded.     

Isolation by distance and sharp discontinuities in gene frequencies: implications for the phylogeography of an alpine insect species, Carabus solieri

Analysis of genetic isolation by distance (IBD) is of prime importance for the study of processes responsible for spatial population genetic structure and is thus frequently used in case studies. However, the identification of a significant IBD pattern does not necessarily imply the absence of sharp discontinuities in gene frequencies. Therefore, identifying barriers to gene flow and/or secondary contact between differentiated entities remains a major challenge in population biology. Geographical genetic structure of 41 populations (1080 individuals) of an alpine insect species, Carabus solieri, was studied using 10 microsatellite loci. All populations were significantly differentiated and spatially structured according to IBD over the entire range. However, clustering analyses clearly identified three main clusters of populations, which correspond to geographical entities. Whereas IBD also occurs within each cluster, population structure was different according to which group of populations was considered. The southernmost cluster corresponds to the most fragmented part of the range. Consistently, it was characterized by relatively high levels of differentiation associated with low genetic diversity, and the slope of the regression of genetic differentiation against geographical distances was threefold those of the two other clusters. Comparisons of within-cluster and between-cluster IBD patterns revealed barriers to gene flow. A comparison of the two approaches, IBD and clustering analyses, provided us with valuable information with which to infer the phylogeography of the species, and in particular to propose postglacial colonization routes from two potential refugia located in Italy and in southeastern France. Our study highlights strongly the possible confounding contribution of barriers to gene flow to IBD pattern and emphasizes the utility of the model-based clustering analysis to identify such barriers.     

HapFABIA: Identification of very short segments of identity by descent characterized by rare variants in large sequencing data

Identity by descent (IBD) can be reliably detected for long shared DNA segments, which are found in related individuals. However, many studies contain cohorts of unrelated individuals that share only short IBD segments. New sequencing technologies facilitate identification of short IBD segments through rare variants, which convey more information on IBD than common variants. Current IBD detection methods, however, are not designed to use rare variants for the detection of short IBD segments. Short IBD segments reveal genetic structures at high resolution. Therefore, they can help to improve imputation and phasing, to increase genotyping accuracy for low-coverage sequencing and to increase the power of association studies. Since short IBD segments are further assumed to be old, they can shed light on the evolutionary history of humans. We propose HapFABIA, a computational method that applies biclustering to identify very short IBD segments characterized by rare variants. HapFABIA is designed to detect short IBD segments in genotype data that were obtained from next-generation sequencing, but can also be applied to DNA microarray data. Especially in next-generation sequencing data, HapFABIA exploits rare variants for IBD detection. HapFABIA significantly outperformed competing algorithms at detecting short IBD segments on artificial and simulated data with rare variants. HapFABIA identified 160 588 different short IBD segments characterized by rare variants with a median length of 23 kb (mean 24 kb) in data for chromosome 1 of the 1000 Genomes Project. These short IBD segments contain 752 000 single nucleotide variants (SNVs), which account for 39% of the rare variants and 23.5% of all variants. The vast majority—152 000 IBD segments—are shared by Africans, while only 19 000 and 11 000 are shared by Europeans and Asians, respectively. IBD segments that match the Denisova or the Neandertal genome are found significantly more often in Asians and Europeans but also, in some cases exclusively, in Africans. The lengths of IBD segments and their sharing between continental populations indicate that many short IBD segments from chromosome 1 existed before humans migrated out of Africa. Thus, rare variants that tag these short IBD segments predate human migration from Africa. The software package HapFABIA is available from Bioconductor. All data sets, result files and programs for data simulation, preprocessing and evaluation are supplied at http://www.bioinf.jku.at/research/short-IBD.     

Estimation of the inbreeding coefficient through use of genomic data

Many linkage studies are performed in inbred populations, either small isolated populations or large populations with a long tradition of marriages between relatives. In such populations, there exist very complex genealogies with unknown loops. Therefore, the true inbreeding coefficient of an individual is often unknown. Good estimators of the inbreeding coefficient (f) are important, since it has been shown that underestimation of f may lead to false linkage conclusions. When an individual is genotyped for markers spanning the whole genome, it should be possible to use this genomic information to estimate that individual's f. To do so, we propose a maximum-likelihood method that takes marker dependencies into account through a hidden Markov model. This methodology also allows us to infer the full probability distribution of the identity-by-descent (IBD) status of the two alleles of an individual at each marker along the genome (posterior IBD probabilities) and provides a variance for the estimates. We simulate a full genome scan mimicking the true autosomal genome for (1) a first-cousin pedigree and (2) a quadruple-second-cousin pedigree. In both cases, we find that our method accurately estimates f for different marker maps. We also find that the proportion of genome IBD in an individual with a given genealogy is very variable. The approach is illustrated with data from a study of demyelinating autosomal recessive Charcot-Marie-Tooth disease.