Coordinated conditional simulation with SLINK and SUP of many markers linked or associated to a trait in large pedigrees

Simulation of genotypes in pedigrees is an important tool to evaluate the power of a linkage or an association study and to assess the empirical significance of results. SLINK is a widely-used package for pedigree simulations, but its implementation has not previously been described in a published paper. SLINK was initially derived from the LINKAGE programs. Over the 20 years since its release, SLINK has been modified to incorporate faster algorithms, notably from the linkage analysis package FASTLINK, also derived from LINKAGE. While SLINK can simulate genotypes on pedigrees of high complexity, one limitation of SLINK, as with most methods based on peeling algorithms to evaluate pedigree likelihoods, is the small number of linked markers that can be generated. The software package SUP includes an elegant wrapper for SLINK that circumvents the limitation on number of markers by using descent markers generated by SLINK to simulate a much larger number of markers on the same chromosome, linked and possibly associated with a trait locus. We have released new coordinated versions of SLINK (3.0; available from http://watson.hgen.pitt.edu) and SUP (v090804; available from http://mlemire.freeshell.org/software or http://watson.hgen.pitt.edu) that integrate the two software packages. Thereby, we have removed some of the previous limitations on the joint functionality of the programs, such as the number of founders in a pedigree. We review the history of SLINK and describe how SLINK and SUP are now coordinated to permit the simulation of large numbers of markers linked and possibly associated with a trait in large pedigrees.     

pedantics: an r package for pedigree-based genetic simulation and pedigree manipulation, characterization and viewing

Analyses of pedigrees and pedigree-derived parameters (e.g. relatedness and fitness) provide some of the most informative types of studies in evolutionary biology. The r package pedantics implements tools to facilitate power and sensitivity analyses of pedigree-related studies of natural populations. Functions are available to permute pedigree data in various ways with the goal of mimicking patterns of pedigree errors and missingness that occur in studies of natural populations. Another set of functions simulates genetic and phenotypic data based on arbitrary pedigrees. Finally, functions are also available with which visual and numerical representations of pedigree structure can be generated.     

Breaking loops in large complex pedigrees

For pedigrees with multiple loops, exact likelihoods could not be computed in an acceptable time frame and thus, approximate methods are used. Some of these methods are based on breaking loops and approximations of complex pedigree likelihoods using the exact likelihood of the corresponding zero-loop pedigree. Due to ignoring loops, this method results in a loss of genetic information and a decrease in the power to detect linkage. To minimize this loss, an optimal set of loop breakers has to be selected. In this paper, we present a graph theory based algorithm for automatic selection of an optimal set of loop breakers. We propose using a total relationship between measured pedigree members as a proxy to power. To minimize the loss of genetic information, we suggest selection of such breakers whose duplication in a pedigree would be accompanied by a minimal loss of total relationship between measured pedigree members. We show that our algorithm compares favorably with other existing loop-breaker selection algorithms in terms of conservation of genetic information, statistical power and CPU time of subsequent linkage analysis. We implemented our method in a software package LOOP_EDGE, which is available at http://mga.bionet.nsc.ru/nlru/.     

Parametric and nonparametric linkage analysis: a unified multipoint approach.

In complex disease studies, it is crucial to perform multipoint linkage analysis with many markers and to use robust nonparametric methods that take account of all pedigree information. Currently available methods fall short in both regards. In this paper, we describe how to extract complete multipoint inheritance information from general pedigrees of moderate size. This information is captured in the multipoint inheritance distribution, which provides a framework for a unified approach to both parametric and nonparametric methods of linkage analysis. Specifically, the approach includes the following: (1) Rapid exact computation of multipoint LOD scores involving dozens of highly polymorphic markers, even in the presence of loops and missing data. (2) Non-parametric linkage (NPL) analysis, a powerful new approach to pedigree analysis. We show that NPL is robust to uncertainty about mode of inheritance, is much more powerful than commonly used nonparametric methods, and loses little power relative to parametric linkage analysis. NPL thus appears to be the method of choice for pedigree studies of complex traits. (3) Information-content mapping, which measures the fraction of the total inheritance information extracted by the available marker data and points out the regions in which typing additional markers is most useful. (4) Maximum-likelihood reconstruction of many-marker haplotypes, even in pedigrees with missing data. We have implemented NPL analysis, LOD-score computation, information-content mapping, and haplotype reconstruction in a new computer package, GENEHUNTER. The package allows efficient multipoint analysis of pedigree data to be performed rapidly in a single user-friendly environment.     

Identifying marker typing incompatibilities in linkage analysis.

A common problem encountered in linkage analyses is that execution of the computer program is halted because of genotypes in the data that are inconsistent with Mendelian inheritance. Such inconsistencies may arise because of pedigree errors or errors in typing. In some cases, the source of the inconsistencies is easily identified by examining the pedigree. In others, the error is not obvious, and substantial time and effort are required to identify the responsible genotypes. We have developed two methods for automatically identifying those individuals whose genotypes are most likely the cause of the inconsistencies. First, we calculate the posterior probability of genotyping error for each member of the pedigree, given the marker data on all pedigree members and allowing anyone in the pedigree to have an error. Second, we identify those individuals whose genotypes could be solely responsible for the inconsistency in the pedigree. We illustrate these methods with two examples: one a pedigree error, the second a genotyping error. These methods have been implemented as a module of the pedigree analysis program package MENDEL.     

Segregation and linkage analysis.

Computer programs are available in the software package SAGE to perform a variety of segregation and linkage analyses used by human geneticists. These methods are designed specifically to uncover major gene segregation in pedigree data coming from non-inbred populations. With the aid of a closely linked polymorphic marker, they can detect a locus that contributes as little as 10% to the variation of a quantitative trait in a pedigree sample of several hundred individuals.     

Rapid multipoint linkage analysis via inheritance vectors in the Elston-Stewart algorithm

The calculation of multipoint likelihoods of pedigree data is crucial for extracting the full available information needed for both parametric and nonparametric linkage analysis. Recent mathematical advances in both the Elston-Stewart and Lander-Green algorithms for computing exact multipoint likelihoods of pedigree data have enabled researchers to analyze data sets containing more markers and more individuals both faster and more efficiently. This paper presents novel algorithms that further extend the computational boundary of the Elston-Stewart algorithm. They have been implemented into the software package VITESSE v. 2 and are shown to be several orders of magnitude faster than the original implementation of the Elston-Stewart algorithm in VITESSE v. 1 on a variety of real pedigree data. VITESSE v. 2 was faster by a factor ranging from 168 to over 1,700 on these data sets, thus making a qualitative difference in the analysis. The main algorithm is based on the faster computation of the conditional probability of a component nuclear family within the pedigree by summing over the joint genotypes of the children instead of the parents as done in the VITESSE v. 1. This change in summation allows the parent-child transmission part of the calculation to be not only computed for each parent separately, but also for each locus separately by using inheritance vectors as is done in the Lander-Green algorithm. Computing both of these separately can lead to substantial computational savings. The use of inheritance vectors in the nuclear family calculation represents a partial synthesis of the techniques of the Lander-Green algorithm into the Elston-Stewart algorithm. In addition, the technique of local set recoding is introduced to further reduce the complexity of the nuclear family computation. These new algorithms, however, are not universally faster on all types of pedigree data compared to the method implemented in VITESSE v. 1 of summing over the parents. Therefore, a hybrid algorithm is introduced which combines the strength of both summation methods by using a numerical heuristic to decide which of the two to use for a given nuclear family within the pedigree and is shown to be faster than either method on its own. Finally, this paper discusses various complexity issues regarding both the Elston-Stewart and Lander-Green algorithms and possible future directions of further synthesis.     

Handling marker-marker linkage disequilibrium: pedigree analysis with clustered markers

Single-nucleotide polymorphisms (SNPs) are rapidly replacing microsatellites as the markers of choice for genetic linkage studies and many other studies of human pedigrees. Here, we describe an efficient approach for modeling linkage disequilibrium (LD) between markers during multipoint analysis of human pedigrees. Using a gene-counting algorithm suitable for pedigree data, our approach enables rapid estimation of allele and haplotype frequencies within clusters of tightly linked markers. In addition, with the use of a hidden Markov model, our approach allows for multipoint pedigree analysis with large numbers of SNP markers organized into clusters of markers in LD. Simulation results show that our approach resolves previously described biases in multipoint linkage analysis with SNPs that are in LD. An updated version of the freely available Merlin software package uses the approach described here to perform many common pedigree analyses, including haplotyping and haplotype frequency estimation, parametric and nonparametric multipoint linkage analysis of discrete traits, variance-components and regression-based analysis of quantitative traits, calculation of identity-by-descent or kinship coefficients, and case selection for follow-up association studies. To illustrate the possibilities, we examine a data set that provides evidence of linkage of psoriasis to chromosome 17.     

Estimating ethnic admixture from pedigree data

This paper introduces a likelihood method of estimating ethnic admixture that uses individuals, pedigrees, or a combination of individuals and pedigrees. For each founder of a pedigree, admixture proportions are calculated by conditioning on the pedigree-wide genotypes at all ancestry-informative markers. These estimates are then propagated down the pedigree to the nonfounders by a simple averaging process. The large-sample standard errors of the founders' proportions can be similarly transformed into standard errors for the admixture proportions of the descendants. These standard errors are smaller than the corresponding standard errors when each individual is treated independently. Both hard and soft information on a founder's ancestry can be accommodated in this scheme, which has been implemented in the genetic software package Mendel. The utility of the method is demonstrated on simulated data and a real data example involving Mexican families of mixed Amerindian and Spanish ancestry.     

Relatedness coefficients in pedigrees with inbred founders

We study an extension of the standard framework for pedigree analysis, in which we allow pedigree founders to be inbred. This solves a number of practical challenges in calculating coefficients of relatedness, including condensed identity coefficients. As a consequence we expand considerably the class of pedigrees for which such coefficients may be efficiently computed. An application of this is the modelling of background inbreeding as a continuous effect. We also use inbred founders to shed new light on constructibility of relatedness coefficients, i.e., the problem of finding a genealogy yielding a given set of coefficients. In particular, we show that any theoretically admissible coefficients for a pair of noninbred individuals can be produced by a finite pedigree with inbred founders. Coupled with our computational methods, implemented in the R package ribd, this allows for the first time computer analysis of general constructibility solutions, thus making them accessible for practical use.

     

A simulation module in the computer program colony for sibship and parentage analysis

A simulation module is built into the software package colony to simulate marker genotype data of individuals with a predefined parentage and sibship structure. The simulated data can then be used to compare the accuracy, robustness and computational efficiency of different methods for sibship and parentage reconstruction, to examine the impact of different parameter options in a software on its accuracy and computational efficiency and to assess the information sufficiency of a given set of markers for a sibship and parentage analysis. This computer note describes the method used for simulating genotype data with a pedigree and its possible applications. The method can quickly generate genotype data for a one‐ or two‐generation pedigree of virtually any complexity with up to 30k offspring, at up to 30k codominant or dominant loci with an arbitrary degree of linkage and a user‐defined mistyping rate. The data can be fed directly into the colony program for analysis by three sibship and parentage reconstruction methods and can also be imported into other programs such as Excel and R. With slight modification, the data can be analysed by other relationship analysis software.     

一个先天性眼球震颤家系致病基因的初步定位

为确定一个X染色体显性遗传先天性眼球震颤家系的致病基因与X染色体的连锁关系, 选用X染色体上的DXS1214、DXS1068、DXS993、DXS8035、DXS1047、DXS8033、DXS1192和DXS1232共8个微卫星DNA标记对该家系进行基因扫描与基因分型,并利用LINKAGE等软件包对基因分型结果进行分析,探讨该家系致病基因与X染色体的连锁关系。 两点连锁分析时X染色体短臂4个基因座最大LOD值均小于-1,不支持与该家系致病基因连锁; X染色体长臂4个基因座中最大LOD值达到2,提示存在较大的连锁可能性。该家系的致病基因可初步定位于X染色体长臂,且提示Xq26-Xq28区间附近可能是先天性眼球震颤一个共同的致病基因座,但区间范围仍较大,仍须进一步选择合适的微卫星标记进行精确的定位以缩小候选基因的筛查范围。Abstract： To investigate the relationship between X chromosome and obligatory gene of a pedigree with congenital nystagmus,we used the following markers: DXS1214、DXS1068、DXS993、DXS8035、DXS1047、DXS8033、DXS1192 and DXS1232.Genome screening and genotyping were conducted in this pedigree of congenital nystagmus, and linkage analysis by LINKAGE package was used to determine the potential location. The linkage was not found on the Xp ( All LOD score <-1) but on Xq (the maximum LOD score=2). The related gene of this pedigree was located on the long arm of X chromosome. We demonstrate that Xq26-Xq28 is a common locus for CMN. It bring us closer to the identification of a gene responsible for X-linked CMN.     

Improving linkage analysis in outcrossed forest trees - an example from Acacia mangium

Mapping in forest trees generally relies on outbred pedigrees in which genetic segregation is the result of meiotic recombination from both parents. The currently available mapping packages are not optimal for outcrossed pedigrees as they either cannot order phase-ambiguous data or only use pairwise information when ordering loci within linkage groups. A new package, OUTMAP, has been developed for mapping codominant loci in outcrossed trees. A comparison of maps produced using linkage data from two pedigrees of Acacia mangium Willd demonstrated that the marker orders produced using OUTMAP were consistently of higher likelihood than those produced by JOINMAP. In addition, the maps were produced more efficiently, without the need for recoding data or the detailed investigation of pairwise recombination fractions which was necessary to select the optimal marker order using JOINMAP. Distances between markers often varied from those calculated by JOINMAP, resulting in an increase in the estimated genome length. OUTMAP can be used with all segregation types to determine phase and to calculate the likelihood of alternative marker orders, with a choice of three optimisation methods.     

An algorithm of step-by-step pedigree drawing

An algorithm for drawing large, complex pedigrees containing inbred loops and multiple-mate families is presented. The algorithm is based on a step-by-step approach to imaging, when the researcher determines the direction of further extension of the scheme. The algorithm is implemented as the PedigreeQuery software package written in Java. The software has a convenient graphical interface. The software package permits constructing not only whole pedigrees, but also their fragments that are particularly interesting for research. It also allows for adding new information on the phenotypes and genotypes of pedigree members. PedigreeQuery is distributed free of charge; it is available at http://mga.bionet.msc.ru/PedigreeQuery/PedigreeQuery.html and ftp://mga.bionet.msc.ru/PedigreeQuery/.     

An Algorithm of Step-by-step Pedigree Drawing

An algorithm for drawing large, complex pedigrees containing inbred loops and multiple-mate families is presented. The algorithm is based on a step-by-step approach to imaging, when the researcher determines the direction of further extension of the scheme. The algorithm is implemented as the PedigreeQuery software package written in Java. The software has a convenient graphical interface. The software package permits constructing not only whole pedigrees, but also their fragments that are particularly interesting for research. It also allows for adding new information on the phenotypes and genotypes of pedigree members. PedigreeQuery is distributed free of charge; it is available at http://mga.bionet.msc.ru/PedigreeQuery/PedigreeQuery.html and ftp://mga.bionet.nsc.ru/PedigreeQuery/.     

The Galton–Darwin–Wedgwood Pedigree of H. H. Laughlin

A pedigree of the Galton–Darwin–Wedgwood families that was exhibited as a poster at the Third International Congress of Eugenics in 1932 at the American Museum of Natural History has been located in the archives of Truman State University in Kirksville, Missouri. This pedigree was prepared by Harry Hamilton Laughlin, Director of the Eugenics Record Office of the Carnegie Institute. The pedigree shows consanguineous marriages within the three families. A special collection of rare Darwin family photographs assembled by Leonard Darwin has also been found in the Truman State University archives. These photographs were exhibited as a poster alongside the pedigree at the 1932 Eugenics Congress. The poster of the Galton–Darwin–Wedgwood pedigree is published here, together with a tabular version providing ready access to the information contained in the pedigree. Also included are the Darwin family photographs and a biographical sketch of Laughlin. © 2010 The Linnean Society of London, Biological Journal of the Linnean Society, 2010, 101 , 228–241.     

一个可用于复杂大群体的可视化系谱绘制和分析软件

对于在遗传研究和家系研究中大的系谱结构图还很难分析。系谱的绘制通常是遗传性状的分析研究的第一步。系图可以反映整个群体的结构、每个个体之间的相互关系以及基因流的走向,便于理解遗传性状的本质。因为所用家系数目的增大和复杂性的增加,绘制1个清晰的系谱有时变得十分困难。因此开发了1种名为Pedigraph软件,可以解决这个问题。Pedigraph能够完成对于大的复杂的群体的系谱绘制工作,并能进行相应的系谱分析。初步的测试表明这个软件在研究动植物的遗传育种中是1个有用的工具,同时它也可以用于人类的群体和历史等方面的研究。     

Multipoint quantitative-trait linkage analysis in general pedigrees.

Multipoint linkage analysis of quantitative-trait loci (QTLs) has previously been restricted to sibships and small pedigrees. In this article, we show how variance-component linkage methods can be used in pedigrees of arbitrary size and complexity, and we develop a general framework for multipoint identity-by-descent (IBD) probability calculations. We extend the sib-pair multipoint mapping approach of Fulker et al. to general relative pairs. This multipoint IBD method uses the proportion of alleles shared identical by descent at genotyped loci to estimate IBD sharing at arbitrary points along a chromosome for each relative pair. We have derived correlations in IBD sharing as a function of chromosomal distance for relative pairs in general pedigrees and provide a simple framework whereby these correlations can be easily obtained for any relative pair related by a single line of descent or by multiple independent lines of descent. Once calculated, the multipoint relative-pair IBDs can be utilized in variance-component linkage analysis, which considers the likelihood of the entire pedigree jointly. Examples are given that use simulated data, demonstrating both the accuracy of QTL localization and the increase in power provided by multipoint analysis with 5-, 10-, and 20-cM marker maps. The general pedigree variance component and IBD estimation methods have been implemented in the SOLAR (Sequential Oligogenic Linkage Analysis Routines) computer package.     

Estimation and visualization of identity-by-descent within pedigrees simplifies interpretation of complex trait analysis

Linkage analysis identifies markers that appear to be co-inherited with a trait within pedigrees. The inheritance of a chromosomal segment may be probabilistically reconstructed, with missing data complicating inference. Inheritance patterns are further obscured in the analysis of complex traits, where variants in one or more genes may contribute to phenotypic variation within a pedigree. In this case, determining which relatives share a trait variant is not simple. We describe how to represent these patterns of inheritance for marker loci. We summarize how to sample patterns of inheritance consistent with genotypic and pedigree data using gl_auto, available in MORGAN v3.0. We describe identification of classes of equivalent inheritance patterns with the program IBDgraph. We finally provide an example of how these programs may be used to simplify interpretation of linkage analysis of complex traits in general pedigrees. We borrow information across loci in a parametric linkage analysis of a large pedigree. We explore the contribution of each equivalence class to a linkage signal, illustrate estimated patterns of identity-by-descent sharing, and identify a haplotype tagging the chromosomal segment driving the linkage signal. Haplotype carriers are more likely to share the linked trait variant, and can be prioritized for subsequent DNA sequencing.     

Identity-by-descent estimation and mapping of qualitative traits in large, complex pedigrees

Computing identity-by-descent sharing between individuals connected through a large, complex pedigree is a computationally demanding task that often cannot be done using exact methods. What I present here is a rapid computational method for estimating, in large complex pedigrees, the probability that pairs of alleles are IBD given the single-point genotype data at that marker for all individuals. The method can be used on pedigrees of essentially arbitrary size and complexity without the need to divide the individuals into separate subpedigrees. I apply the method to do qualitative trait linkage mapping using the nonparametric sharing statistic S(pairs). The validity of the method is demonstrated via simulation studies on a 13-generation 3028-person pedigree with 700 genotyped individuals. An analysis of an asthma data set of individuals in this pedigree finds four loci with P-values <10(-3) that were not detected in prior analyses. The mapping method is fast and can complete analyses of approximately 150 affected individuals within this pedigree for thousands of markers in a matter of hours.