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.     

An analytical model for the estimation of chromosome substitution effects in the offspring of individuals heterozygous at a segregating marker locus

Summary Use of marker genes for quantitative traits has been suggested as a supplement to selection for livestock species. Linkage relationships can be estimated by using data from offspring of a heterozygous parent, if offspring can be positively assigned segregation of one or the other of the marker alleles. In field data, some data on offspring can be characterized and used to estimate the difference in chromosome substitution effects, but other matings result in uncertain transfer of the marker alleles. In this study, an alternative estimation procedure is proposed that would allow incorporation of data on all offspring of a heterozygous parent, even those where chromosome segregation is ambiguous. If the frequency of the marker alleles is known in the population of mates of a heterozygous individual, the mean and variance of the heterozygous offspring can be used in a generalized leastsquares model to estimate the chromosome substitution effect. When gene frequencies are not known, maximum likelihood estimates can be obtained from the data for use in a conditional estimate. Monte Carlo simulations of data following the assumed genetic model were analyzed as proposed, and parameter estimates were characterized. Estimates of chromosome substitution effects were reasonable approximations of input values. Distributions of t-statistics testing the null hypothesis of no difference between marked chromosome segments were unbiased, with only slightly larger variance than expected. Addition of data from heterozygous offspring improved the efficiency of detection of chromosome substitution effects by more than four times when marker gene frequencies were low.     

Proportion of genome shared identical by descent by relatives: concept, computation, and applications.

One widely used measure of genetic similarity for pairs of relatives is gene identity-by-descent (IBD) sharing. Genes that are copies of a single gene in a common ancestor of the individuals who now carry them are said to be IBD. One obvious extension of the IBD concept is IBD gene(s) shared by more than two individuals. In this paper, I further extend the gene IBD concept to the proportion of genomes shared IBD by every member of a group of relatives. Genome may refer either to the entire autosomal genome or to one or more chromosomal segments or regions with known lengths. Consideration of a genome instead of one or two loci has several advantages. I present a model to describe the crossover process, based on the work of K. P. Donnelly. On the basis of this model, I give a mathematical definition of the proportion of genome shared IBD by relatives, or IBDP for short. Since the distribution of the IBDP is in general very difficult to determine, and since in most applications the mean and variance of the IBDP will suffice, I then provide a method for computing the first two moments of the IBDP. Applications to assessing gene survival, to genetic resemblance between two relatives, and to gene mapping are illustrated with examples. Finally, I discuss the utility of the IBDP in other areas.     

Robust variance-components approach for assessing genetic linkage in pedigrees.

To assess evidence for genetic linkage from pedigrees, I developed a limited variance-components approach. In this method, variability among trait observations from individuals within pedigrees is expressed in terms of fixed effects from covariates and effects due to an unobservable trait-affecting major locus, random polygenic effects, and residual nongenetic variance. The effect attributable to a locus linked to a marker is a function of the additive and dominance components of variance of the locus, the recombination fraction, and the proportion of genes identical by descent at the marker locus for each pair of sibs. For unlinked loci, the polygenic variance component depends only on the relationship between the relative pair. Parameters can be estimated by either maximum-likelihood methods or quasi-likelihood methods. The forms of quasi-likelihood estimators are provided. Hypothesis tests derived from the maximum-likelihood approach are constructed by appeal to asymptotic theory. A simulation study showed that the size of likelihood-ratio tests was appropriate but that the monogenic component of variance was generally underestimated by the likelihood approach.     

Transmission test for linkage disequilibrium: the insulin gene region and insulin-dependent diabetes mellitus (IDDM).

A population association has consistently been observed between insulin-dependent diabetes mellitus (IDDM) and the "class 1" alleles of the region of tandem-repeat DNA (5'' flanking polymorphism [5''FP]) adjacent to the insulin gene on chromosome 11p. This finding suggests that the insulin gene region contains a gene or genes contributing to IDDM susceptibility. However, several studies that have sought to show linkage with IDDM by testing for cosegregation in affected sib pairs have failed to find evidence for linkage. As means for identifying genes for complex diseases, both the association and the affected-sib-pairs approaches have limitations. It is well known that population association between a disease and a genetic marker can arise as an artifact of population structure, even in the absence of linkage. On the other hand, linkage studies with modest numbers of affected sib pairs may fail to detect linkage, especially if there is linkage heterogeneity. We consider an alternative method to test for linkage with a genetic marker when population association has been found. Using data from families with at least one affected child, we evaluate the transmission of the associated marker allele from a heterozygous parent to an affected offspring. This approach has been used by several investigators, but the statistical properties of the method as a test for linkage have not been investigated. In the present paper we describe the statistical basis for this "transmission test for linkage disequilibrium" (transmission/disequilibrium test [TDT]). We then show the relationship of this test to tests of cosegregation that are based on the proportion of haplotypes or genes identical by descent in affected sibs. The TDT provides strong evidence for linkage between the 5''FP and susceptibility to IDDM. The conclusions from this analysis apply in general to the study of disease associations, where genetic markers are usually closely linked to candidate genes. When a disease is found to be associated with such a marker, the TDT may detect linkage even when haplotype-sharing tests do not.     

Marker-assisted selection to increase effective population size by reducing Mendelian segregation variance

Using both the genetic drift and inbreeding approaches, we derive more general equations for effective size (N(e)) of a diploid species under random mating. These equations show explicitly that inbreeding or genetic drift comes from two sources, the variation in the number of offspring from each parent and the variation in contribution between these parents' own paternally and maternally derived genes to their offspring. The first source can be easily and effectively controlled by choosing an equal number of offspring from each family, while the second can be manipulated by using information on genetic markers to reduce the variance due to Mendelian segregation. Marker-assisted selection (MAS) methods to increase N(e) for the whole genome with single or multiple marker loci per chromosome, different numbers of males, and females are developed and implemented in stochastic simulations. The analytical and simulation results show that, although in principle N(e) can be increased indefinitely, the efficiency of MAS is restricted in practice by the amount of marker information, the genome size, and the number of marker-genotyped offspring per family. The assumptions made in developing the theory and methods and the applications of MAS in conservation are discussed.     

Target selected insertional mutagenesis on chromosome IV of Arabidopsis using the En-I transposon system

Reverse genetics using insertional mutagenesis is an efficient experimental strategy for assessing gene functions. The maize Enhancer-Inhibitor (En-I) transposable element system was used to develop an effective reverse genetics strategy in Arabidopsis based on transposons. To generate insertion mutations in a specific chromosomal region we developed a strategy for local transposition mutagenesis. A small population of 960 plants, containing independent I transpositions was used to study local mutagenesis on chromosome IV of Arabidopsis. A total of 15 genes, located on chromosome IV, were tested for I insertions and included genes identified by the European ESSA I sequencing programme. These genes were of particular interest since homologies to other genes and gene families were identified, but their exact functions were unknown. Somatic insertions were identified for all genes tested in a few specific plants. Analysis of these progeny plants over several generations revealed that the ability to generate somatic insertions in the target gene were heritable. These genotypes that show high levels of somatic insertions can be used to identify germinal insertions in the progeny.     

Assessment of parent-of-origin effects in linkage analysis of quantitative traits

Methods are presented for incorporation of parent-of-origin effects into linkage analysis of quantitative traits. The estimated proportion of marker alleles shared identical by descent is first partitioned into a component derived from the mother and a component derived from the father. These parent-specific estimates of allele sharing are used in variance-components or Haseman-Elston methods of linkage analysis so that the effect of the quantitative-trait locus carried on the maternally derived chromosome is potentially different from the effect of the locus on the paternally derived chromosome. Statistics for linkage between trait and marker loci derived from either or both parents are then calculated, as are statistics for testing whether the effect of the maternally derived locus is equal to that of the paternally derived locus. Analyses of data simulated for 956 siblings from 263 nuclear families who had participated in a linkage study revealed that type I error rates for these statistics were generally similar to nominal values. Power to detect an imprinted locus was substantially increased when analyzed with a model allowing for parent-of-origin effects, compared with analyses that assumed equal effects; for example, for an imprinted locus accounting for 30% of the phenotypic variance, the expected LOD score was 4.5 when parent-of-origin effects were incorporated into the analysis, compared with 3.1 when these effects were ignored. The ability to include parent-of-origin effects within linkage analysis of quantitative traits will facilitate genetic dissection of complex traits.     

Forward genetics and map-based cloning approaches

Whereas reverse genetics strategies seek to identify and select mutations in a known sequence, forward genetics requires the cloning of sequences underlying a particular mutant phenotype. Map-based cloning is tedious, hampering the quick identification of candidate genes. With the unprecedented progress in the sequencing of whole genomes, and perhaps even more with the development of saturating marker technologies, map-based cloning can now be performed so efficiently that, at least for some plant model systems, it has become feasible to identify some candidate genes within a few months. This, in turn, will boost the use of forward genetics approaches, as applied (for example) to isolating genes involved in natural variation and genes causing phenotypic mutations as derived from (second-site) mutagenesis screens.     

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 of relatedness by DNA fingerprinting

The recent discovery of hypervariable VNTR (variable number of tandem repeat) loci has led to much excitement among population biologists regarding the feasibility of deriving individual estimates of relatedness in field populations by DNA fingerprinting. It is shown that unbiased estimates of relatedness cannot be obtained at the individual level without knowledge of the allelic distributions in both the individuals of interest and the base population unless the proportion of shared marker alleles between unrelated individuals is essentially zero. Since the latter is usually on the order of 0.1-0.5 and since there are enormous practical difficulties in obtaining the former, only an approximate estimator for the relatedness can be given. The bias of this estimator is individual specific and inversely related to the number of marker loci and frequencies of marker alleles. Substantial sampling variance in estimates of relatedness arises from variation in identity by descent within and between loci and, with finite numbers of alleles, from variation in identity in state between genes that are not identical by descent. In the extreme case of 25 assayed loci, each with an effectively infinite number of alleles, the standard error of a relatedness estimate is no less than 14%, 20%, 35%, and 53% of the expectation for full sibs and second-, third-, and fourth-order relationships, respectively. Attempts to ascertain relatedness by means of DNA fingerprinting should proceed with caution.      

Prediction of additive genetic effects for the QTL-cluster on the basis of data on surrounding markers in outbred populations

This paper described a method for predicting additive effects of a cluster of tightly linked QTLs for outbred populations of animals in the situation where the QTLs are located on a chromosome segment surrounded by multiple linked DNA markers. We present a mixed model method for best linear unbiased prediction (conditional to the marker data) of the additive effects of the QTL-cluster and of the remaining QTLs unlinked to the marker linkage group. This method takes into consideration the identity-by-descent proportion (IBDP) for the particular chromosomal segment, in contrast to some other methods which use IBD probabilities at one specific location. In this method, fully informative data on different flanking markers is used to calculate the values of the expectations of the IBDPs (EIBDPs) between gametes for animals to be evaluated. Then the expected values are used as the elements of the gametic relationship matrix required in the best linear unbiased prediction. Giving a small numerical example, we illustrate how the present method can be used for the prediction of the QTL-cluster effects and for genetic evaluation of animals in outbred populations. A computational strategy is discussed on the basis of the calculation of the EIBDPs and the inverted gametic relationship matrix in complex pedigrees.     

Multipoint analysis of human quantitative genetic variation.

A unique method of partitioning human quantitative genetic variation into effects due to specific chromosomal regions is presented. This method is based on estimating the proportion of genetic material, R, shared identical by descent (IBD) by sibling pairs in a specified chromosomal region, on the basis of their marker genotypes at a set of marker loci spanning the region. The mean and variance of the distribution of R conditional on IBD status and recombination pattern between two marker loci are derived as a function of the distance between the two loci. The distribution of the estimates of R is exemplified using data on 22 loci on chromosome 7. A method of using the estimated R values and observed values of a quantitative trait in a set of sibships to estimate the proportion of total genetic variance explained by loci in the region of interest is presented. Monte Carlo simulation techniques are used to show that this method is more powerful than existing methods of quantitative linkage analysis based on sib pairs. It is also shown through simulation studies that the proposed method is sensitive to genetic variation arising from both a single locus of large effect as well as from several loosely linked loci of moderate phenotypic effect.     

Marker-based prediction of the parental genome contribution to inbred lines derived from biparental crosses

Molecular markers can be employed to predict the parental genome contribution to inbred lines. The proportion alpha of alleles originating from parent P1 at markers polymorphic between the parental lines P1 and P2 is commonly used as a predictor for the genome contribution of parent P1 to an offspring line. Our objectives were to develop a new marker-based predictor xi for the parental genome contribution, which takes into account not only the alleles at marker loci but also their map distance, and to compare the prediction precision of xi with that of alternative methods. We derived formulas for xi for inbreds derived from biparental crosses (F1 and backcrosses) with the single-seed descent or double-haploid method and presented an extension xi* possessing statistical optimum properties. In a simulation study, alpha showed a systematic overestimation of large parental genome contribution that was not observed for xi. The mean squared prediction error of xi was at least 50% smaller than that of alpha for linkage maps with unequal distances between adjacent markers. A data set from a study on plant variety protection in maize was used to illustrate the application of xi. We conclude that xi provides substantially greater prediction precision than the commonly used predictor alpha in a broad range of applications in genetics and breeding.     

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.     

Perinatal loss of Ts65Dn Down syndrome mice

Ts65Dn mice inherit a marker chromosome, T(17(16))65Dn, producing segmental trisomy for orthologs of about half of the genes on human chromosome 21. These mice display a number of phenotypes that are directly comparable to those in humans with trisomy 21 and are the most widely used animal model of Down syndrome (DS). However, the husbandry of Ts65Dn mice is complicated. Males are sterile, and only 20-40% of the offspring of Ts65Dn mothers are trisomic at weaning. The lower-than-expected frequency of trisomic offspring has been attributed to losses at meiosis, during gestation and at postnatal stages, but no systematic studies support any of these suppositions. We show that the T(17(16))65Dn marker chromosome is inherited at expected frequency and is fully compatible with development to midgestation. Disproportional loss of trisomic offspring occurs in late gestation and continues through birth to weaning. Different maternal H2 haplotypes are significantly associated with the frequency of trisomy at weaning in patterns different from those reported previously. The proportion of trisomic mice per litter decreases with age of the Ts65Dn mother. These results provide the first statistical and numerical evidence supporting the prenatal and perinatal pattern of loss in the Ts65Dn mouse model of DS.     

Acromesomelic dysplasia Maroteaux type maps to human chromosome 9.

Acromesomelic dysplasias are skeletal disorders that disproportionately affect the middle and distal segments of the appendicular skeleton. We report genetic mapping studies in four families with acromesomelic dysplasia Maroteaux type (AMDM), an autosomal recessive osteochondrodysplasia. A peak LOD score of 5.1 at recombination fraction 0 was obtained with fully informative markers on human chromosome 9. In three of the four families, the affected offspring are products of consanguineous marriages; if it is assumed that these affected offspring are homozygous by descent for the region containing the AMDM locus, a 6.9-cM AMDM candidate interval can be defined by markers D9S1853 and D9S1874. The mapping of the AMDM locus to human chromosome 9 indicates that AMDM is genetically distinct from the two other mapped acromesomelic dysplasias, Hunter-Thompson type and Grebe type, which are caused by mutations in CDMP1 on human chromosome 20.     

Analysis of Downs syndrome with molecular techniques for future diagnoses

Down syndrome (DS) is a genetic disorder appeared due to the presence of trisomy in chromosome 21 in the G-group of the acrocentric region. DS is also known as non-Mendelian inheritance, due to the lack of Mendel’s laws. The disorder in children is identified through clinical symptoms and chromosomal analysis and till now there are no biochemical and molecular analyses. Presently, whole exome sequencing (WES) has largely contributed in identifying the new disease-causing genes and represented a significant breakthrough in the field of human genetics and this technique uses high throughput sequencing technologies to determine the arrangement of DNA base pairs specifying the protein coding regions of an individual’s genome. Apart from this next generation sequencing and whole genome sequencing also contribute for identifying the disease marker. From this review, the suggestion was to perform the WES is DS children to identify the marker region.     

Ineffectivity of accessory bisatellited marker chromosomes in inducing meiotic nondisjunction

It has been postulated that accessory marker chromosomes, which frequently show satellites, are effective in inducing meiotic nondisjunction in the carrier. This hypothesis has been tested by comparing expectations derived from it with actual data. Due to the discrepancies between these expectations and actual observations this hypothesis does not hold true: The frequency of trisomy 21 in the offspring of a carrier of an accessory bisatellited marker chromosome cannot be shown to be actually increased, and there is no increase of either the rate of miscarriages to such carriers or the frequency of an accessory marker chromosome among the individuals with regular trisomy 21. This indicates that the risk of trisomy in the offspring of a carrier of an accessory marker chromosome corresponds to the overall incidence of this trisomy.     

Fine mapping of a quantitative trait locus for twinning rate using combined linkage and linkage disequilibrium mapping

A novel and robust method for the fine-scale mapping of genes affecting complex traits, which combines linkage and linkage-disequilibrium information, is proposed. Linkage information refers to recombinations within the marker-genotyped generations and linkage disequilibrium to historical recombinations before genotyping started. The identity-by-descent (IBD) probabilities at the quantitative trait locus (QTL) between first generation haplotypes were obtained from the similarity of the marker alleles surrounding the QTL, whereas IBD probabilities at the QTL between later generation haplotypes were obtained by using the markers to trace the inheritance of the QTL. The variance explained by the QTL is estimated by residual maximum likelihood using the correlation structure defined by the IBD probabilities. Unlinked background genes were accounted for by fitting a polygenic variance component. The method was used to fine map a QTL for twinning rate in cattle, previously mapped on chromosome 5 by linkage analysis. The data consisted of large half-sib families, but the method could also handle more complex pedigrees. The likelihood of the putative QTL was very small along most of the chromosome, except for a sharp likelihood peak in the ninth marker bracket, which positioned the QTL within a region <1 cM in the middle part of bovine chromosome 5. The method was expected to be robust against multiple genes affecting the trait, multiple mutations at the QTL, and relatively low marker density.