Combination of linkage evidence in complex inheritance

The central problem of complex inheritance is to combine evidence from data that typically differ in markers, phenotypes, ascertainment, and other factors, without sacrificing the reliability that lods have given to linkage mapping for major loci. Here we evaluate 5 possible solutions on 200 replicates simulated in Genetic Analysis Workshop 10. Two methods differ from less efficient ones by distinguishing the tails of a normal distribution. Maximum likelihood scores (currently implemented only for the BETA model) and the approach of Self and Liang perform about as well as pooling samples, which is not feasible with heterogeneous data. With moderately heterogeneous data the Self and Liang method appears to be more efficient than maximum likelihood scores. Although improvements are being made in sample design and statistical analysis, the problem of combining linkage evidence from multiple data sets appears to have been solved. Allelic association presents different problems not yet addressed.     

Estimation of linkage in trisomic inheritance

 Based on F₂ families derived from selfed F₁ trisomic plants we have developed a genetic model to estimate linkage relationships between pairs of loci located on the extra chromosome. Genotypic frequencies of each class expected in a trisomic F₂ family have been calculated and the maximum-likelihood equations for recombination-fraction estimation have been derived for a variety of genetic situations. Morton’s test of homogeneity was used to compare recombination fractions estimated between loci exhibiting trisomic segregation to those obtained in families where the same loci showed Mendelian segregation. This method has been applied to an analysis of morphological, isozyme and RAPD data from faba bean (Vicia faba L.). Received: 11 October 1996 / Accepted: 21 March 1997     

RFLP inheritance and linkage in walnut

Thirty-two low-copy-number genomic DNA clones from a walnut (Juglans sp.) Pst I genomic library were used to establish a molecular-marker linkage map for walnut. The clones were hybridized to restriction-endonuclease-digested DNA from parent walnut trees involved in an interspecific backcross of (J. hindsii x J. regia) x J. regia in order to identify parental polymorphism. Sixty-three backcross progeny were analyzed to determine the inheritance and linkage of 48 RFLP loci. Sixty-six percent of the walnut cloned sequences detected duplicated, but unlinked, loci. Twelve linkage groups were identified by 42 of the RFLP loci. A Poisson probability method for estimating genome size was utilized to calculate the approximate walnut genome length as 1660 cM and to estimate that 138 markers would be needed to cover 95% of the walnut genome within 20 cM of each marker.     

Dissecting the genetics of complex inheritance: linkage disequilibrium mapping provides insight into Crohn disease

Family studies for Crohn disease (CD) report extensive linkage on chromosome 16q and pinpoint NOD2 as a possible causative locus. However, linkage is also observed in families that do not bear the most frequent NOD2 causative mutations, but no other signals on 16q have been found so far in published genome-wide association studies. Our aim is to identify this missing genetic contribution. We apply a powerful genetic mapping approach to the Wellcome Trust Case-Control Consortium and the National Institute of Diabetes and Digestive and Kidney Diseases genome-wide association data on CD. This method takes into account the underlying structure of linkage disequilibrium (LD) by using genetic distances from LD maps and provides a location for the causal agent. We find genetic heterogeneity within the NOD2 locus and also show an independent and unsuspected involvement of the neighboring gene, CYLD. We find associations with the IRF8 region and the region containing CDH1 and CDH3, as well as substantial phenotypic and genetic heterogeneity for CD itself. The genes are known to be involved in inflammation and immune dysregulation. These findings provide insight into the genetics of CD and suggest promising directions for understanding disease heterogeneity. The application of this method thus paves the way for understanding complex inheritance in general, leading to the dissection of different pathways and ultimately, personalized treatment.     

Complex inheritance of ABCR mutations in Stargardt disease: linkage disequilibrium, complex alleles, and pseudodominance

Stargardt disease is a recessively transmitted disease caused by mutations in the ABCR gene. Linkage disequilibrium has recently been reported between a polymorphism, 2828 A, and a common Western European founder mutation, 2588 C. Here, we confirm this linkage disequilibrium in a North American population. We also describe two complex alleles involving the 2828 A and 2588 C alterations and suggest a possible order of clinical severity of mutations identified in trans to the complex alleles. Finally, we report pseudodominance of Stargardt disease in a family with the 2588 C mutation, further supporting a high frequency of carriers for ABCR mutations in our population.     

Optimized group sequential study designs for tests of genetic linkage and association in complex diseases

The study of genetic linkage or association in complex traits requires large sample sizes, as the expected effect sizes are small and extremely low significance levels need to be adopted. One possible way to reduce the numbers of phenotypings and genotypings is the use of a sequential study design. Here, average sample sizes are decreased by conducting interim analyses with the possibility to stop the investigation early if the result is significant. We applied optimized group sequential study designs to the analysis of genetic linkage (one-sided mean test) and association (two-sided transmission/disequilibrium test). For designs with two and three stages at overall significance levels of.05 and.0001 and a power of.8, we calculated necessary sample sizes, time points, and critical boundaries for interim and final analyses. Monte Carlo simulation analyses were performed to confirm the validity of the asymptotic approximation. Furthermore, we calculated average sample sizes required under the null and alternative hypotheses in the different study designs. It was shown that the application of a group sequential design led to a maximal increase in sample size of 8% under the null hypothesis, compared with the fixed-sample design. This was contrasted by savings of up to 20% in average sample sizes under the alternative hypothesis, depending on the applied design. These savings affect the amounts of genotyping and phenotyping required for a study and therefore lead to a significant decrease in cost and time.     

A genetic model having complex linkage behaviour

Summary A genetic model is discussed in which the position and nature of equilibrium points for gamete frequencies depends in an unusual way on the degree of linkage between the loci involved. A complete mathematical analysis is made of the model: this is followed by a verbal discussion of the effect of linkage on such models.

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Zusammenfassung Es wird ein genetisches Modell behandelt, in demdie Lage und Art der Gleichgewichtspunkte für die Gametenfrequenz in ungewöhnlicher Weise von dem Grad der Kopplung zwischen den beiden in Frage kommenden Loci abhängen. Für das Modell wird eine vollständige mathematische Analyse vorgelegt und anschließend die Wirkung besprochen, welche die Kopplung in derartigen Modellen hat.

     

Significance levels in complex inheritance.

A LOD score >=3 is necessary but not sufficient to make a linkage test reliable, and this applies to complex inheritance as well as to major loci. Factors that affect this threshold are considered here. A LOD score as small as 2 is suggestive but is unreliable except as confirmation of either a significant linkage or a strong candidate locus. A threshold as great as 4 is unnecessarily conservative if multipoint tests are used sensibly. Marker density is not a major factor, and biases in the evaluation of LOD scores-especially inadequate allowance for estimation of nuisance parameters in multiple models-are paramount. Allelic association increases resolution for oligogenes within a candidate region and remains the only practical method to locate polygenes. The method sketched here combines multipoint linkage and allelic association to test efficiently for a regional candidate locus.     

Efficient multipoint linkage analysis through reduction of inheritance space

Computational constraints currently limit exact multipoint linkage analysis to pedigrees of moderate size. We introduce new algorithms that allow analysis of larger pedigrees by reducing the time and memory requirements of the computation. We use the observed pedigree genotypes to reduce the number of inheritance patterns that need to be considered. The algorithms are implemented in a new version (version 2.1) of the software package GENEHUNTER. Performance gains depend on marker heterozygosity and on the number of pedigree members available for genotyping, but typically are 10-1,000-fold, compared with the performance of the previous release (version 2.0). As a result, families with up to 30 bits of inheritance information have been analyzed, and further increases in family size are feasible. In addition to computation of linkage statistics and haplotype determination, GENEHUNTER can also perform single-locus and multilocus transmission/disequilibrium tests. We describe and implement a set of permutation tests that allow determination of empirical significance levels in the presence of linkage disequilibrium among marker loci.     

Detecting and mapping repulsion-phase linkage in polyploids with polysomic inheritance

It has been suggested that ratios of coupling- to repulsion-phase linked markers can be used to distinguish between allopolyploids and autopolyploids, because repulsion-phase linkages are much more difficult to detect in autopolyploids with polysomic inheritance than allopolyploids with disomic inheritance. In this report, we analyze the segregation pattern of repulsion-phase linked markers in polyploids without complete preferential pairing. The observed repulsion-phase recombination fraction (R) in such polyploids is composed of a fraction due to crossing-over (R_c) and another fraction due to independent assortment (R_i). R_i is the minimum distance that can be detected between repulsion-phase linked markers. Because R_i is high in autopolyploids (0.3373, 0.4000, 0.4286 and 0.4444) for autopolyploids of 2n=4x, 6x, 8x and 10x), large population sizes are required to reliably detect repulsion linkages. In addition, the default linkage used in mapping-programs must be greater than the corresponding R_i to determine whether a polyploid is a true autopolyploid. Unfortunately, much lower default linkages than the R_is have been used in recent polyploid studies to determine polyploid type, and markers have been incorporated into polyploid maps based on the R values. Herein, we describe how mapping repulsion linkages can result in spurious results, and present methods to accurately detect the degree of preferential pairing in polyploids using repulsion linkage analysis. Received: 29 February 2000 / Accepted: 17 July 2000     

Mitotic inheritance of the Golgi complex

In mammals, the Golgi complex is structured in the form of a continuous membranous system composed of stacks connected by tubular bridges, the “Golgi ribbon”. At the onset of mitosis, the Golgi complex undergoes a multi-step fragmentation process that is required for its correct partition into the dividing cells. Regulation of Golgi fragmentation and cell cycle progression appear to be precisely coordinated. Here, we review recent studies that are revealing the fundamental mechanisms, the molecular players and the biological significance of the mitotic inheritance of the Golgi complex in mammalian cells.     

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.     

Genome-wide linkage analysis assessing parent-of-origin effects in the inheritance of birth weight

Family studies suggest that genetic variation may influence birth weight. We have assessed linkage of birth weight in a genome-wide scan in 269 Pima Indian siblings (334 sibling pairs, 92 families). As imprinting (expression of only a single copy of a gene depending on parent-of-origin), is commonly found in genes that affect fetal growth, we used a recently described modification of standard multipoint variance-component methods of linkage analysis of quantitative traits. This technique allows for comparison of linkage models that incorporate imprinting effects (in which the strength of linkage is expressed as LOD(IMP)) and models where parent-of-origin effects are not included (LOD(EQ)). Where significant evidence of linkage was present, separate contributions of alleles derived from father (LOD(FA)) or mother (LOD(MO)) to the imprinting model were estimated. Significant evidence of linkage was found on chromosome 11 (at map position 88 cM, LOD(IMP)=3.4) with evidence for imprinting (imprinting model superior, P<0.001). In this region, birth weight was linked predominantly to paternally derived alleles (LOD(FA)=4.1, LOD(MO)=0.0). An imprinted gene on chromosome 11 may influence birth weight in the Pima population. This chromosome contains one of the two major known clusters of imprinted genes in the human genome, lending biological plausibility to our findings.     

Statistical properties of affected sib-pair linkage tests

Genetic linkage analysis is a powerful tool for the identification of disease susceptibility loci. Among the most commonly applied genetic linkage strategies are affected sib-pair tests, but the statistical properties of these tests have not been well characterized. Here, we present a study of the distribution of affected sib-pair tests comparing the type I error rate and the power of the mean test and the proportion test, which are the most commonly used, along with a novel exact test. In contrast to existing literature, our findings showed that the mean and proportion tests have inflated type I error rates, especially when used with small samples. We developed and applied corrections to the tests which provide an excellent adjustment to the type I error rate for both small and large samples. We also developed a novel approach to identify the areas of higher power for the mean test versus the proportion test, providing a wider and simpler comparison with fewer assumptions about parameter values than existing approaches require.     

Comparison of multivariate tests for genetic linkage

OBJECTIVES: Multivariate tests for linkage can provide improved power over univariate tests but the type I error rates and comparative power of commonly used methods have not previously been compared. Here we studied the behavior of bivariate formulations of the variance component (VC) and Haseman-Elston (H-E) approaches. METHODS: We compared through simulation studies the bivariate H-E test with the unconstrained bivariate VC approach and with a VC approach in which the major-gene correlation is constrained to +/-1. We also compared these methods to univariate methods. RESULTS: Bivariate approaches are more powerful than univariate analyses unless the traits are very highly positively correlated. The power of the bivariate H-E test was less than the VC procedures. The constrained test was often less powerful than the unconstrained test. The empirical distributions of the bivariate H-E test and the unconstrained bivariate VC test conformed with asymptotic distributions for samples of 100 or more sibships of size 4. CONCLUSIONS: The unconstrained VC test is valuable for testing for preliminary linkages using multivariate phenotypes. The bivariate H-E test was less powerful than the bivariate VC tests.     

Family-based tests of association in the presence of linkage

Linkage analysis may not provide the necessary resolution for identification of the genes underlying phenotypic variation. This is especially true for gene-mapping studies that focus on complex diseases that do not exhibit Mendelian inheritance patterns. One positional genomic strategy involves application of association methodology to areas of identified linkage. Detection of association in the presence of linkage localizes the gene(s) of interest to more-refined regions in the genome than is possible through linkage analysis alone. This strategy introduces a statistical complexity when family-based association tests are used: the marker genotypes among siblings are correlated in linked regions. Ignoring this correlation will compromise the size of the statistical hypothesis test, thus clouding the interpretation of test results. We present a method for computing the expectation of a wide range of association test statistics under the null hypothesis that there is linkage but no association. To standardize the test statistic, an empirical variance-covariance estimator that is robust to the sibling marker-genotype correlation is used. This method is widely applicable: any type of phenotypic measure or family configuration can be used. For example, we analyze a deletion in the A2M gene at the 5' splice site of "exon II" of the bait region in Alzheimer disease (AD) discordant sibships. Since the A2M gene lies in a chromosomal region (chromosome 12p) that consistently has been linked to AD, association tests should be conducted under the null hypothesis that there is linkage but no association.