An unknown genetic defect increases venous thrombosis risk, through interaction with protein C deficiency.

We used two-locus segregation analysis to test whether an unknown genetic defect interacts with protein C deficiency to increase susceptibility to venous thromboembolic disease in a single large pedigree. Sixty-seven pedigree members carry a His107Pro mutation in the protein C gene, which reduces protein C levels to a mean of 46% of normal. Twenty-one carriers of the mutation and five other pedigree members had verified thromboembolic disease. We inferred the presence in this pedigree of a thrombosis-susceptibility gene interacting with protein C deficiency, by rejecting the hypothesis that the cases of thromboembolic disease resulted from protein C deficiency alone and by not rejecting Mendelian transmission of the interacting gene. When coinherited with protein C deficiency, the interacting gene conferred a probability of a thrombotic episode of approximately 79% for men and approximately 99% for women, before age 60 years.     

Genetic analysis of total cholesterol and triglycerides in a pedigree of St. Thomas rabbits

A pedigree consisting of 103 New Zealand White hyperlipidemic and normal rabbits was used in a genetic analysis of total cholesterol and triglyceride levels to test for Mendelian control of hyperlipidemia. The founder male of this pedigree was identified through hypercholesterolemia and evidence suggested vertical transmission of a hypercholesterolemic phenotype in this pedigree, although a combined hyperlipidemia phenotype (elevated cholesterol and triglycerides) also occurred in many descendents of the original founders. Segregation analysis of quantitative measures of total cholesterol and triglycerides in this pedigree was employed to test hypotheses about Mendelian control in the presence of substantial inbreeding. A simple Mendelian model was the best explanation for triglycerides in these animals. This best fitting model was essentially co-dominant with genotypic specific variances, where the heterozygote was hypertriglyceridemic and the mutant homozygote showed even more extreme values. The observed distribution of total cholesterol was also compatible with a mixture of distinct genotypic distributions, but there was evidence of non-Mendelian transmission in this pedigree. The observed hypertriglyceridemia in these animals may reflect an abnormality of very low density lipoprotein metabolism described previously. Further studies will be required to elucidate the genetic control of hypercholesterolemia and the associated combined hyperlipidemia in these rabbits.     

Estimating the power of a proposed linkage study for a complex genetic trait.

Many genetic traits have complex modes of inheritance; they may exhibit incomplete or age-dependent penetrance or fail to show any clear Mendelian inheritance pattern. As primary linkage maps for the human genome near completion, it is becoming increasingly possible to map these traits. Prior to undertaking a linkage study, it is important to consider whether the pedigrees available for the proposed study are likely to provide sufficient information to demonstrate linkage, assuming a linked marker is tested. In the current paper, we describe a computer simulation method to estimate the power of a proposed study to detect linkage for a complex genetic trait, given a hypothesized genetic model for the trait. Our method simulates trait locus genotypes consistent with observed trait phenotypes, in such a way that the probability to detect linkage can be estimated by sample statistics of the maximum lod score distribution. The method uses terms available when calculating the likelihood of the trait phenotypes for the pedigree and is applicable to any trait determined by one or a few genetic loci; individual-specific environmental effects can also be dealt with. Our method provides an objective answer to the question, Will these pedigrees provide sufficient information to map this complex genetic trait?     

A deductive method of haplotype analysis in pedigrees.

Derivation of haplotypes from pedigree data by means of likelihood techniques requires large computational resources and is thus highly limited in terms of the complexity of problems that can be analyzed. The present paper presents 20 rules of logic that are both necessary and sufficient for deriving haplotypes by means of nonstatistical techniques. As a result, automated haplotype analysis that uses these rules is fast and efficient, requiring computer memory that increases only linearly (rather than exponentially) with family size and the number of factors under analysis. Some error analysis is also possible. The rules are completely general with regard to any system of completely linked, discrete genetic markers that are autosomally inherited. There are no limitations on pedigree structure or the amount of missing data, although the existence of incomplete data usually reduces the fraction of haplotypes that can be completely determined.     

FamSeq: A Variant Calling Program for Family-Based Sequencing Data Using Graphics Processing Units

Various algorithms have been developed for variant calling using next-generation sequencing data, and various methods have been applied to reduce the associated false positive and false negative rates. Few variant calling programs, however, utilize the pedigree information when the family-based sequencing data are available. Here, we present a program, FamSeq, which reduces both false positive and false negative rates by incorporating the pedigree information from the Mendelian genetic model into variant calling. To accommodate variations in data complexity, FamSeq consists of four distinct implementations of the Mendelian genetic model: the Bayesian network algorithm, a graphics processing unit version of the Bayesian network algorithm, the Elston-Stewart algorithm and the Markov chain Monte Carlo algorithm. To make the software efficient and applicable to large families, we parallelized the Bayesian network algorithm that copes with pedigrees with inbreeding loops without losing calculation precision on an NVIDIA graphics processing unit. In order to compare the difference in the four methods, we applied FamSeq to pedigree sequencing data with family sizes that varied from 7 to 12. When there is no inbreeding loop in the pedigree, the Elston-Stewart algorithm gives analytical results in a short time. If there are inbreeding loops in the pedigree, we recommend the Bayesian network method, which provides exact answers. To improve the computing speed of the Bayesian network method, we parallelized the computation on a graphics processing unit. This allowed the Bayesian network method to process the whole genome sequencing data of a family of 12 individuals within two days, which was a 10-fold time reduction compared to the time required for this computation on a central processing unit.

This is a PLOS Computational Biology Software Article

     

Quantitative genetic variance associated with chromosomal markers in segregating populations

Summary Use of chromosomal markers can accelerate genetic progress for quantitative traits in pedigree selection programs by providing early information on Mendelian segregation effects for individual progeny. Potential effectiveness of selection using markers is determined by the amount of additive genetic variance traced from parents to progeny by the markers. Theoretical equations for the amount of additive genetic variance associated with a marker were derived at the individual level and for a segregating population in joint linkage equilibrium. Factors considered were the number of quantitative trait loci linked to the marker, their individual effects, and recombination rates with the marker. Subsequently, the expected amount of genetic variance associated with a marker in a segregating population was derived. In pedigree selection programs in segregating populations, a considerable fraction of the genetic variance on a chromosome is expected to be associated with a marker located on that chromosome. For an average chromosome in the bovine, this fraction is approximately 40% of the Mendelian segregation variance contributed by the chromosome. The effects of interference and position of the marker on this expectation are relative small. Length of the chromosome has a large effect on the expected variance. Effectiveness of MAS is, however, greatly reduced by lack of polymorphism at the marker and inaccuracy of estimation of chromosome substitution effects. The size of the expected amount of genetic variance associated with a chromosomal marker indicates that, even when the marker is not the active locus, large chromosome substitution effects are not uncommon in segregating populations.     

An optimal algorithm for automatic genotype elimination

In an effort to accelerate likelihood computations on pedigrees, Lange and Goradia defined a genotype-elimination algorithm that aims to identify those genotypes that need not be considered during the likelihood computation. For pedigrees without loops, they showed that their algorithm was optimal, in the sense that it identified all genotypes that lead to a Mendelian inconsistency. Their algorithm, however, is not optimal for pedigrees with loops, which continue to pose daunting computational challenges. We present here a simple extension of the Lange-Goradia algorithm that we prove is optimal on pedigrees with loops, and we give examples of how our new algorithm can be used to detect genotyping errors. We also introduce a more efficient and faster algorithm for carrying out the fundamental step in the Lange-Goradia algorithm-namely, genotype elimination within a nuclear family. Finally, we improve a common algorithm for computing the likelihood of a pedigree with multiple loops. This algorithm breaks each loop by duplicating a person in that loop and then carrying out a separate likelihood calculation for each vector of possible genotypes of the loop breakers. This algorithm, however, does unnecessary computations when the loop-breaker vector is inconsistent. In this paper we present a new recursive loop breaker-elimination algorithm that solves this problem and illustrate its effectiveness on a pedigree with six loops.     

Evaluating pedigree data. II. Identifying the cause of error in families with inconsistencies

Pedigree data can be evaluated, and subsequently corrected, by analysis of the distribution of genetic markers, taking account of the possibility of mistyping . Using a model of pedigree error developed previously, we obtained the maximum likelihood estimates of error parameters in pedigree data from Tokelau. Posterior probabilities for the possible true relationships in each family are conditional on the putative relationships and the marker data are calculated using the parameter estimates. These probabilities are used as a basis for discriminating between pedigree error and genetic marker errors in families where inconsistencies have been observed. When applied to the Tokelau data and compared with the results of retyping inconsistent families, these statistical procedures are able to discriminate between pedigree and marker error, with approximately 90% accuracy, for families with two or more offspring. The large proportion of inconsistencies inferred to be due to marker error (61%) indicates the importance of discriminating between error sources when judging the reliability of putative relationship data. Application of our model of pedigree error has proved to be an efficient way of determining and subsequently correcting sources of error in extensive pedigree data collected in large surveys.     

Multifactorial genetic models for quantitative traits in humans.

Quantitative traits measured in human families can be analyzed to partition the total population variance into genetic and environmental components, or to elucidate the genetic mechanism involved. We review the estimation of variance components directly from human pedigree data, or in the form of path coefficients from correlations between pairs of relatives. To elucidate genetic mechanisms, a mixed model that allows for segregation at a major locus, a polygenic effect and a sibling environmental correlation is described for nuclear families. In each case appropriate likelihoods are derived as a basis, using numerical maximum likelihood methods, for parameter estimation and hypothesis testing. A general model is then described that allows for several familial sources of environmental variation, assortative mating, and both major gene and polygenic effects; and an algorithm for calculating the likelihood of a pedigree under this model is indicated. Finally, some of the remaining problems in this area of biometric analysis are pointed out.     

Estimation of segregation and linkage parameters in simulated data. I. Segregation analyses with different ascertainment schemes.

We report the results of a simulation study designed to assess the capability of segregation analysis to detect Mendelian transmission and to estimate genetic model parameters for complex qualitative traits, characterized by heritability in the range 0.20-0.45 and low heterozygote penetrance. The pedigree analysis package, PAP, was used to perform the analyses. For all data sets, models of no transmission could be rejected. In most cases, models of Mendelian transmission could not be rejected; however, several samples approached significance levels. When Mendelian transmission was assumed, reasonably good parameter estimates were obtained, although heterozygote penetrances were often overestimated. Different sampling schemes were imposed on the simulated data in order to examine the extent of information loss with the reduction in sample size. One of these strategies (a sequential sampling scheme) appears to have resulted in critical loss of information in some cases.     

Determining informativity of marker typing for genetic counseling in a pedigree

Summary For the situation of a Mendelian disease linked to a genetic marker, a new method is described that allows evaluating for genetic counseling the information potentially available from the linked marker before the marker data are actually obtained, that is, prior to drawing blood for marker typing. For a consultand in a family pedigree, the method determines the risk distribution (small families) or an approximation to it (larger families) and calculates the probability that the risk will deviate beyond certain limits from its a priori value, which exists without marker data, for example, that the risk will be smaller than 0.10 or larger than 0.90. The method was applied here to a pedigree of 15 individuals for which analytical calculations would be difficult to carry out.     

Genetic analysis of plasma sitosterol, apoprotein B, and lipoproteins in a large Amish pedigree with sitosterolemia.

We previously reported the finding of phytosterolemia, xanthomatosis, and hyperapobetalipoproteinemia (hyperapoB) in five siblings in a large Amish pedigree ascertained through a 13-year-old boy who died suddenly from advanced coronary atherosclerosis. Here, we present further analyses of the plasma levels of the plant sterol, sitosterol, of low density (beta) lipoprotein (LDL) sterol, and of LDL B protein. Of 254 relatives and spouses of the proband, 90.5% were examined. A series of genetic models were explored using a pedigree analysis where parameters reflecting frequency, transmission, and penetrance of putative genotypes were examined simultaneously using a maximum likelihood approach. Segregation analysis of the sitosterol levels showed that the phenotype of sitosterolemia was controlled by a rare autosomal recessive gene. There was also significant familial correlation in plasma sitosterol levels that was attributed to a polygenic component under a mixed model but could also be due to shared environments such as diets. The recessive model was supported by our finding that the plasma sitosterol levels in the parents and in six children born to three of the five sitosterolemics were less than 1 mg/dl, well within the normal range. The phenotype of hyperapoB is based on an elevated level of LDL B protein in the presence of a normal LDL cholesterol level (low LDL sterol to LDL B ratio). For both LDL sterol and LDL B, a polygenic model showed a slightly greater improvement in ln likelihood than did the Mendelian single locus model when both were compared to a sporadic model. Similar results were obtained for sterol levels of high density (alpha) lipoprotein (HDL) sterol. When segregation analysis was performed using the ratio of LDL sterol to LDL B, the Mendelian single locus model gave a slightly better fit to the data than did the polygenic model. While the analyses presented here provided unequivocal evidence for the recessive phenotype of phytosterolemia, we also identified a possible single gene factor that could account for the major portion of the strong familial aggregation in the ratio of LDL sterol to LDL B, and to a lesser extent LDL B. However, there is clear evidence of familial aggregation for these traits in this pedigree beyond that due to Mendelian components.     

Computing the minimum recombinant haplotype configuration from incomplete genotype data on a pedigree by integer linear programming.

We study the problem of reconstructing haplotype configurations from genotypes on pedigree data with missing alleles under the Mendelian law of inheritance and the minimum-recombination principle, which is important for the construction of haplotype maps and genetic linkage/association analyses. Our previous results show that the problem of finding a minimum-recombinant haplotype configuration (MRHC) is in general NP-hard. This paper presents an effective integer linear programming (ILP) formulation of the MRHC problem with missing data and a branch-and-bound strategy that utilizes a partial order relationship and some other special relationships among variables to decide the branching order. Nontrivial lower and upper bounds on the optimal number of recombinants are introduced at each branching node to effectively prune the search tree. When multiple solutions exist, a best haplotype configuration is selected based on a maximum likelihood approach. The paper also shows for the first time how to incorporate marker interval distance into a rule-based haplotyping algorithm. Our results on simulated data show that the algorithm could recover haplotypes with 50 loci from a pedigree of size 29 in seconds on a Pentium IV computer. Its accuracy is more than 99.8% for data with no missing alleles and 98.3% for data with 20% missing alleles in terms of correctly recovered phase information at each marker locus. A comparison with a statistical approach SimWalk2 on simulated data shows that the ILP algorithm runs much faster than SimWalk2 and reports better or comparable haplotypes on average than the first and second runs of SimWalk2. As an application of the algorithm to real data, we present some test results on reconstructing haplotypes from a genome-scale SNP dataset consisting of 12 pedigrees that have 0.8% to 14.5% missing alleles.     

Identification of Mendelian inconsistencies between SNP and pedigree information of sibs

Background

Using SNP genotypes to apply genomic selection in breeding programs is becoming common practice. Tools to edit and check the quality of genotype data are required. Checking for Mendelian inconsistencies makes it possible to identify animals for which pedigree information and genotype information are not in agreement.

Methods

Straightforward tests to detect Mendelian inconsistencies exist that count the number of opposing homozygous marker (e.g. SNP) genotypes between parent and offspring (PAR-OFF). Here, we develop two tests to identify Mendelian inconsistencies between sibs. The first test counts SNP with opposing homozygous genotypes between sib pairs (SIBCOUNT). The second test compares pedigree and SNP-based relationships (SIBREL). All tests iteratively remove animals based on decreasing numbers of inconsistent parents and offspring or sibs. The PAR-OFF test, followed by either SIB test, was applied to a dataset comprising 2,078 genotyped cows and 211 genotyped sires. Theoretical expectations for distributions of test statistics of all three tests were calculated and compared to empirically derived values. Type I and II error rates were calculated after applying the tests to the edited data, while Mendelian inconsistencies were introduced by permuting pedigree against genotype data for various proportions of animals.

Results

Both SIB tests identified animal pairs for which pedigree and genomic relationships could be considered as inconsistent by visual inspection of a scatter plot of pairwise pedigree and SNP-based relationships. After removal of 235 animals with the PAR-OFF test, SIBCOUNT (SIBREL) identified 18 (22) additional inconsistent animals.Seventeen animals were identified by both methods. The numbers of incorrectly deleted animals (Type I error), were equally low for both methods, while the numbers of incorrectly non-deleted animals (Type II error), were considerably higher for SIBREL compared to SIBCOUNT.

Conclusions

Tests to remove Mendelian inconsistencies between sibs should be preceded by a test for parent-offspring inconsistencies. This parent-offspring test should not only consider parent-offspring pairs based on pedigree data, but also those based on SNP information. Both SIB tests could identify pairs of sibs with Mendelian inconsistencies. Based on type I and II error rates, counting opposing homozygotes between sibs (SIBCOUNT) appears slightly more precise than comparing genomic and pedigree relationships (SIBREL) to detect Mendelian inconsistencies between sibs.     

COLONY: a program for parentage and sibship inference from multilocus genotype data

Pedigrees, depicting genealogical relationships between individuals, are important in several research areas. Molecular markers allow inference of pedigrees in wild species where relationship information is impossible to collect by observation. Marker data are analysed statistically using methods based on Mendelian inheritance rules. There are numerous computer programs available to conduct pedigree analysis, but most software is inflexible, both in terms of assumptions and data requirements. Most methods only accommodate monogamous diploid species using codominant markers without genotyping error. In addition, most commonly used methods use pairwise comparisons rather than a full-pedigree likelihood approach, which considers the likelihood of the entire pedigree structure and allows the simultaneous inference of parentage and sibship. Here, we describe colony, a computer program implementing full-pedigree likelihood methods to simultaneously infer sibship and parentage among individuals using multilocus genotype data. colony can be used for both diploid and haplodiploid species; it can use dominant and codominant markers, and can accommodate, and estimate, genotyping error at each locus. In addition, colony can carry out these inferences for both monoecious and dioecious species. The program is available as a Microsoft Windows version, which includes a graphical user interface, and a Macintosh version, which uses an R-based interface.     

Testing genetic models in populations which contain pedigree errors

In a genetic analysis of a polymorphic system, differences between the observed type of an individual and that expected from the parental types can arise either from an incorrect model or from pedigree errors. Such pedigree errors can cause severe difficulties in studies of the mode of inheritance of a novel polymorphic system. A method is proposed which overcomes the problem by including sire and dam error rates explicitly in the genetic model. The error rates are estimated by maximum likelihood, and likelihood ratio tests used to compare different models or estimates from different data sets. The proposals are applied to a study of the inheritance of the bovine serum AmI amylases.     

Maximum likelihood haplotyping for general pedigrees

Haplotype data is valuable in mapping disease-susceptibility genes in the study of Mendelian and complex diseases. We present algorithms for inferring a most likely haplotype configuration for general pedigrees, implemented in the newest version of the genetic linkage analysis system SUPERLINK. In SUPERLINK, genetic linkage analysis problems are represented internally using Bayesian networks. The use of Bayesian networks enables efficient maximum likelihood haplotyping for more complex pedigrees than was previously possible. Furthermore, to support efficient haplotyping for larger pedigrees, we have also incorporated a novel algorithm for determining a better elimination order for the variables of the Bayesian network. The presented optimization algorithm also improves likelihood computations. We present experimental results for the new algorithms on a variety of real and semiartificial data sets, and use our software to evaluate MCMC approximations for haplotyping.     

An efficient algorithm to compute marginal posterior genotype probabilities for every member of a pedigree with loops

Background

Marginal posterior genotype probabilities need to be computed for genetic analyses such as geneticcounseling in humans and selective breeding in animal and plant species.

Methods

In this paper, we describe a peeling based, deterministic, exact algorithm to compute efficiently genotype probabilities for every member of a pedigree with loops without recourse to junction-tree methods from graph theory. The efficiency in computing the likelihood by peeling comes from storing intermediate results in multidimensional tables called cutsets. Computing marginal genotype probabilities for individual i requires recomputing the likelihood for each of the possible genotypes of individual i. This can be done efficiently by storing intermediate results in two types of cutsets called anterior and posterior cutsets and reusing these intermediate results to compute the likelihood.

Examples

A small example is used to illustrate the theoretical concepts discussed in this paper, and marginal genotype probabilities are computed at a monogenic disease locus for every member in a real cattle pedigree.     

Detection rates for genotyping errors in SNPs using the trio design

One well-known approach for the analysis of transmission-disequilibrium is the investigation of single nucleotide polymorphisms (SNPs) in trios consisting of an affected child and its parents. Results may be biased by erroneously given genotypes. Various reasons, among them sample swap or wrong pedigree structure, represent a possible source for biased results. As these can be partly ruled out by good study conditions together with checks for correct pedigree structure by a series of independent markers, the remaining main cause for errors is genotyping errors. Some of the errors can be detected by Mendelian checks whilst others are compatible with the pedigree structure. The extent of genotyping errors can be estimated by investigating the rate of detected genotyping errors by Mendelian checks. In many studies only one SNP of a specific genomic region is investigated by TDT which leaves Mendelian checks as the only tool to control genotyping errors. From the rate of detected errors the true error rate can be estimated. Gordon et al. [Hum Hered 1999;49:65-70] considered the case of genotyping errors that occur randomly and independently with some fixed probability for the wrong ascertainment of an allele. In practice, instead of single alleles, SNP genotypes are determined. Therefore, we study the proportion of detected errors (detection rate) based on genotypes. In contrast to Gordon et al., who reported detection rates between 25 and 30%, we obtain higher detection rates ranging from 39 up to 61% considering likely error structures in the data. We conclude that detection rates are probably substantially higher than those reported by Gordon et al.