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.     

Using dominance relationship coefficients based on linkage disequilibrium and linkage with a general complex pedigree to increase mapping resolution

Dominance (intralocus allelic interactions) plays often an important role in quantitative trait variation. However, few studies about dominance in QTL mapping have been reported in outbred animal or human populations. This is because common dominance effects can be predicted mainly for many full sibs, which do not often occur in outbred or natural populations with a general pedigree. Moreover, incomplete genotypes for such a pedigree make it infeasible to estimate dominance relationship coefficients between individuals. In this study, identity-by-descent (IBD) coefficients are estimated on the basis of population-wide linkage disequilibrium (LD), which makes it possible to track dominance relationships between unrelated founders. Therefore, it is possible to use dominance effects in QTL mapping without full sibs. Incomplete genotypes with a complex pedigree and many markers can be efficiently dealt with by a Markov chain Monte Carlo method for estimating IBD and dominance relationship matrices (D(RM)). It is shown by simulation that the use of D(RM) increases the likelihood ratio at the true QTL position and the mapping accuracy and power with complete dominance, overdominance, and recessive inheritance modes when using 200 genotyped and phenotyped individuals.     

The genotypic probability structure of an individual at the head of a pedigree

A proper probabilistical proof of a generalization of Wright's classical formula relating the coefficient of inbreeding of an individual at the head of a pedigree to the genotypic probability structure of this individual at one gene locus is presented. It is shown that in general the knowledge of gene frequencies realized within the initial populations from which individuals entering the pedigree are selected at random is not sufficient to predict expected genotypic frequencies in the resulting inbred population. To treat any arbitrary situation concerning the choice of individuals and genotypes to enter the pedigree, it is necessary to determine an additional set of coefficients, which merely depend on the type of the pedigree. A basic method for computing these coefficients is outlined briefly.     

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.     

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.     

Error detection for genetic data, using likelihood methods.

As genetic maps become denser, the effect of laboratory typing errors becomes more serious. We review a general method for detecting errors in pedigree genotyping data that is a variant of the likelihood-ratio test statistic. It pinpoints individuals and loci with relatively unlikely genotypes. Power and significance studies using Monte Carlo methods are shown by using simulated data with pedigree structures similar to the CEPH pedigrees and a larger experimental pedigree used in the study of idiopathic dilated cardiomyopathy (DCM). The studies show the index detects errors for small values of theta with high power and an acceptable false positive rate. The method was also used to check for errors in DCM laboratory pedigree data and to estimate the error rate in CEPH-chromosome 6 data. The errors flagged by our method in the DCM pedigree were confirmed by the laboratory. The results are consistent with estimated false-positive and false-negative rates obtained using simulation.     

Extensions to pedigree analysis. V. Optimal calculation of Mendelian likelihoods

Mendelian likelihoods are computed from human pedigree data for purposes of gene mapping, risk prediction in genetic counseling, and hypothesis testing in genetic epidemiology. The Mendelian likelihood of an extended pedigree can be written as a sum of products, the sum ranging over all possible genotypic combinations for the individuals in the pedigree. Exclusion of genotypes incompatible with the phenotypic information and pedigree structure reduces the ranges of summation and simplifies the likelihood calculation. To evaluate the likelihood with the fewest possible arithmetic operations requires carrying out the summations over one individual at a time and the intervening multiplications in some appropriate order. Each such removal of an individual reduces the likelihood evaluation to another evaluation of the same numerical form. Greedy-type algorithms are suggested for determining an order in which the summations and multiplications may be carried out. The greedy methods are fast and appear to generate good removal sequences. They are shown to work well when applied to a large, complex pedigree.     

A note on algorithms for genotype and allele elimination in complex pedigrees with incomplete genotype data

Elimination of genotypes or alleles for each individual or meiosis, which are inconsistent with observed genotypes, is a component of various genetic analyses of complex pedigrees. Computational efficiency of the elimination algorithm is critical in some applications such as genotype sampling via descent graph Markov chains. We present an allele elimination algorithm and two genotype elimination algorithms for complex pedigrees with incomplete genotype data. We modify all three algorithms to incorporate inheritance restrictions imposed by a complete or incomplete descent graph such that every inconsistent complete descent graph is detected in any pedigree, and every inconsistent incomplete descent graph is detected in any pedigree without loops with the genotype elimination algorithms. Allele elimination requires less CPU time and memory, but does not always eliminate all inconsistent alleles, even in pedigrees without loops. The first genotype algorithm produces genotype lists for each individual, which are identical to those obtained from the Lange-Goradia algorithm, but exploits the half-sib structure of some populations and reduces CPU time. The second genotype elimination algorithm deletes more inconsistent genotypes in pedigrees with loops and detects more illegal, incomplete descent graphs in such pedigrees.     

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.     

Efficient genotype elimination via adaptive allele consolidation

We propose the technique of Adaptive Allele Consolidation, that greatly improves the performance of the Lange-Goradia algorithm for genotype elimination in pedigrees, while still producing equivalent output. Genotype elimination consists in removing from a pedigree those genotypes that are impossible according to the Mendelian law of inheritance. This is used to find errors in genetic data and is useful as a preprocessing step in other analyses (such as linkage analysis or haplotype imputation). The problem of genotype elimination is intrinsically combinatorial, and Allele Consolidation is an existing technique where several alleles are replaced by a single “lumped” allele in order to reduce the number of combinations of genotypes that have to be considered, possibly at the expense of precision. In existing Allele Consolidation techniques, alleles are lumped once and for all before performing genotype elimination. The idea of Adaptive Allele Consolidation is to dynamically change the set of alleles that are lumped together during the execution of the Lange-Goradia algorithm, so that both high performance and precision are achieved. We have implemented the technique in a tool called Celer and evaluated it on a large set of scenarios, with good results.     

Likelihood approach for detecting imprinting and in utero maternal effects using general pedigrees from prospective family-based association studies

Genetic imprinting and in utero maternal effects are causes of parent-of-origin effect but they are confounded with each other. Tests attempting to detect only one of these effects would have a severely inflated type I error rate if the assumption of the absence of the other effect is violated. Some existing methods avoid the potential confounding by modeling imprinting and in utero maternal effect simultaneously. However, these methods are not amendable to extended families, which are commonly recruited in family-based studies. In this article, we propose a likelihood approach for detecting imprinting and maternal effects (LIME) using general pedigrees from prospective family-based association studies. LIME formulates the probability of familial genotypes without the Hardy-Weinberg equilibrium assumption by introducing a novel concept called conditional mating type between marry-in founders and their nonfounder spouses. Further, a logit link is used to model the penetrance. To deal with the issue of incomplete pedigree genotypic data, LIME imputes the unobserved genotypes implicitly by considering all compatible ones conditional on the observed genotypes. We carried out a simulation study to evaluate the relative power and type I error of LIME and two existing methods. The results show that the use of extended pedigree data, even with incomplete information, can achieve much greater power than using nuclear families for detecting imprinting and in utero maternal effects without leading to inflated type I error rates.     

Markov chain Monte Carlo segregation and linkage analysis for oligogenic models.

A new method for segregation and linkage analysis, with pedigree data, is described. Reversible jump Markov chain Monte Carlo methods are used to implement a sampling scheme in which the Markov chain can jump between parameter subspaces corresponding to models with different numbers of quantitative-trait loci (QTL's). Joint estimation of QTL number, position, and effects is possible, avoiding the problems that can arise from misspecification of the number of QTL's in a linkage analysis. The method is illustrated by use of a data set simulated for the 9th Genetic Analysis Workshop; this data set had several oligogenic traits, generated by use of a 1,497-member pedigree. The mixing characteristics of the method appear to be good, and the method correctly recovers the simulated model from the test data set. The approach appears to have great potential both for robust linkage analysis and for the answering of more general questions regarding the genetic control of complex traits.     

A user-friendly Hypercard interface for human linkage analysis

The availability of a large number of highly informative geneticmarkers has made human linkage analysis faster and easier toperform. However, current linkage analysis software does notprovide an organizational database into which a large body oflinkage data can be easily stored and manipulated. This manualentry and editing of linkage data is often time consuming andprone to typing errors. In addition, the large number of allelesin many of these markers must be reduced in order to performlinkage analysis with multiple loci across large genetic distances.This reduction in allele number is often difficult and confusing,especially in large pedigrees. We have taken advantage of theMacintosh-based Hypercard program to develop an interface withwhich linkage data can be easily stored, retrieved and edited.For each family, the components of the pedigree, including IDnumbers, sex and affection status, only need to be entered once.The program (Linkage Interface) retrieves this information eachtime the data from a new polymorphic marker is entered. LinkageInterface has flexible editing capabilities that allow the userto change any portion of the pedigree, including the additionor deletion of family members, without affecting previouslyentered genotype data. Linkage Interface can also analyze boththe pedigree and marker data and will detect any inconsistenciesin inheritance patterns. In addition, the program can reducethe number of alleles for a polynwrphic marker. Linkage Interfacewill then compare the ‘reduced’ data to the originalmarker data and assists in maintaining all informative meiosesby pointing out which meioses have become non-informative. Oncepolymorphic marker data are entered, the pedigree data, includingthe marker genotypes, are easily exported to a text file. Thistext file can be transferred to an IBM-compatible computer fordirect use with DOS-based linkage programs.     

PedCheck: a program for identification of genotype incompatibilities in linkage analysis.

Prior to performance of linkage analysis, elimination of all Mendelian inconsistencies in the pedigree data is essential. Often, identification of erroneous genotypes by visual inspection can be very difficult and time consuming. In fact, sometimes the errors are not recognized until the stage of running linkage-analysis software. The effort then required to find the erroneous genotypes and to cross-reference pedigree and marker data that may have been recoded and renumbered can be not only tedious but also quite daunting, in the case of very large pedigrees. We have implemented four error-checking algorithms in a new computer program, PedCheck, which will assist researchers in identifying all Mendelian inconsistencies in pedigree data and will provide them with useful and detailed diagnostic information to help resolve the errors. Our program, which uses many of the algorithms implemented in VITESSE, handles large data sets quickly and efficiently, accepts a variety of input formats, and offers various error-checking algorithms that match the subtlety of the pedigree error. These algorithms range from simple parent-offspring-compatibility checks to a single-locus likelihood-based statistic that identifies and ranks the individuals most likely to be in error. We use various real data sets to illustrate the power and effectiveness of our program.     

Characterization of the genetic changes in a multi-generational pedigree of an elite Canadian soybean cultivar

Genotyping through the pedigrees of elite soybean [Glycine max (L.) Merr.] cultivars developed by a breeding program represents an opportunity to explore and characterize various molecular and genetic changes that are a direct result of long-term selection by soybean breeders. For soybeans bred for Ontario Canada, one such elite cultivar was OAC Bayfield, which had exceptional commercial success as well as being a parent of a number of successful cultivars developed by multiple independent breeding programs. A total of 42 genotypes from six different breeding programs, comprising the multi-generational pedigree of OAC Bayfield were genotyped with molecular markers and chromosomal inheritance was tracked throughout the pedigree. Cluster analysis showed high congruence with the known pedigree and identified three distinct ancestral groups. The ancestral genotypes contained the majority of the rare alleles, with the cultivar CNS having the greatest number of unique alleles. The graphical genotype profile for the 20 chromosomes revealed conserved allelic composition which has been assembled in certain chromosomes in the form of specific linkage blocks, which were either a result of recombination involving ancestral linkage blocks or linkage blocks introduced from the cultivar Fiskeby-V. The identification of highly structured, conserved genomic regions are important for future breeding efforts as they are indicators of preferentially selected regions, or conversely, may be a contributing factor to low genetic gains due to mass fixation across a breeding program’s germplasm.     

Monte Carlo pedigree disequilibrium test for markers on the X chromosome

Because of the need for fine mapping of disease loci and the availability of dense single-nucleotide-polymorphism markers, many forms of association tests have been developed. Most of them are applicable only to triads, whereas some are amenable to nuclear families (sibships). Although there are a number of methods that can deal with extended families (e.g., the pedigree disequilibrium test [PDT]), most of them cannot accommodate incomplete data. Furthermore, despite a large body of literature on association mapping, only a very limited number of publications are applicable to X-chromosomal markers. In this report, we first extend the PDT to markers on the X chromosome for testing linkage disequilibrium in the presence of linkage. This method is applicable to any pedigree structure and is termed "X-chromosomal pedigree disequilibrium test" (XPDT). We then further extend the XPDT to accommodate pedigrees with missing genotypes in some of the individuals, especially founders. Monte Carlo (MC) samples of the missing genotypes are generated and used to calculate the XMCPDT (X-chromosomal MC PDT) statistic, which is defined as the conditional expectation of the XPDT statistic given the incomplete (observed) data. This MC version of the XPDT remains a valid test for association under linkage with the assumption that the pedigrees and their associated affection patterns are drawn randomly from a population of pedigrees with at least one affected offspring. This set of methods was compared with existing approaches through simulation, and substantial power gains were observed in all settings considered, with type I error rates closely tracking their nominal values.     

Molecular characterization and similarity relationships among apricot ( Prunus armeniaca L.) genotypes using simple sequence repeats

A collection of 48 apricot genotypes, originated from diverse geographic areas, have been screened with 37 SSR primer pairs developed in different species of Prunus in order to identify and characterize the genotypes and establish their genetic relations. Thirty one of those primer pairs resulted in correct amplifications and 20 produced polymorphic repeatable amplification patterns with the 48 genotypes studied. A total of 82 alleles were detected for the 20 loci. All the genotypes studied could be unequivocally distinguished with the combination of SSRs used. The results obtained evidence for the cross-species transportability of microsatellite sequences, allowing the discrimination among different genotypes of a given fruit-tree species with sequences developed in other species. UPGMA cluster analysis of the similarity data grouped the genotypes studied according to their geographic origin and/or their pedigree information. Received: 5 April 2001 / Accepted: 4 May 2001     

Developmental bias in evolution: evolutionary accessibility of phenotypes in a model evo-devo system

SUMMARY The success of the modern synthesis has resulted in forces of evolutionary change other than natural selection being marginalized. However, recent work has attempted to show the importance of non-selective influences in shaping organic form. One such force is developmental bias, in which phenotypes are differentially produced. We use a simulation model of neural development to explore questions of general interest about developmental systems. From this analysis, we find that the pattern of developmental bias varies strongly with the genotype even among phenotypically-neutral genotypes. In addition to this genotype-dependent developmental bias ( local bias ), an intrinsic bias exists in the developmental system ( global bias ). We also show that developmental bias varies among related genotypes that produce the same phenotype. Finally, we illustrate how a pattern of bias emerges from the manner in which mutations affect the regulatory structure of the wild-type genotype. These results suggest that developmental bias could have a strong influence on the direction of evolutionary modification.     

Integrating microsatellite and pedigree analyses to facilitate the captive management of the endangered Mississippi sandhill crane (Grus canadensis pulla)

The minimization of kinship in captive populations is usually achieved through the use of pedigree information. However, pedigree knowledge alone is not sufficient if pedigree information is missing, questionable, or when the founders of the captive population are related to one another. If this is the case, higher levels of inbreeding and lower levels of genetic diversity may be present in a captive population than those calculated by pedigree analyses alone. In this study, the genetic status of the critically endangered Mississippi sandhill crane (MSC) (Grus canadensis pulla) was analyzed using studbook data from the U.S. Fish and Wildlife Service managed captive breeding program as well as microsatellite DNA data. These analyses provided information on shared founder genotypes, allowing for refined analysis of genetic variation in the population, and the development of a new DNA-based studbook pedigree that will assist in the genetic management of the MSC population.     

Conditional probability methods for haplotyping in pedigrees

Efficient haplotyping in pedigrees is important for the fine mapping of quantitative trait locus (QTL) or complex disease genes. To reconstruct haplotypes efficiently for a large pedigree with a large number of linked loci, two algorithms based on conditional probabilities and likelihood computations are presented. The first algorithm (the conditional probability method) produces a single, approximately optimal haplotype configuration, with computing time increasing linearly in the number of linked loci and the pedigree size. The other algorithm (the conditional enumeration method) identifies a set of haplotype configurations with high probabilities conditional on the observed genotype data for a pedigree. Its computing time increases less than exponentially with the size of a subset of the set of person-loci with unordered genotypes and linearly with its complement. The size of the subset is controlled by a threshold parameter. The set of identified haplotype configurations can be used to estimate the identity-by-descent (IBD) matrix at a map position for a pedigree. The algorithms have been tested on published and simulated data sets. The new haplotyping methods are much faster and provide more information than several existing stochastic and rule-based methods. The accuracies of the new methods are equivalent to or better than those of these existing methods.