Two statistical tests for meiotic breakpoint analysis.

Meiotic breakpoint analysis (BPA), a statistical method for ordering genetic markers, is increasing in importance as a method for building genetic maps of human chromosomes. Although BPA does not provide estimates of genetic distances between markers, it efficiently locates new markers on already defined dense maps, when likelihood analysis becomes cumbersome or the sample size is small. However, until now no assessments of statistical significance have been available for evaluating the possibility that the results of a BPA were produced by chance. In this paper, we propose two statistical tests to determine whether the size of a sample and its genetic information content are sufficient to distinguish between "no linkage" and "linkage" of a marker mapped by BPA to a certain region. Both tests are exact and should be conducted after a BPA has assigned the marker to an interval on the map. Applications of the new tests are demonstrated by three examples: (1) a synthetic data set, (2) a data set of five markers on human chromosome 8p, and (3) a data set of four markers on human chromosome 17q.     

The potential of probabilistic graphical models in linkage map construction

Key message

Probabilistic graphical models show great potential for robust and reliable construction of linkage maps. We show how to use probabilistic graphical models to construct high-quality linkage maps in the face of data perturbations caused by genotyping errors and reciprocal translocations.

Abstract

It has been shown that linkage map construction can be hampered by the presence of genotyping errors and chromosomal rearrangements such as inversions and translocations. Here, we report a novel method for linkage map construction using probabilistic graphical models. The method is proven, both theoretically and practically, to be effective in filtering out markers that contain genotyping errors. In particular, it carries out marker filtering and ordering simultaneously, and is therefore superior to the standard post hoc filtering using nearest-neighbour stress. Furthermore, we demonstrate empirically that the proposed method offers a promising solution to linkage map construction in the case of a reciprocal translocation.

     

The Use of Multiple Markers in a Bayesian Method for Mapping Quantitative Trait Loci

Information on multiple linked genetic markers was used in a Bayesian method for the statistical mapping of quantitative trait loci (QTL). Bayesian parameter estimation and hypothesis testing were implemented via Markov chain Monte Carlo algorithms. Variables sampled were the augmented data (marker-QTL genotypes, polygenic effects), an indicator variable for linkage or nonlinkage, and the parameters. The parameter vector included allele frequencies at the markers and the QTL, map distances of the markers and the QTL, QTL substitution effect, and polygenic and residual variances. The criterion for QTL detection was the marginal posterior probability of a QTL being located on the chromosome carrying the markers. The method was evaluated empirically by analyzing simulated granddaughter designs consisting of 2000 sons, 20 related sires, and their ancestors.     

Construction of an AFLP genetic map with nearly complete genome coverage in Pinus taeda

  De novo construction of complete genetic linkage maps requires large mapping populations, large numbers of genetic markers, and efficient algorithms for ordering markers and evaluating order confidence. We constructed a complete genetic map of an individual loblolly pine (Pinus taeda L.) using amplified fragment length polymorphism (AFLP) markers segregating in haploid megagametophytes and PGRI mapping software. We generated 521 polymorphic fragments from 21 AFLP primer pairs. A total of 508 fragments mapped to 12 linkage groups, which is equal to the Pinus haploid chromosome number. Bootstrap locus order matrices and recombination matrices generated by PGRI were used to select 184 framework markers that could be ordered confidently. Order support was also evaluated using log likelihood criteria in MAPMAKER. Optimal marker orders from PGRI and MAPMAKER were identical, but the implied reliability of orders differed greatly. The framework map provides nearly complete coverage of the genome, estimated at approximately 1700 cM in length using a modified estimator. This map should provide a useful framework for merging existing loblolly pine maps and adding multiallelic markers as they become available. Map coverage with dominant markers in both linkage phases will make the map useful for subsequent quantitative trait locus mapping in families derived by self-pollination. Received: 7 August 1998 / Accepted: 27 October 1998     

Molecular tagging of a rust resistance gene in cultivated groundnut (Arachis hypogaea L.) introgressed from Arachis cardenasii

Rust is a serious and the most prevalent groundnut disease in tropical and subtropical growing regions of the world. A total of 164 recombinant inbred lines derived from resistant (VG 9514) and susceptible (TAG 24) cultivated groundnut parents were screened for rust resistance in five environments. Subsequent genotyping of these lines with 109 simple sequence repeat (SSR) markers generated a genetic linkage map with 24 linkage groups. The total length of the linkage map was 882.9 cM with an average of 9.0 cM between neighbouring markers. The markers pPGPseq4A05 and gi56931710 flanked the rust resistance gene at map distances of 4.7 cM and 4.3 cM, respectively, in linkage group 2. The significant association of these two markers with the rust reaction was also confirmed by discriminant analysis. The informative SSR markers classified rust-resistant and susceptible groups with 99.97% correctness. The SSR markers pPGPseq4A05 and gi56931710 were able to identify all the susceptible genotypes from a set of 20 cultivated genotypes differing in rust reaction. Tagging of the rust resistance locus with linked SSR markers will be useful in selecting the rust resistant genotypes from segregating populations and in introgressing the rust resistance genes from diploid wild species.     

A Multi-Population Consensus Genetic Map Reveals Inconsistent Marker Order among Maps Likely Attributed to Structural Variations in the Apple Genome

Genetic maps serve as frameworks for determining the genetic architecture of quantitative traits, assessing structure of a genome, as well as aid in pursuing association mapping and comparative genetic studies. In this study, a dense genetic map was constructed using a high-throughput 1,536 EST-derived SNP GoldenGate genotyping platform and a global consensus map established by combining the new genetic map with four existing reliable genetic maps of apple. The consensus map identified markers with both major and minor conflicts in positioning across all five maps. These major inconsistencies among marker positions were attributed either to structural variations within the apple genome, or among mapping populations, or genotyping technical errors. These also highlighted problems in assembly and anchorage of the reference draft apple genome sequence in regions with known segmental duplications. Markers common across all five apple genetic maps resulted in successful positioning of 2875 markers, consisting of 2033 SNPs and 843 SSRs as well as other specific markers, on the global consensus map. These markers were distributed across all 17 linkage groups, with an average of 169±33 marker per linkage group and with an average distance of 0.70±0.14 cM between markers. The total length of the consensus map was 1991.38 cM with an average length of 117.14±24.43 cM per linkage group. A total of 569 SNPs were mapped onto the genetic map, consisting of 140 recombinant individuals, from our recently developed apple Oligonucleotide pool assays (OPA). The new functional SNPs, along with the dense consensus genetic map, will be useful for high resolution QTL mapping of important traits in apple and for pursuing comparative genetic studies in Rosaceae.     

A nearest-neighboring-end algorithm for genetic mapping

MOTIVATION: High-throughput methods are beginning to make possible the genotyping of thousands of loci in thousands of individuals, which could be useful for tightly associating phenotypes to candidate loci. Current mapping algorithms cannot handle so many data without building hierarchies of framework maps. RESULTS: A version of Kruskal's minimum spanning tree algorithm can solve any genetic mapping problem that can be stated as marker deletion from a set of linkage groups. These include backcross, recombinant inbred, haploid and double-cross recombinational populations, in addition to conventional deletion and radiation hybrid populations. The algorithm progressively joins linkage groups at increasing recombination fractions between terminal markers, and attempts to recognize and correct erroneous joins at peaks in recombination fraction. The algorithm is O (mn3) for m individuals and n markers, but the mean run time scales close to mn2. It is amenable to parallel processing and has recovered true map order in simulations of large backcross, recombinant inbred and deletion populations with up to 37,005 markers. Simulations were used to investigate map accuracy in response to population size, allelic dominance, segregation distortion, missing data and random typing errors. It produced accurate maps when marker distribution was sufficiently uniform, although segregation distortion could induce translocated marker orders. The algorithm was also used to map 1003 loci in the F7 ITMI population of bread wheat, Triticum aestivum L. emend Thell., where it shortened an existing standard map by 16%, but it failed to associate blocks of markers properly across gaps within linkage groups. This was because it depends upon the rankings of recombination fractions at individual markers, and is susceptible to sampling error, typing error and joint selection involving the terminal markers of nearly finished linkage groups. Therefore, the current form of the algorithm is useful mainly to improve local marker ordering in linkage groups obtained in other ways. AVAILABILITY: The source code and supplemental data are http://www.iubio.bio.indiana.edu/soft/molbio/qtl/flipper/ CONTACT: ccrane@purdue.edu.     

Spurious linkage between markers in QTL mapping

Selective genotyping of extreme progeny is a powerful method to increase the information content per individual when looking for quantitative trait loci (QTLs) using molecular markers for which a map is known. However, if marker information from the selected individuals is used to construct the map of the markers, this can lead to distorted segregation of the markers that in turn can lead to the estimation of a spurious linkage between independently inherited markers. The mistaken estimation of linkage between independently inherited markers will occur when there are two (or more) independently inherited QTLs linked to two (or more) markers and the same individuals are used to estimate the map of the markers and to do the QTL estimation. The incorrect linkage occurs because in selecting individuals from the tails of the phenotypic distribution we will also be selecting certain combinations of the markers instead of obtaining a random sample of the true distribution of the marker genotypes. Analytical results are outlined and the analyses of a simulated data set illustrate the problems that could arise when data from individuals chosen by selective genotyping are incorrectly employed to construct a marker map. A strategy is proposed to remedy this problem.     

Bayesian association-based fine mapping in small chromosomal segments

A Bayesian method for fine mapping is presented, which deals with multiallelic markers (with two or more alleles), unknown phase, missing data, multiple causal variants, and both continuous and binary phenotypes. We consider small chromosomal segments spanned by a dense set of closely linked markers and putative genes only at marker points. In the phenotypic model, locus-specific indicator variables are used to control inclusion in or exclusion from marker contributions. To account for covariance between consecutive loci and to control fluctuations in association signals along a candidate region we introduce a joint prior for the indicators that depends on genetic or physical map distances. The potential of the method, including posterior estimation of trait-associated loci, their effects, linkage disequilibrium pattern due to close linkage of loci, and the age of a causal variant (time to most recent common ancestor), is illustrated with the well-known cystic fibrosis and Friedreich ataxia data sets by assuming that haplotypes were not available. In addition, simulation analysis with large genetic distances is shown. Estimation of model parameters is based on Markov chain Monte Carlo (MCMC) sampling and is implemented using WinBUGS. The model specification code is freely available for research purposes from http://www.rni.helsinki.fi/~mjs/.     

A mapped set of DNA markers for human chromosome 17

We have developed and mapped by genetic linkage a primary set of markers for chromosome 17. The map consists of 21 loci derived from 27 probe/enzyme systems, including eight highly informative markers at loci containing a variable number of tandemly repeated DNA sequences (VNTRs). The map is continuous from the telomeric region of the short arm to the telomeric region of the long arm, covering estimated genetic distances of 218 cM in males and 279 cM in females. The average heterozygosity among all 21 loci in the population sample analyzed is 58%; 77% heterozygosity was observed among the eight VNTR markers that were highly informative. This map will make it possible to detect by linkage the location of genetic defects associated with chromosome 17 and will also provide anchor points for a high-resolution map of this chromosome.     

Linkage mapping in populations with karyotypic rearrangements

A simulation study was used to examine the consequences of karyotypic rearrangements on molecular genetic map construction. Two groups of 50 datasets were created for F2 populations segregating for a reciprocal translocation of chromosomal segments or a reciprocal translocation and inversion. Multiple attempts were made to construct maps for each dataset using MapMaker/EXP. As expected, the markers from segments involved in the translocation formed one linkage group. Maps that corresponded to the known marker order within a segment could be constructed by the following method. The separation of markers distal to the translocation breakpoints into their respective segments could be made by constructing multiple maps, using distinct orders of marker entry, and observing the variances in intermarker distances: variances between pairs of markers from the same segment were an order of magnitude less compared to pairs where markers were from different segments. The order of markers within a segment could be determined from combining the pairwise linkage results from multiple maps, or from maps including all markers from a segment. No bias in map distances was observed. These results indicate that, under conditions similar to those tested, genetic maps corresponding to the segments conserved in translocations can be constructed.     

Construction of a genetic linkage map in tetraploid species using molecular markers

This article presents methodology for the construction of a linkage map in an autotetraploid species, using either codominant or dominant molecular markers scored on two parents and their full-sib progeny. The steps of the analysis are as follows: identification of parental genotypes from the parental and offspring phenotypes; testing for independent segregation of markers; partition of markers into linkage groups using cluster analysis; maximum-likelihood estimation of the phase, recombination frequency, and LOD score for all pairs of markers in the same linkage group using the EM algorithm; ordering the markers and estimating distances between them; and reconstructing their linkage phases. The information from different marker configurations about the recombination frequency is examined and found to vary considerably, depending on the number of different alleles, the number of alleles shared by the parents, and the phase of the markers. The methods are applied to a simulated data set and to a small set of SSR and AFLP markers scored in a full-sib population of tetraploid potato.     

A 3.9-centimorgan-resolution human single-nucleotide polymorphism linkage map and screening set

Recent advances in technologies for high-throughout single-nucleotide polymorphism (SNP)-based genotyping have improved efficiency and cost so that it is now becoming reasonable to consider the use of SNPs for genomewide linkage analysis. However, a suitable screening set of SNPs and a corresponding linkage map have yet to be described. The SNP maps described here fill this void and provide a resource for fast genome scanning for disease genes. We have evaluated 6,297 SNPs in a diversity panel composed of European Americans, African Americans, and Asians. The markers were assessed for assay robustness, suitable allele frequencies, and informativeness of multi-SNP clusters. Individuals from 56 Centre d'Etude du Polymorphisme Humain pedigrees, with >770 potentially informative meioses altogether, were genotyped with a subset of 2,988 SNPs, for map construction. Extensive genotyping-error analysis was performed, and the resulting SNP linkage map has an average map resolution of 3.9 cM, with map positions containing either a single SNP or several tightly linked SNPs. The order of markers on this map compares favorably with several other linkage and physical maps. We compared map distances between the SNP linkage map and the interpolated SNP linkage map constructed by the deCode Genetics group. We also evaluated cM/Mb distance ratios in females and males, along each chromosome, showing broadly defined regions of increased and decreased rates of recombination. Evaluations indicate that this SNP screening set is more informative than the Marshfield Clinic's commonly used microsatellite-based screening set.     

Genetic mapping in the presence of genotyping errors

Genetic maps are built using the genotypes of many related individuals. Genotyping errors in these data sets can distort genetic maps, especially by inflating the distances. We have extended the traditional likelihood model used for genetic mapping to include the possibility of genotyping errors. Each individual marker is assigned an error rate, which is inferred from the data, just as the genetic distances are. We have developed a software package, called TMAP, which uses this model to find maximum-likelihood maps for phase-known pedigrees. We have tested our methods using a data set in Vitis and on simulated data and confirmed that our method dramatically reduces the inflationary effect caused by increasing the number of markers and leads to more accurate orders.     

Mapping Mendelian Factors Underlying Quantitative Traits Using RFLP Linkage Maps

The advent of complete genetic linkage maps consisting of codominant DNA markers [typically restriction fragment length polymorphisms (RFLPs)] has stimulated interest in the systematic genetic dissection of discrete Mendelian factors underlying quantitative traits in experimental organisms. We describe here a set of analytical methods that modify and extend the classical theory for mapping such quantitative trait loci (QTLs). These include: (i) a method of identifying promising crosses for QTL mapping by exploiting a classical formula of SEWALL WRIGHT; (ii) a method (interval mapping) for exploiting the full power of RFLP linkage maps by adapting the approach of LOD score analysis used in human genetics, to obtain accurate estimates of the genetic location and phenotypic effect of QTLs; and (iii) a method (selective genotyping) that allows a substantial reduction in the number of progeny that need to be scored with the DNA markers. In addition to the exposition of the methods, explicit graphs are provided that allow experimental geneticists to estimate, in any particular case, the number of progeny required to map QTLs underlying a quantitative trait.     

SMOOTH: a statistical method for successful removal of genotyping errors from high-density genetic linkage data

High-density genetic linkage maps can be used for purposes such as fine-scale targeted gene cloning and anchoring of physical maps. However, their construction is significantly complicated by even relatively small amounts of scoring errors. Currently available software is not able to solve the ordering ambiguities in marker clusters, which inhibits the application of high-density maps. A statistical method named SMOOTH was developed to remove genotyping errors from genetic linkage data during the mapping process. The program SMOOTH calculates the difference between the observed and predicted values of data points based on data points of neighbouring loci in a given marker order. Highly improbable data points are removed by the program in an iterative process with a mapping algorithm that recalculates the map after cleaning. SMOOTH has been tested with simulated data and experimental mapping data from potato. The simulations prove that this method is able to detect a high amount of scoring errors and demonstrates that the program enables mapping software to successfully construct a very accurate high-density map. In potato the application of the program resulted in a reliable placement of nearly 1,000 markers in one linkage group.     

Bayesian and maximum likelihood estimation of genetic maps

There has recently been increased interest in the use of Markov Chain Monte Carlo (MCMC)-based Bayesian methods for estimating genetic maps. The advantage of these methods is that they can deal accurately with missing data and genotyping errors. Here we present an extension of the previous methods that makes the Bayesian method applicable to large data sets. We present an extensive simulation study examining the statistical properties of the method and comparing it with the likelihood method implemented in Mapmaker. We show that the Maximum A Posteriori (MAP) estimator of the genetic distances, corresponding to the maximum likelihood estimator, performs better than estimators based on the posterior expectation. We also show that while the performance is similar between Mapmaker and the MCMC-based method in the absence of genotyping errors, the MCMC-based method has a distinct advantage in the presence of genotyping errors. A similar advantage of the Bayesian method was not observed for missing data. We also re-analyse a recently published set of data from the eggplant and show that the use of the MCMC-based method leads to smaller estimates of genetic distances.     

Use of VeraCode 384-plex assays for watermelon diversity analysis and integrated genetic map of watermelon with single nucleotide polymorphisms and simple sequence repeats

Watermelon (Citrullus lanatus var. lanatus) is one of the most important vegetable crops in the world. Molecular markers have become the tools of choice for resolving watermelon taxonomic relationships and evolution. Increased numbers of single nucleotide polymorphism (SNP) markers together with simple sequence repeat (SSR) markers would be useful for phylogenetic analyses of germplasm accessions and for linkage mapping for marker-assisted breeding with quantitative trait loci and single genes. We aimed to construct a genetic map based on SNPs (generated by Illumina Veracode multiplex assays for genotyping) and SSR markers and evaluate relationships inferred from SNP genotypes between 130 watermelon accessions collected throughout the world. We incorporated 282 markers (232 SNPs and 50 SSRs) into the linkage map. The genetic map consisted of 11 linkage groups spanning 924.72 cM with an average distance of 3.28 cM between markers. Because all of the SNP-containing sequences were assembled with the whole-genome sequence draft for watermelon, chromosome numbers could be readily assigned for all the linkage groups. We found that 134 SNPs were polymorphic in 130 watermelon accessions chosen for diversity studies. The current 384-plex SNP set is a powerful tool for characterizing genetic relatedness and for developing medium-resolution genetic maps.     

Constructing the parental linkage phase and the genetic map over distances <1 cM using pooled haploid DNA

A new statistical approach for construction of the genetic linkage map and estimation of the parental linkage phase based on allele frequency data from pooled gametic (sperm or egg) samples is introduced. This method can be applied for estimation of recombination fractions (over distances <1 cM) and ordering of large numbers (even hundreds) of closely linked markers. This method should be extremely useful in species with a long generation interval and a large genome size such as in dairy cattle or in forest trees; the conifer species have haploid tissues available in megagametophytes. According to Mendelian expectation, two parental alleles should occur in gametes in 1:1 proportions, if segregation distortion does not occur. However, due to mere sampling variation, the observed proportions may deviate from their expected value in practice. These deviations and their dependence along the chromosome can provide information on the parental linkage phase and on the genetic linkage map. Usefulness of the method is illustrated with simulations. The role of segregation distortion as a source of these deviations is also discussed. The software implementing this method is freely available for research purposes from the authors.     

Breakpoint analysis: precise localization of genetic markers by means of nonstatistical computation using relatively few genotypes.

Placing new markers on a previously existing genetic map by using conventional methods of multilocus linkage analysis requires that a large number of reference families be genotyped. This paper presents a methodology for placing new markers on existing genetic maps by genotyping only a few individuals in a selected subset of the reference panel. We show that by identifying meiotic breakpoint events within existing genetic maps and genotyping individuals who exhibit these events, along with one nonrecombinant sibling and their parents, we can determine precise location for new markers even within subcentimorgan chromosomal regions. This method also improves detection of errors in genotyping and assists in the observation of chromosome behavior in specific regions.