Combined linkage disequilibrium and linkage mapping: Bayesian multilocus approach

Quantitative trait loci (QTL) affecting the phenotype of interest can be detected using linkage analysis (LA), linkage disequilibrium (LD) mapping or a combination of both (LDLA). The LA approach uses information from recombination events within the observed pedigree and LD mapping from the historical recombinations within the unobserved pedigree. We propose the Bayesian variable selection approach for combined LDLA analysis for single-nucleotide polymorphism (SNP) data. The novel approach uses both sources of information simultaneously as is commonly done in plant and animal genetics, but it makes fewer assumptions about population demography than previous LDLA methods. This differs from approaches in human genetics, where LDLA methods use LA information conditional on LD information or the other way round. We argue that the multilocus LDLA model is more powerful for the detection of phenotype–genotype associations than single-locus LDLA analysis. To illustrate the performance of the Bayesian multilocus LDLA method, we analyzed simulation replicates based on real SNP genotype data from small three-generational CEPH families and compared the results with commonly used quantitative transmission disequilibrium test (QTDT). This paper is intended to be conceptual in the sense that it is not meant to be a practical method for analyzing high-density SNP data, which is more common. Our aim was to test whether this approach can function in principle.     

Sheep linkage mapping: RFLP markers for comparative mapping studies

Restriction fragment length polymorphisms (RFLPs) detected using cDNA probes for conserved genes provide an important set of markers that anchor or link syntenic groups in a range of divergent mammalian species. DNA probes from sheep, cattle, pig, human and mouse were screened against sheep DNA samples and 24 new RFLP markers for sheep were identified. Among the loci tested, 22 had a homologue that has been mapped in humans. An RFLP for fibronectin (FN1) was linked to α-inhibin (INHA) at a distance of 5cM. The FN1 locus has been assigned to sheep chromosome 2q41–q44 and linkage between FN1 and INHA assigns INHA to the same chromosome in sheep. In addition to the new loci reported here, 28 RFLPs have been published previously by this group and these are collated together with RFLPs published from other laboratories. RFLPs have been reported for 86 loci in sheep. Fifty-four loci have been mapped to 16 different chromosomes.     

Human QTL linkage mapping

Human quantitative trait locus (QTL) linkage mapping, although based on classical statistical genetic methods that have been around for many years, has been employed for genome-wide screening for only the last 10–15 years. In this time, there have been many success stories, ranging from QTLs that have been replicated in independent studies to those for which one or more genes underlying the linkage peak have been identified to a few with specific functional variants that have been confirmed in in vitro laboratory assays. Despite these successes, there is a general perception that linkage approaches do not work for complex traits, possibly because many human QTL linkage studies have been limited in sample size and have not employed the family configurations that maximize the power to detect linkage. We predict that human QTL linkage studies will continue to be productive for the next several years, particularly in combination with RNA expression level traits that are showing evidence of regulatory QTLs of large effect sizes and in combination with high-density genome-wide SNP panels. These SNP panels are being used to identify QTLs previously localized by linkage and linkage results are being used to place informative priors on genome-wide association studies.     

DMLE+: Bayesian linkage disequilibrium gene mapping

SUMMARY: The program DMLE+ allows Bayesian inference of the location of a gene carrying a mutation influencing a discrete trait (such as a disease) and/or other parameters of interest (such as mutation age) based on the observed linkage disequilibrium at multiple genetic markers. DMLE+ uses either individual marker genotypes, or haplotypes, integrates over uncertain population allele frequencies, and can incorporate prior information about gene location from an annotated human genome sequence. AVAILABILITY: DMLE+ is available in both Windows GUI and portable UNIX command line versions at http://dmle.org.     

Happy mapping: a proposal for linkage mapping the human genome.

A theoretical approach for linkage mapping the genome of any higher eukaryote is described. It uses the polymerase chain reaction, oligonucleotides of random sequence and single haploid cells. Markers are defined and then the DNA of a single sperm is broken at random (eg by gamma-rays) and physically split into 3 aliquots. Each aliquot is screened for the presence of each marker. Closely-linked markers are more likely to be found in the same aliquot than unlinked markers. The entire process is repeated with further sperm and the frequency that any two markers co-segregate determined. Closely-linked markers co-segregate from most cells; unlinked markers do so rarely. A map can then be constructed from these co-segregation frequencies. A specific application for determining the order and distance between sets of closely-linked and previously-defined markers is also described.     

Joint linkage and linkage disequilibrium mapping in natural populations

A new strategy for studying the genome structure and organization of natural populations is proposed on the basis of a combined analysis of linkage and linkage disequilibrium using known polymorphic markers. This strategy exploits a random sample drawn from a panmictic natural population and the open-pollinated progeny of the sample. It is established on the principle of gene transmission from the parental to progeny generation during which the linkage between different markers is broken down due to meiotic recombination. The strategy has power to simultaneously capture the information about the linkage of the markers (as measured by recombination fraction) and the degree of their linkage disequilibrium created at a historic time. Simulation studies indicate that the statistical method implemented by the Fisher-scoring algorithm can provide accurate and precise estimates for the allele frequencies, recombination fractions, and linkage disequilibria between different markers. The strategy has great implications for constructing a dense linkage disequilibrium map that can facilitate the identification and positional cloning of the genes underlying both simple and complex traits.     

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

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

Data mining applied to linkage disequilibrium mapping

We introduce a new method for linkage disequilibrium mapping: haplotype pattern mining (HPM). The method, inspired by data mining methods, is based on discovery of recurrent patterns. We define a class of useful haplotype patterns in genetic case-control data and use the algorithm for finding disease-associated haplotypes. The haplotypes are ordered by their strength of association with the phenotype, and all haplotypes exceeding a given threshold level are used for prediction of disease susceptibility-gene location. The method is model-free, in the sense that it does not require (and is unable to utilize) any assumptions about the inheritance model of the disease. The statistical model is nonparametric. The haplotypes are allowed to contain gaps, which improves the method's robustness to mutations and to missing and erroneous data. Experimental studies with simulated microsatellite and SNP data show that the method has good localization power in data sets with large degrees of phenocopies and with lots of missing and erroneous data. The power of HPM is roughly identical for marker maps at a density of 3 single-nucleotide polymorphisms/cM or 1 microsatellite/cM. The capacity to handle high proportions of phenocopies makes the method promising for complex disease mapping. An example of correct disease susceptibility-gene localization with HPM is given with real marker data from families from the United Kingdom affected by type 1 diabetes. The method is extendable to include environmental covariates or phenotype measurements or to find several genes simultaneously.     

Methods for linkage disequilibrium mapping in crops

Linkage disequilibrium (LD) mapping in plants detects and locates quantitative trait loci (QTL) by the strength of the correlation between a trait and a marker. It offers greater precision in QTL location than family-based linkage analysis and should therefore lead to more efficient marker-assisted selection, facilitate gene discovery and help to meet the challenge of connecting sequence diversity with heritable phenotypic differences. Unlike family-based linkage analysis, LD mapping does not require family or pedigree information and can be applied to a range of experimental and non-experimental populations. However, care must be taken during analysis to control for the increased rate of false positive results arising from population structure and variety interrelationships. In this review, we discuss how suitable the recently developed alternative methods of LD mapping are for crops.     

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.     

Gene mapping by linkage and association analysis

Genetic analysis is used to map genes, including disease loci, to positions within the human genome. Linkage analysis depends on the co-segregation of a gene (locus) and a phenotype through a pedigree, while association analysis, or linkage disequilibrium mapping, depends on measuring deviation from the random occurrence of alleles in a haplotype in unrelated individuals or nuclear families. Complex computer programs may be used in both forms of analysis. In recent years most interest has focused on identifying genes involved in common, multifactorial diseases. Here I review some current and developing techniques of genetic analysis and give references to where further information can be obtained.     

Joint linkage and linkage disequilibrium mapping of quantitative trait loci in natural populations

Linkage analysis and allelic association (also referred to as linkage disequilibrium) studies are two major approaches for mapping genes that control simple or complex traits in plants, animals, and humans. But these two approaches have limited utility when used alone, because they use only part of the information that is available for a mapping population. More recently, a new mapping strategy has been designed to integrate the advantages of linkage analysis and linkage disequilibrium analysis for genome mapping in outcrossing populations. The new strategy makes use of a random sample from a panmictic population and the open-pollinated progeny of the sample. In this article, we extend the new strategy to map quantitative trait loci (QTL), using molecular markers within the EM-implemented maximum-likelihood framework. The most significant advantage of this extension is that both linkage and linkage disequilibrium between a marker and QTL can be estimated simultaneously, thus increasing the efficiency and effectiveness of genome mapping for recalcitrant outcrossing species. Simulation studies are performed to test the statistical properties of the MLEs of genetic and genomic parameters including QTL allele frequency, QTL effects, QTL position, and the linkage disequilibrium of the QTL and a marker. The potential utility of our mapping strategy is discussed.     

Developments in gene mapping with linkage methods.

Recent developments in the application of linkage analysis to gene mapping are reviewed. Advances in computational efficiency, through vectorization and parallelization of computer programs, are described. Some developments in methods for mapping the genes for non-mendelian (quantitative and discrete) traits are discussed.     

RFLP analysis and linkage mapping in Solanum tuberosum

Summary A morphologically and agronomically heterogeneous collection of 38 diploid potato lines was analysed for restriction fragment length polymorphisms (RFLPs) with 168 potato probes, including random genomic and cDNA sequences as well as characterized potato genes of known function. The use of four cutter restriction enzymes and a fragment separation range from 250 to 2,000 bases on denaturing polyacrylamide gels allowed the detection of RFLPs of a few nucleotides. With this system, 90% of all probes tested showed useful polymorphism, and 95% of those were polymorphic with two or all three enzymes used. On the average, 80% of the probes were informative in all pairwise comparisons of the 38 lines with a minimum of 49% and a maximum of 95%. The percentage of heterozygosity was determined relative to each other for each line and indicated that direct segregation analysis in F1 populations should be feasible for most combinations. From a backcross involving one pair of the 38 lines, a RFLP linkage map with 141 loci was constructed, covering 690 cMorgan of the Solanum tuberosum genome.     

Haplotype-based linkage disequilibrium mapping via direct data mining

MOTIVATION: With the availability of large-scale, high-density single-nucleotide polymorphism markers and information on haplotype structures and frequencies, a great challenge is how to take advantage of haplotype information in the association mapping of complex diseases in case-control studies. RESULTS: We present a novel approach for association mapping based on directly mining haplotypes (i.e. phased genotype pairs) produced from case-control data or case-parent data via a density-based clustering algorithm, which can be applied to whole-genome screens as well as candidate-gene studies in small genomic regions. The method directly explores the sharing of haplotype segments in affected individuals that are rarely present in normal individuals. The measure of sharing between two haplotypes is defined by a new similarity metric that combines the length of the shared segments and the number of common alleles around any marker position of the haplotypes, which is robust against recent mutations/genotype errors and recombination events. The effectiveness of the approach is demonstrated by using both simulated datasets and real datasets. The results show that the algorithm is accurate for different population models and for different disease models, even for genes with small effects, and it outperforms some recently developed methods.     

Multitrait fine mapping of quantitative trait loci using combined linkage disequilibria and linkage analysis

A novel multitrait fine-mapping method is presented. The method is implemented by a model that treats QTL effects as random variables. The covariance matrix of allelic effects is proportional to the IBD matrix, where each element is the probability that a pair of alleles is identical by descent, given marker information and QTL position. These probabilities are calculated on the basis of similarities of marker haplotypes of individuals of the first generation of genotyped individuals, using "gene dropping" (linkage disequilibrium) and transmission of markers from genotyped parents to genotyped offspring (linkage). A small simulation study based on a granddaughter design was carried out to illustrate that the method provides accurate estimates of QTL position. Results from the simulation also indicate that it is possible to distinguish between a model postulating one pleiotropic QTL affecting two traits vs. one postulating two closely linked loci, each affecting one of the traits.     

Optimization of linkage mapping strategy and construction of a high-density American lotus linkage map

Background

Lotus is a diploid plant with agricultural, medicinal, and ecological significance. Genetic linkage maps are fundamental resources for genome and genetic study, and also provide molecular markers for breeding in agriculturally important species. Genotyping by sequencing revolutionized genetic mapping, the restriction-site associated DNA sequencing (RADseq) allowed rapid discovery of thousands of SNPs markers, and a crucial aspect of the sequence based mapping strategy is the reference sequences used for marker identification.

Results

We assessed the effectiveness of linkage mapping using three types of references for scoring markers: the unmasked genome, repeat masked genome, and gene models. Overall, the repeat masked genome produced the optimal genetic maps. A high-density genetic map of American lotus was constructed using an F₁ population derived from a cross between Nelumbo nucifera ‘China Antique’ and N. lutea ‘AL1’. A total of 4,098 RADseq markers were used to construct the American lotus ‘AL1’ genetic map, and 147 markers were used to construct the Chinese lotus ‘China Antique’ genetic map. The American lotus map has 9 linkage groups, and spans 494.3 cM, with an average distance of 0.7 cM between adjacent markers. The American lotus map was used to anchor scaffold sequences in the N. nucifera ‘China Antique’ draft genome. 3,603 RADseq markers anchored 234 individual scaffold sequences into 9 megascaffolds spanning 67% of the 804 Mb draft genome.

Conclusions

Among the unmasked genome, repeat masked genome and gene models, the optimal reference sequences to call RADseq markers for map construction is repeat masked genome. This high density genetic map is a valuable resource for genomic research and crop improvement in lotus.     

FLOSS: flexible ordered subset analysis for linkage mapping of complex traits

The FLOSS software package is a flexible framework for ordered subset analysis. FLOSS is specifically designed for use with the Merlin linkage analysis package, but FLOSS can be used with any linkage analysis software package that reports NPL Z-scores for each locus and family. When FLOSS is used with the Merlin linkage analysis package, one can use either non-parametric Z-scores or Kong and Cox linear allele sharing model LOD scores. Monte Carlo P-values are calculated using a permutation test with an efficient Besag-Clifford sequential stopping rule. FLOSS also has a flexible tool for assigning family covariate scores from Merlin input files. FLOSS includes user documentation and is written in Java for easy portability. The FLOSS source code is documented and designed to be extensible.