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PubMed2006

A simple linear regression method for quantitative trait loci linkage analysis with censored observations.

Standard quantitative trait loci (QTL) mapping techniques commonly assume that the trait is both fully observed and normally distributed. When considering survival or age-at-onset traits these assumptions are often incorrect. Methods have been developed to map QTL for survival traits; however, they are both computationally intensive and not available in standard genome analysis software packages. We propose a grouped linear regression method for the analysis of continuous survival data. Using simulation we compare this method to both the Cox and Weibull proportional hazards models and a standard linear regression method that ignores censoring. The grouped linear regression method is of equivalent power to both the Cox and Weibull proportional hazards methods and is significantly better than the standard linear regression method when censored observations are present. The method is also robust to the proportion of censored individuals and the underlying distribution of the trait. On the basis of linear regression methodology, the grouped linear regression model is computationally simple and fast and can be implemented readily in freely available statistical software.

Chromosome Mapping↗

PubMed2003

A consensus linkage map for sugi (Cryptomeria japonica) from two pedigrees, based on microsatellites and expressed sequence tags.

A consensus map for sugi (Cryptomeria japonica) was constructed by integrating linkage data from two unrelated third-generation pedigrees, one derived from a full-sib cross and the other by self-pollination of F1 individuals. The progeny segregation data of the first pedigree were derived from cleaved amplified polymorphic sequences, microsatellites, restriction fragment length polymorphisms, and single nucleotide polymorphisms. The data of the second pedigree were derived from cleaved amplified polymorphic sequences, isozyme markers, morphological traits, random amplified polymorphic DNA markers, and restriction fragment length polymorphisms. Linkage analyses were done for the first pedigree with JoinMap 3.0, using its parameter set for progeny derived by cross-pollination, and for the second pedigree with the parameter set for progeny derived from selfing of F1 individuals. The 11 chromosomes of C. japonica are represented in the consensus map. A total of 438 markers were assigned to 11 large linkage groups, 1 small linkage group, and 1 nonintegrated linkage group from the second pedigree; their total length was 1372.2 cM. On average, the consensus map showed 1 marker every 3.0 cM. PCR-based codominant DNA markers such as cleaved amplified polymorphic sequences and microsatellite markers were distributed in all linkage groups and occupied about half of mapped loci. These markers are very useful for integration of different linkage maps, QTL mapping, and comparative mapping for evolutional study, especially for species with a large genome size such as conifers.

Base Sequence↗

PubMed2005

Methodological aspects of the genetic dissection of gene expression.

MOTIVATION: Dissection of the genetics underlying gene expression utilizes techniques from microarray analyses as well as quantitative trait loci (QTL) mapping. Available QLT mapping methods are not tailored for the highly automated analyses required to deal with the thousand of gene transcripts encountered in the mapping of QTL affecting gene expression (sometimes referred to as eQTL). This report focuses on the adaptation of QTL mapping methodology to perform automated mapping of QTL affecting gene expression. RESULTS: The analyses of expression data on > 12,000 gene transcripts in BXD recombinant inbred mice found, on average, 629 QTL exceeding the genome-wide 5% threshold. Using additional information on trait repeatabilities and QTL location, 168 of these were classified as 'high confidence' QTL. Current sample sizes of genetical genomics studies make it possible to detect a reasonable number of QTL using simple genetic models, but considerably larger studies are needed to evaluate more complex genetic models. After extensive analyses of real data and additional simulated data (altogether > 300,000 genome scans) we make the following recommendations for detection of QTL for gene expression: (1) For populations with an unbalanced number of replicates on each genotype, weighted least squares should be preferred above ordinary least squares. Weights can be based on repeatability of the trait and the number of replicates. (2) A genome scan based on multiple marker information but analysing only at marker locations is a good approximation to a full interval mapping procedure. (3) Significance testing should be based on empirical genome-wide significance thresholds that are derived for each trait separately. (4) The significant QTL can be separated into high and low confidence QTL using a false discovery rate that incorporates prior information such as transcript repeatabilities and co-localization of gene-transcripts and QTL. (5) Including observations on the founder lines in the QTL analysis should be avoided as it inflates the test statistic and increases the Type I error. (6) To increase the computational efficiency of the study, use of parallel computing is advised. These recommendations are summarized in a possible strategy for mapping of QTL in a least squares framework. AVAILABILITY: The software used for this study is available on request from the authors.

Algorithms↗

PubMed2003

[Research progress in forest tree genetic linkage map construction and its future prospects].

The research progress in genetic linkage map construction of forest tree species both at home and abroad were reviewed in the paper. Two main problems involved in the field were discussed. One was the limitation of the number of individuals of mapping populations and the other was the random markers mostly employed by the majority of studies. These problems have resulted in crossing combination specificity in the constructed maps and the QTLs located on the basis of the maps. As a result,the QTLs discovered up to now have low credibility and poor practicability in marker-assisted selection. Therefore considering the biological characteristics of forest tree species,the selection of the most suitable genetic markers is crucial to obtain a high quality genetic linkage map, and it is both important and necessary to carry out comparative genetic mapping. Progress in the ongoing expressed sequence tag (EST) sequencing projects were summarized and EST polymorphism (ESTP), the most informative and highly conservative marker with known function,as well as the main ESTP detection techniques were elaborated. It was pointed out that ESTP markers should be integrated into the present studies of genetic linkage map construction, QTL mapping and genome comparative mapping. Finally the future prospects in the fields of genetic linkage map and QTL mapping were discussed. In China, such studies around Populus, especially in the local Populus species should make a breakthrough in the related fields.

English Abstract↗

PubMed2005

A comparison of interval mapping procedures including the QTL-cluster mapping.

Using the deterministic sampling, patterns of the log-likelihood surfaces expected in some interval mapping procedures for estimating the position of, and the effect for, QTL(s) were investigated for the situations where a single QTL or closely linked QTLs are contained in a chromosome segment bracketed with two markers. The mapping procedures compared were the conventional, likelihood-based interval mapping (IM), the regression interval mapping (RIM), and the QTL-cluster mapping (CM) in which the conditional probabilities of transmission of the whole segment marked by the flanking markers were taken into consideration. The half-sib design was used here, and several cases of the true genetic model were considered, differing in the number of QTLs contained in the marker interval, the linkage phase for the sire, and the magnitude of the QTL(s) effect. For the true genetic models where a single QTL or closely linked QTLs being in coupling phase are contained in the interval, with (R)IM, clear global maxima of the log-likelihood were observed within the range of the marker interval. It was shown that the estimates of the QTL(s) effect at the marked segment level are expected to be unbiased. On the other hand, in a setting where the linkage phase for the linked QTLs located in the interval was different from coupling and repulsion, there was found a ridge along the interval for the log-likelihood surface with (R)IM, indicating the dependency between the estimates of the position of, and the effect for, the putative QTL. For this case, it was found that the position of the putative QTL could be estimated as that of one of the flanking markers, and the estimate of the QTL effect be biased. In contrast, it was revealed that CM is expected to provide the unbiased estimate of the QTL(s)-effect at the segment level for any case of the true genetic models considered here. If the aim is for marker-assisted selection rather than mapping closely linked QTLs individually, then the CM approach is considered to be useful.

Chromosome Mapping↗

PubMed2002

An improved genetic model generates high-resolution mapping of QTL for protein quality in maize endosperm.

The genetic mapping of polymorphic markers in a cross between two inbred plant lines has proven to be a powerful method for detecting quantitative trait loci (QTL) underlying complex traits. However, existing methods of QTL mapping were developed for disomic inheritance of both marker and QTL loci in a diploid population. To map QTL influencing traits expressed in the endosperm, a triploid embryo-nourishing tissue resulting from double fertilization, existing QTL mapping models require modification to consider the trisomic inheritance of the endosperm and the generation difference between the mapping population and the endosperm. Such a model requires simultaneous use of two successive generations, which theoretically can lead to an increase in resolution for QTL mapping compared with the use of a single backcross or F(2) generation. Using a newly developed model based on these considerations, we demonstrate the improved resolution of QTL, influencing protein quality traits in maize endosperm. The increased resolution made possible with this approach makes identified QTL accessible to positional cloning.

Chromosome Mapping↗

PubMed2006

Mapping quantitative trait loci in noninbred mosquito crosses.

The identification of genes that affect quantitative traits has been of great interest to geneticists for many decades, and many statistical methods have been developed to map quantitative trait loci (QTL). Most QTL mapping studies in experimental organisms use purely inbred lines, where the two homologous chromosomes in each individual are identical. As a result, many existing QTL mapping methods developed for experimental organisms are applicable only to genetic crosses between inbred lines. However, it may be difficult to obtain inbred lines for certain organisms, e.g., mosquitoes. Although statistical methods for QTL mapping in outbred populations, e.g., humans, can be applied for such crosses, these methods may not fully take advantage of the uniqueness of these crosses. For example, we can generally assume that the two grandparental lines are homozygous at the QTL of interest, but such information is not be utilized through methods developed for outbred populations. In addition, mating types and phases can be relatively easy to establish through the analysis of adjacent markers due to the large number of offspring that can be collected, substantially simplifying the computational need. In this article, motivated by a mosquito intercross experiment involving two selected lines that are not genetically homozygous across the genome, we develop statistical methods for QTL mapping for genetic crosses involving noninbred lines. In our procedure, we first infer parental mating types and use likelihood-based methods to infer phases in each parent on the basis of genotypes of offspring and one parent. A hidden Markov model is then employed to estimate the number of high-risk alleles at marker positions and putative QTL positions between markers in each offspring, and QTL mapping is finally conducted through the inferred QTL configuration across all offspring in all crosses. The performance of the proposed methods is assessed through simulation studies, and the usefulness of this method is demonstrated through its application to a mosquito data set.

Alleles↗

PubMed2005

Quantitative trait locus (QTL) isogenic recombinant analysis: a method for high-resolution mapping of QTL within a single population.

In the quest for fine mapping quantitative trait loci (QTL) at a subcentimorgan scale, several methods that involve the construction of inbred lines and the generation of large progenies of such inbred lines have been developed (Complex Trait Consortium 2003). Here we present an alternative method that significantly speeds up QTL fine mapping by using one segregating population. As a first step, a rough mapping analysis is performed on a small part of the population. Once the QTL have been mapped to a chromosomal interval by standard procedures, a large population of 1000 plants or more is analyzed with markers flanking the defined QTL to select QTL isogenic recombinants (QIRs). QIRs bear a recombination event in the QTL interval of interest, while other QTL have the same homozygous genotype. Only these QIRs are subsequently phenotyped to fine map the QTL. By focusing at an early stage on the informative individuals in the population only, the efforts in population genotyping and phenotyping are significantly reduced as compared to prior methods. The principles of this approach are demonstrated by fine mapping an erucic acid QTL of rapeseed at a subcentimorgan scale.

Brassica rapa↗

PubMed2002

QTL Express: mapping quantitative trait loci in simple and complex pedigrees.

QTL Express is the first application for Quantitative Trait Locus (QTL) mapping in outbred populations with a web-based user interface. User input of three files containing a marker map, trait data and marker genotypes allows mapping of single or multiple QTL by the regression approach, with the option to perform permutation or bootstrap tests.

Chromosome Mapping↗

PubMed1994

Precision mapping of quantitative trait loci.

Adequate separation of effects of possible multiple linked quantitative trait loci (QTLs) on mapping QTLs is the key to increasing the precision of QTL mapping. A new method of QTL mapping is proposed and analyzed in this paper by combining interval mapping with multiple regression. The basis of the proposed method is an interval test in which the test statistic on a marker interval is made to be unaffected by QTLs located outside a defined interval. This is achieved by fitting other genetic markers in the statistical model as a control when performing interval mapping. Compared with the current QTL mapping method (i.e., the interval mapping method which uses a pair or two pairs of markers for mapping QTLs), this method has several advantages. (1) By confining the test to one region at a time, it reduces a multiple dimensional search problem (for multiple QTLs) to a one dimensional search problem. (2) By conditioning linked markers in the test, the sensitivity of the test statistic to the position of individual QTLs is increased, and the precision of QTL mapping can be improved. (3) By selectively and simultaneously using other markers in the analysis, the efficiency of QTL mapping can be also improved. The behavior of the test statistic under the null hypothesis and appropriate critical value of the test statistic for an overall test in a genome are discussed and analyzed. A simulation study of QTL mapping is also presented which illustrates the utility, properties, advantages and disadvantages of the method.

Chromosome Mapping↗

PubMed2000

QTL fine mapping by measuring and testing for Hardy-Weinberg and linkage disequilibrium at a series of linked marker loci in extreme samples of populations.

It has recently been demonstrated that fine-scale mapping of a susceptibility locus for a complex disease can be accomplished on the basis of deviations from Hardy-Weinberg (HW) equilibrium at closely linked marker loci among affected individuals. We extend this theory to fine-scale localization of a quantitative-trait locus (QTL) from extreme individuals in populations, by means of HW and linkage-disequilibrium (LD) analyses. QTL mapping and/or linkage analyses can establish a large genomic region ( approximately 30 cM) that contains a QTL. The QTL can be fine mapped by examination of the degree of deviation from HW and LD at a series of closely linked marker loci. The tests can be performed for samples of individuals belonging to either high or low percentiles of the phenotype distribution or for combined samples of these extreme individuals. The statistical properties (the power and the size) of the tests of this fine-mapping approach are investigated and are compared extensively, under various genetic models and parameters for the QTL and marker loci. On the basis of the results, a two-stage procedure that uses extreme samples and different tests (for HW and LD) is suggested for QTL fine mapping. This two-step procedure is economic and powerful and can accurately narrow a genomic region containing a QTL from approximately 30-1 cM, a range that renders physical mapping feasible for identification of the QTL. In addition, the relationship between parameterizations of complex diseases, by means of penetrance, and those of complex quantitative traits, by means of genotypic values, is outlined. This means that many statistical genetic methods developed for searching for susceptibility loci of complex diseases can be directly adopted and/or extended to QTL mapping for quantitative traits.

Alleles↗

PubMed1997

Fine-scale mapping of quantitative trait loci using historical recombinations.

With increasing popularity of QTL mapping in economically important animals and experimental species, the need for statistical methodology for fine-scale QTL mapping becomes increasingly urgent. The ability to disentangle several linked QTL depends on the number of recombination events. An obvious approach to increase the recombination events is to increase sample size, but this approach is often constrained by resources. Moreover, increasing the sample size beyond a certain point will not further reduce the length of confidence interval for QTL map locations. The alternative approach is to use historical recombinations. We use analytical methods to examine the properties of fine QTL mapping using historical recombinations that are accumulated through repeated intercrossing from an F2 population. We demonstrate that, using the historical recombinations, both simple and multiple regression models can reduce significantly the lengths of support intervals for estimated QTL map locations and the variances of estimated QTL map locations. We also demonstrate that, while the simple regression model using historical recombinations does not reduce the variances of the estimated additive and dominant effects, the multiple regression model does. We further determine the power and threshold values for both the simple and multiple regression models. In addition, we calculate the Kullback-Leibler distance and Fisher information for the simple regression model, in the hope to further understand the advantages and disadvantages of using historical recombinations relative to F2 data.

Algorithms↗

PubMed2004

Mapping quantitative trait loci in F2 incorporating phenotypes of F3 progeny.

In plants and laboratory animals, QTL mapping is commonly performed using F(2) or BC individuals derived from the cross of two inbred lines. Typical QTL mapping statistics assume that each F(2) individual is genotyped for the markers and phenotyped for the trait. For plant traits with low heritability, it has been suggested to use the average phenotypic values of F(3) progeny derived from selfing F(2) plants in place of the F(2) phenotype itself. All F(3) progeny derived from the same F(2) plant belong to the same F(2:3) family, denoted by F(2:3). If the size of each F(2:3) family (the number of F(3) progeny) is sufficiently large, the average value of the family will represent the genotypic value of the F(2) plant, and thus the power of QTL mapping may be significantly increased. The strategy of using F(2) marker genotypes and F(3) average phenotypes for QTL mapping in plants is quite similar to the daughter design of QTL mapping in dairy cattle. We study the fundamental principle of the plant version of the daughter design and develop a new statistical method to map QTL under this F(2:3) strategy. We also propose to combine both the F(2) phenotypes and the F(2:3) average phenotypes to further increase the power of QTL mapping. The statistical method developed in this study differs from published ones in that the new method fully takes advantage of the mixture distribution for F(2:3) families of heterozygous F(2) plants. Incorporation of this new information has significantly increased the statistical power of QTL detection relative to the classical F(2) design, even if only a single F(3) progeny is collected from each F(2:3) family. The mixture model is developed on the basis of a single-QTL model and implemented via the EM algorithm. Substantial computer simulation was conducted to demonstrate the improved efficiency of the mixture model. Extension of the mixture model to multiple QTL analysis is developed using a Bayesian approach. The computer program performing the Bayesian analysis of the simulated data is available to users for real data analysis.

Algorithms↗

PubMed2006

An updated 'Essex' by 'Forrest' linkage map and first composite interval map of QTL underlying six soybean traits.

DNA marker maps based on single populations are the basis for gene, loci and genomic analyses. Individual maps can be integrated to produce composite maps with higher marker densities if shared marker orders are consistent. However, estimates of marker order in composite maps must include sets of markers that were not polymorphic in multiple populations. Often some of the pooled markers were not codominant, or were not correctly scored. The soybean composite map was composed of data from five separate populations based on northern US germplasm but does not yet include 'Essex' by 'Forrest' recombinant inbred line (RIL) population (E x F) or any southern US soybean cultivars. The objectives were, to update the E x F map with codominant markers, to compare marker orders among this map, the Forrest physical map and the composite soybean map and to compare QTL identified by composite interval maps to the earlier interval maps. Two hundred and thirty seven markers were used to construct the core of the E x F map. The majority of marker orders were consistent between the maps. However, 19 putative marker inversions were detected on 12 of 20 linkage groups (LG). Eleven marker distance compressions were also found. The number of inverted markers ranged from 1 to 2 per LG. Thus, marker order inversions may be common in southern compared to northern US germplasm. A total of 61 QTL among 37 measures of six traits were detected by composite interval maps, interval maps and single point analysis. Seventeen of the QTL found in composite intervals had previously been detected among the 29 QTL found in simple interval maps. The genomic locations of the known QTL were more closely delimited. A genome sequencing project to compare Southern and Northern US soybean cultivars would catalog and delimit inverted regions and the associated QTL. Gene introgression in cultivar development programs would be accelerated.

Chromosome Mapping↗

PubMed2006

The X chromosome in quantitative trait locus mapping.

The X chromosome requires special treatment in the mapping of quantitative trait loci (QTL). However, most QTL mapping methods, and most computer programs for QTL mapping, have focused exclusively on autosomal loci. We describe a method for appropriate treatment of the X chromosome for QTL mapping in experimental crosses. We address the important issue of formulating the null hypothesis of no linkage appropriately. If the X chromosome is treated like an autosome, a sex difference in the phenotype can lead to spurious linkage on the X chromosome. Further, the number of degrees of freedom for the linkage test may be different for the X chromosome than for autosomes, and so an X chromosome-specific significance threshold is required. To address this issue, we propose a general procedure to obtain chromosome-specific significance thresholds that controls the genomewide false positive rate at the desired level. We apply our methods to data on gut length in a large intercross of mice carrying the Sox10Dom mutation, a model of Hirschsprung disease. We identified QTL contributing to variation in gut length on chromosomes 5 and 18. We found suggestive evidence of linkage to the X chromosome, which would be viewed as strong evidence of linkage if the X chromosome was treated as an autosome. Our methods have been implemented in the package R/qtl.

Animals↗

PubMed1996

Extensions to quantitative trait locus mapping in experimental organisms.

Quantitative trait locus (QTL) mapping studies involving inbred model organisms have become important and often-used investigative tools in contemporary genetics research. As a result, a number of statistical methods and study designs have been developed that have made it relatively easy for researchers to determine the rough locations of a number of QTLs that influence traits of all types, including a great many of relevance to hypertension and blood pressure regulation. However, as a whole, these methods and designs are limited in that they are not flexible enough to accommodate many of the complexities associated with quantitative trait expression. In this review, we describe a number of extensions to QTL mapping designs that should make QTL mapping experiments more insightful and compelling. These extensions include multiple QTL modeling with an emphasis on epistatic locus interaction and additive locus effects, the use of multiple phenotypic end points, the design of pharmacogenetic studies, the use of whole-genome parameters in quantitative trait investigations, and issues in mapping QTLs that influence traits that exhibit developmental trends. We use studies investigating the genetic basis of blood pressure regulation to exemplify relevant issues.

Animals↗

PubMed1998

Molecular dissection of developmental behavior of plant height in rice (Oryza sativa L.).

A doubled haploid population of 123 lines from IR64/Azucena was used to dissect the developmental behavior and genotype by environment interaction for plant height by conditional and unconditional quantitative trait loci (QTL) mapping methods in rice. It was shown that the number of QTL detected was different at various measuring stages. Some QTL could be detected at all stages and some only at one or several stages. More QTL could be found on the basis of time-dependent measures of different stages. By conditional QTL mapping of time-dependent measures, it is possible to reveal dynamic gene expression for quantitative traits. Mapping QTL for genetic main effects and GE interaction effects could help us in understanding the nature of QTL x environment interaction for the development of quantitative traits.

Adaptation, Physiological↗

PubMed2001

Population based linkage disequilibrium mapping of QTL: an application to simulated data in an isolated population.

Despite successes in mapping and cloning genes involved in rare Mendelian diseases, genetic dissection of quantitative traits into single Mendelian factors still remains a challenging task. As the dense map of single nucleotide polymorphism (SNP) markers becomes available in the near future, linkage disequilibrium (LD) mapping will become one of major tools for mapping and identifying quantitative trait loci (QTL). In this report, we present a population-based linkage disequilibrium mapping of QTL. This method unifies the analysis of mapping QTL in humans and in model organisms and can be used for randomly sampled individuals. The proposed method is applied to search for polymorphism sites within the candidate genes 2 and 6, which influence quantitative traits Q1 and Q2 or Q5, in a simulated data set in an isolated population.

Chromosome Mapping↗