High-resolution mapping of quantitative trait loci by selective recombinant genotyping

Selective recombinant genotyping (SRG) is a three-stage procedure for high-resolution mapping of a QTL that has previously been mapped to a known confidence interval (target C.I.). In stage 1, a large mapping population is accessed and phenotyped, and a proportion, P, of the high and low tails is selected. In stage 2, the selected individuals are genotyped for a pair of markers flanking the target C.I., and a group of R individuals carrying recombinant chromosomes in the target interval are identified. In stage 3, the recombinant individuals are genotyped for a set of M markers spanning the target C.I. Extensive simulations showed that: (1) Standard error of QTL location (SEQTL) decreased when QTL effect (d) or population size (N) increased, but was constant for given "power factor" (PF = d(2)N); (2) increasing the proportion selected in the tails beyond 0.25 had only a negligible effect on SEQTL; and (3) marker spacing in the target interval had a remarkably powerful effect on SEQTL, yielding a reduction of up to 10-fold in going from highest (24 cM) to lowest (0.29 cM) spacing at given population size and QTL effect. At the densest marker spacing, SEQTL of 1.0-0.06 cM were obtained at PF = 500-16,000. Two new genotyping procedures, the half-section algorithm and the golden section/half-section algorithm, allow the equivalent of complete haplotyping of the target C.I. in the recombinant individuals to be achieved with many fewer data points than would be required by complete individual genotyping.     

Computing power of quantitative trait locus association mapping for haploid loci

Background  

Statistical power calculations are a critical part of any study design for gene mapping. Most calculations assume that the locus of interest is biallelic. However, there are common situations in human genetics such as X-linked loci in males where the locus is haploid. The purpose of this work is to mathematically derive the biometric model for haploid loci, and to compute power for QTL mapping when the loci are haploid.     

High-resolution mapping of quantitative trait loci affecting increased life span in Drosophila melanogaster

Limited life span and senescence are near-universal characteristics of eukaryotic organisms, controlled by many interacting quantitative trait loci (QTL) with individually small effects, whose expression is sensitive to the environment. Analyses of mutations in model organisms have shown that genes affecting stress resistance and metabolism affect life span across diverse taxa. However, there is considerable segregating variation for life span in nature, and relatively little is known about the genetic basis of this variation. Replicated lines of Drosophila that have evolved increased longevity as a correlated response to selection for postponed senescence are valuable resources for identifying QTL affecting naturally occurring variation in life span. Here, we used deficiency complementation mapping to identify at least 11 QTL on chromosome 3 that affect variation in life span between five old (O) lines selected for postponed senescence and their five base (B) population control lines. Most QTL were sex specific, and all but one affected multiple O lines. The latter observation is consistent with alleles at intermediate frequency in the base population contributing to the response to selection for postponed senescence. The QTL were mapped with high resolution and contained from 12 to 170 positional candidate genes.     

Lineage-specific mapping of quantitative trait loci

We present an approach for quantitative trait locus (QTL) mapping, termed as ‘lineage-specific QTL mapping'', for inferring allelic changes of QTL evolution along with branches in a phylogeny. We describe and analyze the simplest case: by adding a third taxon into the normal procedure of QTL mapping between pairs of taxa, such inferences can be made along lineages to a presumed common ancestor. Although comparisons of QTL maps among species can identify homology of QTLs by apparent co-location, lineage-specific mapping of QTL can classify homology into (1) orthology (shared origin of QTL) versus (2) paralogy (independent origin of QTL within resolution of map distance). In this light, we present a graphical method that identifies six modes of QTL evolution in a three taxon comparison. We then apply our model to map lineage-specific QTLs for inbreeding among three taxa of yellow monkey-flower: Mimulus guttatus and two inbreeders M. platycalyx and M. micranthus, but critically assuming outcrossing was the ancestral state. The two most common modes of homology across traits were orthologous (shared ancestry of mutation for QTL alleles). The outbreeder M. guttatus had the fewest lineage-specific QTL, in accordance with the presumed ancestry of outbreeding. Extensions of lineage-specific QTL mapping to other types of data and crosses, and to inference of ancestral QTL state, are discussed.     

A sib-pair approach to interval mapping of quantitative trait loci.

An interval mapping procedure based on the sib-pair method of Haseman and Elston is developed, and simulation studies are carried out to explore its properties. The procedure is analogous to other interval mapping procedures used with experimental material, such as plants and animals, and yields very similar results in terms of the location and effect size of a quantitative trait locus (QTL). The procedure offers an advantage over the conventional Haseman and Elston approach, in terms of power, and provides useful information concerning the location of a QTL. Because of its simplicity, the method readily lends itself to the analysis of selected samples for increased power and the evaluation of multilocus models of complex phenotypes.     

Combined linkage and association mapping of quantitative trait loci by multiple markers

Using multiple diallelic markers, variance component models are proposed for high-resolution combined linkage and association mapping of quantitative trait loci (QTL) based on nuclear families. The objective is to build a model that may fully use marker information for fine association mapping of QTL in the presence of prior linkage. The measures of linkage disequilibrium and the genetic effects are incorporated in the mean coefficients and are decomposed into orthogonal additive and dominance effects. The linkage information is modeled in variance-covariance matrices. Hence, the proposed methods model both association and linkage in a unified model. On the basis of marker information, a multipoint interval mapping method is provided to estimate the proportion of allele sharing identical by descent (IBD) and the probability of sharing two alleles IBD at a putative QTL for a sib-pair. To test the association between the trait locus and the markers, both likelihood-ratio tests and F-tests can be constructed on the basis of the proposed models. In addition, analytical formulas of noncentrality parameter approximations of the F-test statistics are provided. Type I error rates of the proposed test statistics are calculated to show their robustness. After comparing with the association between-family and association within-family (AbAw) approach by Abecasis and Fulker et al., it is found that the method proposed in this article is more powerful and advantageous based on simulation study and power calculation. By power and sample size comparison, it is shown that models that use more markers may have higher power than models that use fewer markers. The multiple-marker analysis can be more advantageous and has higher power in fine mapping QTL. As an application, the Genetic Analysis Workshop 12 German asthma data are analyzed using the proposed methods.     

High-resolution mapping of quantitative trait loci for sternopleural bristle number in Drosophila melanogaster.

We have mapped quantitative trait loci (QTL) harboring naturally occurring allelic variation for Drosophila bristle number. Lines with high (H) and low (L) sternopleural bristle number were derived by artificial selection from a large base population. Isogenic H and L sublines were extracted from the selection lines, and populations of X and third chromosome H/L recombinant isogenic lines were constructed in the homozygous low line background. The polymorphic cytological locations of roo transposable elements provided a dense molecular marker map with an average intermarker distance of 4.5 cM. Two X chromosome and six chromosome 3 QTL affecting response to selection for sternopleural bristle number and three X chromosome and three chromosome 3 QTL affecting correlated response in abdominal bristle number were detected using a composite interval mapping method. The average effects of bristle number QTL were moderately large, and some had sex-specific effects. Epistasis between QTL affecting sternopleural bristle number was common, and interaction effects were large. Many of the intervals containing bristle number QTL coincided with those mapped in previous studies. However, resolution of bristle number QTL to the level of genetic loci is not trivial, because the genomic regions containing bristle number QTL often did not contain obvious candidate loci, and results of quantitative complementation tests to mutations at candidate loci affecting adult bristle number were ambiguous.     

Bayesian LASSO for quantitative trait loci mapping

The mapping of quantitative trait loci (QTL) is to identify molecular markers or genomic loci that influence the variation of complex traits. The problem is complicated by the facts that QTL data usually contain a large number of markers across the entire genome and most of them have little or no effect on the phenotype. In this article, we propose several Bayesian hierarchical models for mapping multiple QTL that simultaneously fit and estimate all possible genetic effects associated with all markers. The proposed models use prior distributions for the genetic effects that are scale mixtures of normal distributions with mean zero and variances distributed to give each effect a high probability of being near zero. We consider two types of priors for the variances, exponential and scaled inverse-chi(2) distributions, which result in a Bayesian version of the popular least absolute shrinkage and selection operator (LASSO) model and the well-known Student's t model, respectively. Unlike most applications where fixed values are preset for hyperparameters in the priors, we treat all hyperparameters as unknowns and estimate them along with other parameters. Markov chain Monte Carlo (MCMC) algorithms are developed to simulate the parameters from the posteriors. The methods are illustrated using well-known barley data.     

Selection bias in quantitative trait loci mapping

A simulation study was performed to see whether selection affected quantitative trait loci (QTL) mapping. Populations under random selection, under selection among full-sib families, and under selection within a full-sib family were simulated each with heritability of 0.3, 0.5, and 0.7. They were analyzed with the marker spacing of 10 cM and 20 cM. The accuracy for QTL detection decreased for the populations under selection within full-sib family. Estimates of QTL effects and positions differed (P < .05) from their input values. The problems could be ignored when mapping a QTL for the populations under selection among full-sib families. A large heritability helped reduction of such problems. When the animals were selected within a full-sib family, the QTL was detected for the populations with heritability of 0.5 or larger using the marker spacing of 10 cM, and with heritability of 0.7 using the marker spacing of 20 cM. This study implied that when selection was introduced, the accuracy for QTL detection decreased and the estimates of QTL effects were biased. A caution was warranted on the decision of data (including selected animals to be genotyped) for QTL mapping.     

High-resolution joint linkage disequilibrium and linkage mapping of quantitative trait loci based on sibship data

This paper proposes variance component models for high resolution joint linkage disequilibrium (LD) and linkage mapping of quantitative trait loci (QTL) based on sibship data; this can include population data if independent individuals are treated as single sibships. One application of these models is late onset complex disease gene mapping, when parental data are not available. The models simultaneously incorporate both LD and linkage information. The LD information is contained in mean coefficients of sibship data. The linkage information is contained in the variance-covariance matrices of trait values for sibships with at least two siblings. We derive formulas for calculating the probability of sharing two trait alleles identical by descent (IBD) for sibpairs in interval mapping of QTL; this is the coefficient of dominant variance of the trait covariance of sibpairs on major QTL. To investigate the performance of the formulas, we calculate the numerical values via the formulas and get satisfactory approximations. We compare the power and sample sizes for both LD and linkage mapping. By simulation and theoretical analysis, we compare the results with those of Fulker and Abecasis "AbAw" approach. It is well known that the resolution of linkage analysis can be low for complex disease gene mapping. LD mapping, on the other hand, can increase mapping precision and is useful in high resolution mapping. Linkage analysis is less sensitive to population subdivisions and admixtures. The level of LD is sensitive to population stratification which may easily lead to spurious association. Performing a joint analysis of LD and linkage mapping can help to overcome the limits of both approaches. Moreover, the advantages of the two complementary strategies can be utilized maximally. In practice, linkage analysis may be performed using pedigree data to identify suggestive linkage between markers and trait loci based on a sparse marker map. In the presence of linkage, joint LD and linkage mapping can be carried out to do fine gene mapping based on a dense genetic map using both pedigree and population data. Population and pedigree data of any type can be combined to perform a joint analysis of high resolution LD and linkage mapping of QTL by generalizing the method.     

Coalescent-based association mapping and fine mapping of complex trait loci

We outline a general coalescent framework for using genotype data in linkage disequilibrium-based mapping studies. Our approach unifies two main goals of gene mapping that have generally been treated separately in the past: detecting association (i.e., significance testing) and estimating the location of the causative variation. To tackle the problem, we separate the inference into two stages. First, we use Markov chain Monte Carlo to sample from the posterior distribution of coalescent genealogies of all the sampled chromosomes without regard to phenotype. Then, averaging across genealogies, we estimate the likelihood of the phenotype data under various models for mutation and penetrance at an unobserved disease locus. The essential signal that these models look for is that in the presence of disease susceptibility variants in a region, there is nonrandom clustering of the chromosomes on the tree according to phenotype. The extent of nonrandom clustering is captured by the likelihood and can be used to construct significance tests or Bayesian posterior distributions for location. A novelty of our framework is that it can naturally accommodate quantitative data. We describe applications of the method to simulated data and to data from a Mendelian locus (CFTR, responsible for cystic fibrosis) and from a proposed complex trait locus (calpain-10, implicated in type 2 diabetes).     

Sib mating designs for mapping quantitative trait loci

The power to separate the variance of a quantitative trait locus (QTL) from the polygenic variance is determined by the variability of genes identical by descent (IBD) at the QTL. This variability may increase with inbreeding. Selfing, the most extreme form of inbreeding, increases the variability of the IBD value shared by siblings, and thus has a higher efficiency for QTL mapping than random mating. In self-incompatible organisms, sib mating is the closest form of inbreeding. Similar to selfing, sib mating may also increase the power of QTL detection relative to random mating. In this study, we develop an IBD-based method under sib mating designs for QTL mapping. The efficiency of sib mating is then compared with random mating. Monte Carlo simulations show that sib mating designs notably increase the power for QTL detection. When power is intermediate, the power to detect a QTL using full-sib mating is, on average, 7% higher than under random mating. In addition, the IBD-based method proposed in this paper can be used to combine data from multiple families. As a result, the estimated QTL parameters can be applied to a wide statistical inference space relating to the entire reference population. This revised version was published online in July 2006 with corrections to the Cover Date.     

Genetic analysis and characterization of a new maize association mapping panel for quantitative trait loci dissection

Association mapping based on the linkage disequilibrium provides a promising tool to identify genes responsible for quantitative variations underlying complex traits. Presented here is a maize association mapping panel consisting of 155 inbred lines with mainly temperate germplasm, which was phenotyped for 34 traits and genotyped using 82 SSRs and 1,536 SNPs. Abundant phenotypic and genetic diversities were observed within the panel based on the phenotypic and genotypic analysis. A model-based analysis using 82 SSRs assigned all inbred lines to two groups with eight subgroups. The relative kinship matrix was calculated using 884 SNPs with minor allele frequency ≥20% indicating that no or weak relationships were identified for most individual pairs. Three traits (total tocopherol content in maize kernel, plant height and kernel length) and 1,414 SNPs with missing data <20% were used to evaluate the performance of four models for association mapping analysis. For all traits, the model controlling relative kinship (K) performed better than the model controlling population structure (Q), and similarly to the model controlling both population structure and relative kinship (Q + K) in this panel. Our results suggest this maize panel can be used for association mapping analysis targeting multiple agronomic and quality traits with optimal association model.     

Marker pair selection for mapping quantitative trait loci

Mapping of quantitative trait loci (QTL) for backcross and F(2) populations may be set up as a multiple linear regression problem, where marker types are the regressor variables. It has been shown previously that flanking markers absorb all information on isolated QTL. Therefore, selection of pairs of markers flanking QTL is useful as a direct approach to QTL detection. Alternatively, selected pairs of flanking markers can be used as cofactors in composite interval mapping (CIM). Overfitting is a serious problem, especially if the number of regressor variables is large. We suggest a procedure denoted as marker pair selection (MPS) that uses model selection criteria for multiple linear regression. Markers enter the model in pairs, which reduces the number of models to be considered, thus alleviating the problem of overfitting and increasing the chances of detecting QTL. MPS entails an exhaustive search per chromosome to maximize the chance of finding the best-fitting models. A simulation study is conducted to study the merits of different model selection criteria for MPS. On the basis of our results, we recommend the Schwarz Bayesian criterion (SBC) for use in practice.     

Multiple interval mapping for quantitative trait loci.

A new statistical method for mapping quantitative trait loci (QTL), called multiple interval mapping (MIM), is presented. It uses multiple marker intervals simultaneously to fit multiple putative QTL directly in the model for mapping QTL. The MIM model is based on Cockerham's model for interpreting genetic parameters and the method of maximum likelihood for estimating genetic parameters. With the MIM approach, the precision and power of QTL mapping could be improved. Also, epistasis between QTL, genotypic values of individuals, and heritabilities of quantitative traits can be readily estimated and analyzed. Using the MIM model, a stepwise selection procedure with likelihood ratio test statistic as a criterion is proposed to identify QTL. This MIM method was applied to a mapping data set of radiata pine on three traits: brown cone number, tree diameter, and branch quality scores. Based on the MIM result, seven, six, and five QTL were detected for the three traits, respectively. The detected QTL individually contributed from approximately 1 to 27% of the total genetic variation. Significant epistasis between four pairs of QTL in two traits was detected, and the four pairs of QTL contributed approximately 10.38 and 14.14% of the total genetic variation. The asymptotic variances of QTL positions and effects were also provided to construct the confidence intervals. The estimated heritabilities were 0.5606, 0.5226, and 0. 3630 for the three traits, respectively. With the estimated QTL effects and positions, the best strategy of marker-assisted selection for trait improvement for a specific purpose and requirement can be explored. The MIM FORTRAN program is available on the worldwide web (http://www.stat.sinica.edu.tw/chkao/).     

In silico mapping of quantitative trait loci in maize

Quantitative trait loci (QTL) are most often detected through designed mapping experiments. An alternative approach is in silico mapping, whereby genes are detected using existing phenotypic and genomic databases. We explored the usefulness of in silico mapping via a mixed-model approach in maize (Zea mays L.). Specifically, our objective was to determine if the procedure gave results that were repeatable across populations. Multilocation data were obtained from the 1995–2002 hybrid testing program of Limagrain Genetics in Europe. Nine heterotic patterns comprised 22,774 single crosses. These single crosses were made from 1,266 inbreds that had data for 96 simple sequence repeat (SSR) markers. By a mixed-model approach, we estimated the general combining ability effects associated with marker alleles in each heterotic pattern. The numbers of marker loci with significant effects—37 for plant height, 24 for smut [Ustilago maydis (DC.) Cda.] resistance, and 44 for grain moisture—were consistent with previous results from designed mapping experiments. Each trait had many loci with small effects and few loci with large effects. For smut resistance, a marker in bin 8.05 on chromosome 8 had a significant effect in seven (out of a maximum of 18) instances. For this major QTL, the maximum effect of an allele substitution ranged from 5.4% to 41.9%, with an average of 22.0%. We conclude that in silico mapping via a mixed-model approach can detect associations that are repeatable across different populations. We speculate that in silico mapping will be more useful for gene discovery than for selection in plant breeding programs.     

Accuracy of mapping quantitative trait loci in autogamous species

Summary The development of linkage maps with large numbers of molecular markers has stimulated the search for methods to map genes involved in quantitative traits (QTLs). A promising method, proposed by Lander and Botstein (1989), employs pairs of neighbouring markers to obtain maximum linkage information about the presence of a QTL within the enclosed chromosomal segment. In this paper the accuracy of this method was investigated by computer simulation. The results show that there is a reasonable probability of detecting QTLs that explain at least 5% of the total variance. For this purpose a minimum population of 200 backcross or F₂ individuals is necessary. Both the number of individuals and the relative size of the genotypic effect of the QTL are important factors determining the mapping precision. On the average, a QTL with 5% or 10% explained variance is mapped on an interval of 40 or 20 centiMorgans, respectively. Of course, QTLs with a larger genotypic effect will be located more precisely. It must be noted, however, that the interval length is rather variable.     

Marker-based mapping of quantitative trait loci using replicated progenies

Summary When heritability of the trait under investigation is low, replicated progenies can bring about a major reduction in the number of individuals that need to be scored for marker genotype in determining linkage between marker loci and quantitative trait loci (QTL). Savings are greatest when heritability of the trait is low, but are much reduced when heritability of the quantitative trait is moderate to high. Required numbers for recombinant inbred lines will be greater than those required for a simple F₂ population when heritabilities are moderate to high and the proportion of recombination between marker locus and quantitative trait locus is substantial.Contribution No. 2613-E of the Agricultural Research Organization, 1989 series