Quantitative Trait Loci Mapping Methods Research Articles

Use of randomization testing to detect multiple epistatic QTLs.

Here, we describe a randomization testing strategy for mapping interacting quantitative trait loci (QTLs). In a forward selection strategy, non-interacting QTLs and simultaneously mapped interacting QTL pairs are added to a total genetic model. Simultaneous mapping of epistatic QTLs increases the power of the mapping strategy by allowing detection of interacting QTL pairs where none of the QTL can be detected by their marginal additive and dominance effects. Randomization testing is used to derive empirical significance thresholds for every model selection step in the procedure. A simulation study was used to evaluate the statistical properties of the proposed randomization tests and for which types of epistasis simultaneous mapping of epistatic QTLs adds power. Least squares regression was used for QTL parameter estimation but any other QTL mapping method can be used. A genetic algorithm was used to search for interacting QTL pairs, which makes the proposed strategy feasible for single processor computers. We believe that this method will facilitate the evaluation of the importance at epistatic interaction among QTLs controlling multifactorial traits and disorders.

Quantitative trait loci for scald resistance in barley localized by a non‐interval mapping procedure

AbstractThree quantitative trait loci (QTL) for scald resistance in barley were identified and mapped in relation to molecular markers using a population of chromosome doubled‐haploid lines produced from the F1 generation of a cross between the spring barley varieties ‘Alexis’ and ‘Regatta’. Two field experiments were conducted in Denmark and two in Norway to assess disease resistance. The percentage leaf area covered with scald (Rhynchosporium secalis) ranged from 0 to 40% in the 189 doubled‐haploid (DH) lines analysed. One quantitative trait locus was localized in the centromeric region of chromosome 3H, Qryn3, using the MAPQTL program. MAPQTL was unable to provide proper localization of the other two resistance genes and so a non‐interval QTL mapping method was used. One was found to be located distally to markers on chromosome 4H (Qryn4) and the other, Qryn6, was located distally to markers on chromosome 6H. The effects of differences between the Qryn3, Qryn4 and Qryn6 alleles in two barley genotypes for the QTL were estimated to be 8.8%, 7.3% and 7.0%, respectively, of leaf covered by scald. No interactions between the QTLs were found.

Bayesian methods for quantitative trait loci mapping based on model selection: approximate analysis using the Bayesian information criterion.

We describe an approximate method for the analysis of quantitative trait loci (QTL) based on model selection from multiple regression models with trait values regressed on marker genotypes, using a modification of the easily calculated Bayesian information criterion to estimate the posterior probability of models with various subsets of markers as variables. The BIC-delta criterion, with the parameter delta increasing the penalty for additional variables in a model, is further modified to incorporate prior information, and missing values are handled by multiple imputation. Marginal probabilities for model sizes are calculated, and the posterior probability of nonzero model size is interpreted as the posterior probability of existence of a QTL linked to one or more markers. The method is demonstrated on analysis of associations between wood density and markers on two linkage groups in Pinus radiata. Selection bias, which is the bias that results from using the same data to both select the variables in a model and estimate the coefficients, is shown to be a problem for commonly used non-Bayesian methods for QTL mapping, which do not average over alternative possible models that are consistent with the data.

Generalized marker regression and interval QTL mapping methods for binary traits in half‐sib family designs

A Generalized Marker Regression Mapping (GMR) approach was developed for mapping Quantitative Trait Loci (QTL) affecting binary polygenic traits in a single‐family half‐sib design. The GMR is based on threshold‐liability model theory and regression of offspring phenotype on expected marker genotypes at flanking marker loci. Using simulation, statistical power and bias of QTL mapping for binary traits by GMR was compared with full QTL interval mapping based on a threshold model (GIM) and with a linear marker regression mapping method (LMR). Empirical significance threshold values, power and estimates of QTL location and effect were identical for GIM and GMR when QTL mapping was restricted to within the marker interval. These results show that the theory of the marker regression method for QTL mapping is also applicable to binary traits and possibly for traits with other non‐normal distributions. The linear and threshold models based on marker regression (LMR and GMR) also resulted in similar estimates and power for large progeny group sizes, indicating that LMR can be used for binary data for balanced designs with large families, as this method is computationally simpler than GMR. GMR may have a greater potential than LMR for QTL mapping for binary traits in complex situations such as QTL mapping with complex pedigrees, random models and models with interactions.

Deficiency mapping of quantitative trait loci affecting longevity in Drosophila melanogaster.

In a previous study, sex-specific quantitative trait loci (QTL) affecting adult longevity were mapped by linkage to polymorphic roo transposable element markers, in a population of recombinant inbred lines derived from the Oregon and 2b strains of Drosophila melanogaster. Two life span QTL were each located on chromosomes 2 and 3, within sections 33E-46C and 65D-85F on the cytological map, respectively. We used quantitative deficiency complementation mapping to further resolve the locations of life span QTL within these regions. The Oregon and 2b strains were each crossed to 47 deficiencies spanning cytological regions 32F-44E and 64C-76B, and quantitative failure of the QTL alleles to complement the deficiencies was assessed. We initially detected a minimum of five and four QTL in the chromosome 2 and 3 regions, respectively, illustrating that multiple linked factors contribute to each QTL detected by recombination mapping. The QTL locations inferred from deficiency mapping did not generally correspond to those of candidate genes affecting oxidative and thermal stress or glucose metabolism. The chromosome 2 QTL in the 35B-E region was further resolved to a minimum of three tightly linked QTL, containing six genetically defined loci, 24 genes, and predicted genes that are positional candidates corresponding to life span QTL. This region was also associated with quantitative variation in life span in a sample of 10 genotypes collected from nature. Quantitative deficiency complementation is an efficient method for fine-scale QTL mapping in Drosophila and can be further improved by controlling the background genotype of the strains to be tested.

A nonparametric bootstrap method for testing close linkage vs. pleiotropy of coincident quantitative trait loci.

A novel method using the nonparametric bootstrap is proposed for testing whether a quantitative trait locus (QTL) at one chromosomal position could explain effects on two separate traits. If the single-QTL hypothesis is accepted, pleiotropy could explain the effect on two traits. If it is rejected, then the effects on two traits are due to linked QTLs. The method can be used in conjunction with several QTL mapping methods as long as they provide a straightforward estimate of the number of QTLs detectable from the data set. A selection step was introduced in the bootstrap procedure to reduce the conservativeness of the test of close linkage vs. pleiotropy, so that the erroneous rejection of the null hypothesis of pleiotropy only happens at a frequency equal to the nominal type I error risk specified by the user. The approach was assessed using computer simulations and proved to be relatively unbiased and robust over the range of genetic situations tested. An example of its application on a real data set from a saline stress experiment performed on a recombinant population of wheat (Triticum aestivum L. ) doubled haploid lines is also provided.

Mapping quantitative trait loci for binary traits using a heterogeneous residual variance model: an application to Marek's disease susceptibility in chickens.

A typical problem in mapping quantitative trait loci (QTLs) comes from missing QTL genotype. A routine method for parameter estimation involving missing data is the mixture model maximum likelihood method. We developed an alternative QTL mapping method that describes a mixture of several distributions by a single model with a heterogeneous residual variance. The two methods produce similar results, but the heterogeneous residual variance method is computationally much faster than the mixture model approach. In addition, the new method can automatically generate sampling variances of the estimated parameters. We derive the new method in the context of QTL mapping for binary traits in a F2 population. Using the heterogeneous residual variance model, we identified a QTL on chromosome IV that controls Marek's disease susceptibility in chickens. The QTL alone explains 7.2% of the total disease variation.

Molecular dissection of a major gene effect on a quantitative trait: the level of alcohol dehydrogenase expression in Drosophila melanogaster.

A molecular mapping experiment shows that a major gene effect on a quantitative trait, the level of alcohol dehydrogenase expression in Drosophila melanogaster, is due to multiple polymorphisms within the Adh gene. These polymorphisms are located in an intron, the coding sequence, and the 3' untranslated region. Because of nonrandom associations among polymorphisms at different sites, the individual effects combine (in some cases epistatically) to produce "superalleles" with large effect. These results have implications for the interpretation of major gene effects detected by quantitative trait locus mapping methods. They show that large effects due to a single locus may be due to multiple associated polymorphisms (or sequential fixations in isolated populations) rather than individual mutations of large effect.

Empirical threshold values for quantitative trait mapping.

The detection of genes that control quantitative characters is a problem of great interest to the genetic mapping community. Methods for locating these quantitative trait loci (QTL) relative to maps of genetic markers are now widely used. This paper addresses an issue common to all QTL mapping methods, that of determining an appropriate threshold value for declaring significant QTL effects. An empirical method is described, based on the concept of a permutation test, for estimating threshold values that are tailored to the experimental data at hand. The method is demonstrated using two real data sets derived from F(2) and recombinant inbred plant populations. An example using simulated data from a backcross design illustrates the effect of marker density on threshold values.

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.