scholarly journals Controlling the type I and type II errors in mapping quantitative trait loci.

Genetics ◽  
1994 ◽  
Vol 138 (3) ◽  
pp. 871-881 ◽  
Author(s):  
R C Jansen
Keyword(s):  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Type I Error ◽  
Interval Mapping ◽  
Mapping Method ◽  
Type I ◽  
Type Ii ◽  
Large Numbers ◽  
Trait Loci ◽  
Type Ii Errors

Abstract Although the interval mapping method is widely used for mapping quantitative trait loci (QTLs), it is not very well suited for mapping multiple QTLs. Here, we present the results of a computer simulation to study the application of exact and approximate models for multiple QTLs. In particular, we focus on an automatic two-stage procedure in which in the first stage "important" markers are selected in multiple regression on markers. In the second stage a QTL is moved along the chromosomes by using the preselected markers as cofactors, except for the markers flanking the interval under study. A refined procedure for cases with large numbers of marker cofactors is described. Our approach will be called MQM mapping, where MQM is an acronym for "multiple-QTL models" as well as for "marker-QTL-marker." Our simulation work demonstrates the great advantage of MQM mapping compared to interval mapping in reducing the chance of a type I error (i.e., a QTL is indicated at a location where actually no QTL is present) and in reducing the chance of a type II error (i.e., a QTL is not detected).

Bayesian Mapping of Multiple Quantitative Trait Loci From Incomplete Inbred Line Cross Data

Genetics ◽  
1998 ◽  
Vol 148 (3) ◽  
pp. 1373-1388
Author(s):  
Mikko J Sillanpää ◽  
Elja Arjas
Keyword(s):  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Composite Interval Mapping ◽  
Backcross Progeny ◽  
Random Variable ◽  
Interval Mapping ◽  
Mapping Method ◽  
Structure Mapping ◽  
Standard Interval ◽  
Trait Loci

Abstract A novel fine structure mapping method for quantitative traits is presented. It is based on Bayesian modeling and inference, treating the number of quantitative trait loci (QTLs) as an unobserved random variable and using ideas similar to composite interval mapping to account for the effects of QTLs in other chromosomes. The method is introduced for inbred lines and it can be applied also in situations involving frequent missing genotypes. We propose that two new probabilistic measures be used to summarize the results from the statistical analysis: (1) the (posterior) QTL-intensity, for estimating the number of QTLs in a chromosome and for localizing them into some particular chromosomal regions, and (2) the location wise (posterior) distributions of the phenotypic effects of the QTLs. Both these measures will be viewed as functions of the putative QTL locus, over the marker range in the linkage group. The method is tested and compared with standard interval and composite interval mapping techniques by using simulated backcross progeny data. It is implemented as a software package. Its initial version is freely available for research purposes under the name Multimapper at URL http://www.rni.helsinki.fi/~mjs.

scholarly journals A Rank-Based Nonparametric Method for Mapping Quantitative Trait Loci in Outbred Half-Sib Pedigrees: Application to Milk Production in a Granddaughter Design

Genetics ◽  
1998 ◽  
Vol 149 (3) ◽  
pp. 1547-1555 ◽  
Author(s):  
Wouter Coppieters ◽  
Alexandre Kvasz ◽  
Frédéric Farnir ◽  
Juan-Jose Arranz ◽  
Bernard Grisart ◽  
...  
Keyword(s):  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Real Data ◽  
Interval Mapping ◽  
Mapping Method ◽  
Residual Variance ◽  
Data Set ◽  
Wilcoxon Rank Sum Test ◽  
Holstein Friesian ◽  
Trait Loci

Abstract We describe the development of a multipoint nonparametric quantitative trait loci mapping method based on the Wilcoxon rank-sum test applicable to outbred half-sib pedigrees. The method has been evaluated on a simulated dataset and its efficiency compared with interval mapping by using regression. It was shown that the rank-based approach is slightly inferior to regression when the residual variance is homoscedastic normal; however, in three out of four other scenarios envisaged, i.e., residual variance heteroscedastic normal, homoscedastic skewed, and homoscedastic positively kurtosed, the latter outperforms the former one. Both methods were applied to a real data set analyzing the effect of bovine chromosome 6 on milk yield and composition by using a 125-cM map comprising 15 microsatellites and a granddaughter design counting 1158 Holstein-Friesian sires.

scholarly journals Precision mapping of quantitative trait loci.

Genetics ◽  
1994 ◽  
Vol 136 (4) ◽  
pp. 1457-1468 ◽  
Author(s):  
Z B Zeng
Keyword(s):  
Quantitative Trait Loci ◽  
Qtl Mapping ◽  
Quantitative Trait ◽  
Interval Mapping ◽  
Mapping Method ◽  
Search Problem ◽  
Test Statistic ◽  
Advantages And Disadvantages ◽  
A Genome ◽  
Trait Loci

Abstract 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.

scholarly journals Precision and High-Resolution Mapping of Quantitative Trait Loci by Use of Recurrent Selection, Backcross or Intercross Schemes

Genetics ◽  
2002 ◽  
Vol 161 (2) ◽  
pp. 915-929
Author(s):  
Z W Luo ◽  
Chung-I Wu ◽  
M J Kearsey
Keyword(s):  
Genetic Variation ◽  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Recurrent Selection ◽  
Wide Spectrum ◽  
Interval Mapping ◽  
Mapping Method ◽  
Dna Polymorphisms ◽  
Quantitative Genetic ◽  
Trait Loci

Abstract Dissecting quantitative genetic variation into genes at the molecular level has been recognized as the greatest challenge facing geneticists in the twenty-first century. Tremendous efforts in the last two decades were invested to map a wide spectrum of quantitative genetic variation in nearly all important organisms onto their genome regions that may contain genes underlying the variation, but the candidate regions predicted so far are too coarse for accurate gene targeting. In this article, the recurrent selection and backcross (RSB) schemes were investigated theoretically and by simulation for their potential in mapping quantitative trait loci (QTL). In the RSB schemes, selection plays the role of maintaining the recipient genome in the vicinity of the QTL, which, at the same time, are rapidly narrowed down over multiple generations of backcrossing. With a high-density linkage map of DNA polymorphisms, the RSB approach has the potential of dissecting the complex genetic architecture of quantitative traits and enabling the underlying QTL to be mapped with the precision and resolution needed for their map-based cloning to be attempted. The factors affecting efficiency of the mapping method were investigated, suggesting guidelines under which experimental designs of the RSB schemes can be optimized. Comparison was made between the RSB schemes and the two popular QTL mapping methods, interval mapping and composite interval mapping, and showed that the scenario of genomic distribution of QTL that was unlocked by the RSB-based mapping method is qualitatively distinguished from those unlocked by the interval mapping-based methods.

scholarly journals Mapping multiple linked quantitative trait loci in non-obese diabetic mice using a stepwise regression strategy

1998 ◽  
Vol 71 (1) ◽  
pp. 51-64 ◽  
Author(s):  
HEATHER J. CORDELL ◽  
JOHN A. TODD ◽  
G. MARK LATHROP
Keyword(s):  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Type I Error ◽  
Strain Analysis ◽  
Chromosome 1 ◽  
Type I ◽  
Trait Loci ◽  
True Type ◽  
Inbred Populations

A simple regression strategy for mapping multiple linked quantitative trait loci (QTLs) in inbred populations is proposed and applied to data from a non-obese diabetic (NOD) mouse backcross. The method involves adding and deleting markers from a linear model in a stepwise manner, allowing the association with a particular marker to be examined once associations with other (in particular neighbouring) markers have been taken into account. This approach has the advantage of using programs available in standard statistical packages while still allowing adequate separation of possible multiple linked effects. For the mouse backcross, using these methods, at least two and possibly three diabetogenic loci are detected on each of chromosomes 1 and 3. Some evidence for epistasis is seen between the loci on chromosome 1, with a possible additional epistatic interaction between the loci on chromosome 3. Congenic strain analysis of the chromosome regions in NOD diabetes suggests that although the true type I error rate may be larger than that suggested by the nominal P values, our results nevertheless correspond well with those disease loci and interactions detected using a congenic approach, indicating that the regression method may be a powerful strategy for the detection and characterization of QTLs in inbred populations.

scholarly journals Interval mapping of multiple quantitative trait loci.

Genetics ◽  
1993 ◽  
Vol 135 (1) ◽  
pp. 205-211 ◽  
Author(s):  
R C Jansen
Keyword(s):  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Interval Mapping ◽  
Inbred Lines ◽  
Mapping Method ◽  
Regression Methods ◽  
Multiple Qtl ◽  
Computational Work ◽  
Trait Loci ◽  
Additional Qtls

Abstract The interval mapping method is widely used for the mapping of quantitative trait loci (QTLs) in segregating generations derived from crosses between inbred lines. The efficiency of detecting and the accuracy of mapping multiple QTLs by using genetic markers are much increased by employing multiple QTL models instead of the single QTL models (and no QTL models) used in interval mapping. However, the computational work involved with multiple QTL models is considerable when the number of QTLs is large. In this paper it is proposed to combine multiple linear regression methods with conventional interval mapping. This is achieved by fitting one QTL at a time in a given interval and simultaneously using (part of) the markers as cofactors to eliminate the effects of additional QTLs. It is shown that the proposed method combines the easy computation of the single QTL interval mapping method with much of the efficiency and accuracy of multiple QTL models.

scholarly journals On the Differences Between Maximum Likelihood and Regression Interval Mapping in the Analysis of Quantitative Trait Loci

Genetics ◽  
2000 ◽  
Vol 156 (2) ◽  
pp. 855-865 ◽  
Author(s):  
Chen-Hung Kao
Keyword(s):  
Quantitative Trait Loci ◽  
Maximum Likelihood ◽  
Qtl Mapping ◽  
Quantitative Trait ◽  
Mean Squared Error ◽  
Interval Mapping ◽  
Size Difference ◽  
Ratio Test ◽  
Trait Loci ◽  
Variance Explained

AbstractThe differences between maximum-likelihood (ML) and regression (REG) interval mapping in the analysis of quantitative trait loci (QTL) are investigated analytically and numerically by simulation. The analytical investigation is based on the comparison of the solution sets of the ML and REG methods in the estimation of QTL parameters. Their differences are found to relate to the similarity between the conditional posterior and conditional probabilities of QTL genotypes and depend on several factors, such as the proportion of variance explained by QTL, relative QTL position in an interval, interval size, difference between the sizes of QTL, epistasis, and linkage between QTL. The differences in mean squared error (MSE) of the estimates, likelihood-ratio test (LRT) statistics in testing parameters, and power of QTL detection between the two methods become larger as (1) the proportion of variance explained by QTL becomes higher, (2) the QTL locations are positioned toward the middle of intervals, (3) the QTL are located in wider marker intervals, (4) epistasis between QTL is stronger, (5) the difference between QTL effects becomes larger, and (6) the positions of QTL get closer in QTL mapping. The REG method is biased in the estimation of the proportion of variance explained by QTL, and it may have a serious problem in detecting closely linked QTL when compared to the ML method. In general, the differences between the two methods may be minor, but can be significant when QTL interact or are closely linked. The ML method tends to be more powerful and to give estimates with smaller MSEs and larger LRT statistics. This implies that ML interval mapping can be more accurate, precise, and powerful than REG interval mapping. The REG method is faster in computation, especially when the number of QTL considered in the model is large. Recognizing the factors affecting the differences between REG and ML interval mapping can help an efficient strategy, using both methods in QTL mapping to be outlined.

scholarly journals Time-Related Mapping of Quantitative Trait Loci Underlying Tiller Number in Rice

Genetics ◽  
1999 ◽  
Vol 151 (1) ◽  
pp. 297-303 ◽  
Author(s):  
Wei-Ren Wu ◽  
Wei-Ming Li ◽  
Ding-Zhong Tang ◽  
Hao-Ran Lu ◽  
A J Worland
Keyword(s):  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Composite Interval Mapping ◽  
Interval Mapping ◽  
Tiller Number ◽  
Multiple Trait ◽  
Phenotypic Data ◽  
Recombinant Inbred Population ◽  
Trait Loci ◽  
Final Observation

Abstract Using time-related phenotypic data, methods of composite interval mapping and multiple-trait composite interval mapping based on least squares were applied to map quantitative trait loci (QTL) underlying the development of tiller number in rice. A recombinant inbred population and a corresponding saturated molecular marker linkage map were constructed for the study. Tiller number was recorded every 4 or 5 days for a total of seven times starting at 20 days after sowing. Five QTL were detected on chromosomes 1, 3, and 5. These QTL explained more than half of the genetic variance at the final observation. All the QTL displayed an S-shaped expression curve. Three QTL reached their highest expression rates during active tillering stage, while the other two QTL achieved this either before or after the active tillering stage.

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