A Logistic Regression Mixture Model for Interval Mapping of Genetic Trait Loci Affecting Binary Phenotypes

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.

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

Genetics ◽

10.1093/genetics/151.1.297 ◽

1999 ◽

Vol 151 (1) ◽

pp. 297-303 ◽

Cited By ~ 3

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

Genetics ◽

10.1093/genetics/148.3.1373 ◽

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.

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

Genetics ◽

10.1093/genetics/149.3.1547 ◽

1998 ◽

Vol 149 (3) ◽

pp. 1547-1555 ◽

Cited By ~ 2

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.

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Mapping of Quantitative Trait Loci Controlling Adaptive Traits in Coastal Douglas Fir. III. Quantitative Trait Loci-by-Environment Interactions

Genetics ◽

10.1093/genetics/165.3.1489 ◽

2003 ◽

Vol 165 (3) ◽

pp. 1489-1506

Author(s):

Kathleen D Jermstad ◽

Daniel L Bassoni ◽

Keith S Jech ◽

Gary A Ritchie ◽

Nicholas C Wheeler ◽

...

Keyword(s):

Quantitative Trait Loci ◽

Quantitative Trait ◽

Complex Traits ◽

Moisture Stress ◽

Interval Mapping ◽

Douglas Fir ◽

Adaptive Traits ◽

Growth Cessation ◽

Trait Loci ◽

Growth Initiation

Abstract Quantitative trait loci (QTL) were mapped in the woody perennial Douglas fir (Pseudotsuga menziesii var. menziesii [Mirb.] Franco) for complex traits controlling the timing of growth initiation and growth cessation. QTL were estimated under controlled environmental conditions to identify QTL interactions with photoperiod, moisture stress, winter chilling, and spring temperatures. A three-generation mapping population of 460 cloned progeny was used for genetic mapping and phenotypic evaluations. An all-marker interval mapping method was used for scanning the genome for the presence of QTL and single-factor ANOVA was used for estimating QTL-by-environment interactions. A modest number of QTL were detected per trait, with individual QTL explaining up to 9.5% of the phenotypic variation. Two QTL-by-treatment interactions were found for growth initiation, whereas several QTL-by-treatment interactions were detected among growth cessation traits. This is the first report of QTL interactions with specific environmental signals in forest trees and will assist in the identification of candidate genes controlling these important adaptive traits in perennial plants.

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