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 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 Multiple Interval Mapping for Quantitative Trait Loci

Genetics ◽  
1999 ◽  
Vol 152 (3) ◽  
pp. 1203-1216
Author(s):  
Chen-Hung Kao ◽  
Zhao-Bang Zeng ◽  
Robert D Teasdale
Keyword(s):  
Genetic Variation ◽  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Genetic Parameters ◽  
Interval Mapping ◽  
Ratio Test ◽  
Data Set ◽  
Multiple Interval Mapping ◽  
Total Genetic Variation ◽  
Trait Loci

Abstract 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 ∼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 ∼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/).

scholarly journals Inheritance Analysis and Quantitative Trait Loci Detection of Head Splitting Resistance in Cabbage (Brassica oleracea L. var. capitata)

HortScience ◽  
2015 ◽  
Vol 50 (7) ◽  
pp. 944-951 ◽  
Author(s):  
Yanbin Su ◽  
Yumei Liu ◽  
Huolin Shen ◽  
Xingguo Xiao ◽  
Zhansheng Li ◽  
...  
Keyword(s):  
Quantitative Trait Loci ◽  
Qtl Mapping ◽  
Quantitative Trait ◽  
Major Gene ◽  
Genetic Regulation ◽  
Interval Mapping ◽  
Phenotypic Data ◽  
Dh Population ◽  
Trait Loci ◽  
Inclusive Composite Interval Mapping

Head splitting resistance (HSR) in cabbage is an important trait closely related to appearance, yield, storability, and mechanical harvestability. In this study, a doubled haploid (DH) population derived from a cross between head splitting-susceptible inbred cabbage line 79-156 and resistant line 96-100 was used to analyze inheritance and detect quantitative trait loci (QTLs) for HSR during 2011–12 in Beijing, China. The analysis was performed using a mixed major gene/polygene inheritance method and QTL mapping. This approach, which uncovered no cytoplasmic effect, indicated that HSR can be attributed to additive-epistatic effects of three major gene pairs combined with those of polygenes. Major gene and polygene heritabilities were estimated to be 88.03% to 88.22% and 5.65% to 7.60%, respectively. Using the DH population, a genetic map was constructed with simple sequence repeat (SSR) markers anchored on nine linkage groups spanning 906.62 cM. Eight QTLs for HSR were located on chromosomes C4, C5, C7, and C9 based on 2 years of phenotypic data using both multiple-QTL mapping and inclusive composite interval mapping. The identified QTLs collectively explained 37.6% to 46.7% of phenotypic variation. Three or four major QTLs (Hsr 4.2, 7.2, 9.3, and/or 9.1) showing a relatively larger effect were robustly detected in different years or with different mapping methods. The HSR trait was shown to have a complex genetic basis. Results from QTL mapping and classical genetic analysis were consistent. Our results provide a foundation for further research on HSR genetic regulation and molecular marker-assisted selection (MAS) for HSR in cabbage.

scholarly journals Aspects of maximum likelihood methods for the mapping of quantitative trait loci in line crosses

1992 ◽  
Vol 60 (2) ◽  
pp. 139-151 ◽  
Author(s):  
S. A. Knott ◽  
C. S. Haley
Keyword(s):  
Quantitative Trait Loci ◽  
Maximum Likelihood ◽  
Quantitative Trait ◽  
Simulated Data ◽  
Interval Mapping ◽  
Likelihood Methods ◽  
Trait Loci ◽  
Marker Loci ◽  
Maximum Likelihood Methods ◽  
Distribution Testing

SummaryMaximum likelihood methods for the mapping of quantitative trait loci (QTL) have been investigated in an F2 population using simulated data. The use of adjacent (flanking) marker pairs gave improved power for the detection of QTL over the use of single markers when markers were widely spaced and the QTL effect large. The use of flanking marker loci also always gave moreaccurate and less biassed estimates for the effect and position of the QTL and made the method less sensitive to violations of assumptions, for example non-normality of the distribution. Testing the hypothesis of a linked QTL against that of no QTL is not biassed by the presence of unlinked QTL. This test is more robust and easier to obtain than the comparison of a linked with an unlinked QTL. Fixing the recombination fraction between the markers at an incorrect value in the analyses with flanking markers does not generally bias the test for QTL or estimates of their effect. The presence of multiple linked QTL bias both tests and estimates of effect with interval mapping, leading to inflated values when QTL are in association in the lines crossed and deflated values when they are in dispersion.

scholarly journals Approximate thresholds of interval mapping tests for QTL detection.

Genetics ◽  
1994 ◽  
Vol 138 (1) ◽  
pp. 235-240 ◽  
Author(s):  
A Rebaï ◽  
B Goffinet ◽  
B Mangin
Keyword(s):  
Quantitative Trait Loci ◽  
Qtl Mapping ◽  
Quantitative Trait ◽  
Interval Mapping ◽  
Qtl Detection ◽  
Recombinant Inbreds ◽  
Codominant Markers ◽  
Trait Loci ◽  
Simulation Results ◽  
General Method

Abstract A general method is proposed for calculating approximate thresholds of interval mapping tests for quantitative trait loci (QTL) detection. Simulation results show that this method, when applied to backcross and F2 populations, gives good approximations and is useful for any situation. Programs which calculate these thresholds for backcross, recombinant inbreds and F2 for any given level and any chromosome with any given distribution of codominant markers were written in Fortran 77 and are available under request. The approach presented here could be used to obtain, after suitable calculations, thresholds for most segregating populations used in QTL mapping experiments.

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.

scholarly journals The Genetic Basis of the Interspecific Differences in Wing Size in Nasonia (Hymenoptera; Pteromalidae): Major Quantitative Trait Loci and Epistasis

Genetics ◽  
2002 ◽  
Vol 161 (2) ◽  
pp. 673-684
Author(s):  
J Gadau ◽  
R E Page ◽  
J H Werren
Keyword(s):  
Quantitative Trait Loci ◽  
Qtl Analysis ◽  
Quantitative Trait ◽  
Wing Length ◽  
Size Difference ◽  
Phenotypic Variance ◽  
Wing Size ◽  
Epistatic Interactions ◽  
Trait Loci ◽  
Wing Width

Abstract There is a 2.5-fold difference in male wing size between two haplodiploid insect species, Nasonia vitripennis and N. giraulti. The haploidy of males facilitated a full genomic screen for quantitative trait loci (QTL) affecting wing size and the detection of epistatic interactions. A QTL analysis of the interspecific wing-size difference revealed QTL with major effects and epistatic interactions among loci affecting the trait. We analyzed 178 hybrid males and initially found two major QTL for wing length, one for wing width, three for a normalized wing-size variable, and five for wing seta density. One QTL for wing width explains 38.1% of the phenotypic variance, and the same QTL explains 22% of the phenotypic variance in normalized wing size. This corresponds to a region previously introgressed from N. giraulti into N. vitripennis that accounts for 44% of the normalized wing-size difference between the species. Significant epistatic interactions were also found that affect wing size and density of setae on the wing. Screening for pairwise epistatic interactions between loci on different linkage groups revealed four additional loci for wing length and four loci for normalized wing size that were not detected in the original QTL analysis. We propose that the evolution of smaller wings in N. vitripennis males is primarily the result of major mutations at few genomic regions and involves epistatic interactions among some loci.

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.

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