Introduction to PLABQTL

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1 Introduction to PLABQTL H.F. Utz Institute of Plant Breeding, Seed Science and Population Genetics, University of Hohenheim Germany Utz Introduction to PLABQTL 1

2 PLABQTL is a computer program for 1. detection and analysis of QTL, 2. prediction of performance of individuals by marker data, using interval mapping (IM) based on multiple regression (MR). PLABQTL is written in Fortran (DOS or WINDOWS computing environments). Features: Simple interval mapping (SIM), Composite interval mapping (CIM) Permutation tests Cross-validation QTL environment analysis For F 2 until RIL, or test cross generations Literature: Utz and Melchinger, and Kearsey and Pooni (1996, Ch. 7) as introduction to QTL mapping Liu (1998) as a text book Lynch and Walsh (1998) as a text book Paterson (1998) for methods and results LOD 3 van Ooijen' s MAPQTL 2 MAPMAKER 1 JIANG PLABQTL MAPMAKER sample file chrom.1 (cm) Figure 1: Comparison of LOD curves from ML and MR programs To the difference of ML and LS: LOD-curves of maximum likelihood (ML) and multiple regression (MR) or least squares method (LS) are very similar (Haley and Knott, 1992) see Figure 1 MR-based IM more robust than ML-based IM against non-normality, MR statistically well-known, better to understand for bioists. MR underestimates R², see XU (1995). Utz Introduction to PLABQTL 2

3 A first trial run with PLABQTL The program is batch-oriented. Some basic subroutines and the handling philosophy are identical with the PLABSTAT program. PLABQTL reads an input file with default extension *.qin which can be prepared with your personal editor or text processing software. This file contains statements to control the analysis and for loading the input file with the marker and phenotypic data. Call in a MS-DOS-Window, e.g.: to analyse the MAPMAKER sample data file with control statements in sample_s.qin and data in sample.qdt plabqtl sample_s The format of input files is similar to the format of MAPMAKER/EXP, GMENDEL, or JOINMAP thus the export of data from the mapping software into PLABQTL can be done easily. The output is written in a file *.qpt which can be viewed with your editing and/or printing tool (here sample_s.qpt). Output pieces are: STATUS OF MARKER DATA * LINKAGE MAP * FREQUENCY of marker pairs within each linkage group * PERCENTAGE OF HOMOZYGOSITY AND GENOME FOR PARENT1 * HISTOGRAM OF HOMOZYGOSITY CRITICAL VALUE FOR LOD SCORE (Bonferroni chi-square approximation) * OVERVIEW ON OBSERVATION VARIABLES PRESELECTION OF MARKER COFACTORS SCATTER PLOT * MEANS OF MARKER CLASSES per linkage group LOD PLOT per linkage group LIST OF DETECTED QTL FINAL SIMULTANEOUS FIT SCATTER PLOT OUTLIER TEST * only if statement first is used Some additional output (LODs, effects, predicted and observed values) may be written on a second output file *.qst which may be displayed with other graphical programs (here sample_s.qst). The postscript file for the LOD curves is named as *.ps. Estimated parameters are written in the file *.qcv if resampling procedures are called by the user. The outcome of analysis is influenced by the choice of parameters, like LOD-threshold or F-to-enter and F-to-delete. The program works with default LOD of 2.5 and default F-to-enter of 3.0. These values are not always appropriate and can be varied with the statements scan and parameter. The output can be controlled by out and first statement. With convert, the data may be written in some other formats to make easier shifting to other programs. Utz Introduction to PLABQTL 3

4 Working with PLABQTL Several analyses steps in QTL analysis with PLABQTL are demonstrated by means of the MAPMAKER/QTL sample file. The output can be compared with the MAPMAKER/QTL tutorial, with little differences due to MR-based IM in PLABQTL. Several files *.qin - one for each analysis step - are prepared. Thus you can activate PLABQTL and see the output of each step: sample_?.qpt, sample_?.qst, sample_?.ps 1. Analysis with SIM: plabqtl sample_s SIM is intended if only one QTL per linkage group can be assumed. This analysis mode is interesting for characterization and proofing of marker and phenotypic data for comparing with MAPMAKER/QTL output. Some statements as first and convert may be choosen in the first step of analysis only. 2. Analysis with CIM: plabqtl sample_c CIM attempts to take into account more than one QTL per linkage group and unbalanced QTL genotype frequencies. The cofactors (representing potential QTL) are automatically selected by forward stepwise regression, with the statement cov SEL. CIM shows often sharper, higher, and more peaks in the LOD curves than SIM which can be recognized very clearly in this data set. See Figure Analysis with permutation test: plabqtl sample_t A permutation test can be used to determine the critical LOD threshold using statement permut 1000 We choose the LOD threshold for a genom-wide error at the 0.05 level from the end of sample_t.qpt. The threshold is 2.57 which is lower than 2.79 which is the Bonferroni chi-square approximation given in sample_s.qpt or sample_c.qpt above. We can finish since the two detected QTL have LOD values greater than the treshold or since the LOD default of 2.5 is not very different from 2.57 produced by permutation. The user may choose in statement scan another LOD threshold, e.g. here analyze at 0.10 genom-wide error level from the end of sample_t.qpt). scan (to 4. Analysis with all linked cofactors: plabqtl sample_p Linked QTL, as much as possible, may be detected using statement cov/+ SEL which uses all markers as cofactors at the chromosome being scanned. We find some smaller peaks lying under the threshold at chromosome 1 at position 0 with reverse sign of QTL effect and on chromsome 2 at position 90. Choosing only those markers as Utz Introduction to PLABQTL 4

5 cofactors closer to peaks (or potential QTL), we reach higher power, e.g. in sample_d.qpt (with cov ) two QTL at chromosome 2 are detected. We see that the position of a QTL and its detectability depends on the choice of cofactor markers and the LOD threshold. A certain subjectivity of cofactor selection and the indeciveness of QTL raise difficulties for the scientist. Further it is not possible to separate between two QTL in adjacent intervals. For usual sample sizes, cofactors should be away on an average about 10 cm from the nearest flanking marker of the interval to be scanned. Otherwise too tightly correlated cofactors can result in ill-conditioned equation systems, diminishing power of detection in the scanned interval, or causing false secondary linked QTL. Some examinations by hand are necessary in each case. A visual comparing of the LOD curves may be helpful, see Figure Analysis with cross-validation (cv): plabqtl sample_v This may be useful in analysing the influence of genotypic and environmental sampling, and determining the bias and sampling error of explained variance. CV can be implemented using the statement cross By default, i.e. 5-fold cross-validation, we get five estimates for R²(adj.) between 3.2 % and 25.1 % which gives on average, a more unbiased estimate for the part of explainable variance with 17.3 %. In mapping programs, R² is mostly used but R²(adj.) is preferable, see Charcosset and Gallais (1996). Different R² estimates are shown below for comparison R²(MAPMAKER/QTL) = 27.0% R²(PLABQTL) = 21.8 % R²(adj, PLABQTL) = 20.2 % R²(adj,val., PLABQTL) = 17.3 % Some more 5-fold cross-validation runs may be necessary to get indications how the number, positions, and effects of QTL are influenced by sampling. Modifying the cross-validation statement to cross/g 1000, i.e. conducting 5x200 = 1000 or 200 independently sampled 5-fold cross-validation runs, we find the following in the sample_v.qcv file: Runs detecting 1 putative QTL occur with 10.3 % frequency, 2 putative QTL with 89.1%, and 3 QTL with 0.5% frequency. The occurence peaks agree with the LOD peaks at chromosome 1 on position 26 cm with 46.9% (or in the interval with 90.3%) and on chromosome 2 on position 28 cm with 39.3% (or in the interval with 91.6%). Outside these intervals QTL were seldom found. So a model with 2 QTL seems adaequate and behaves relatively stable. Cross-validation analyses of several real experiments are given in Utz et al. (2000). 6. Analysis of gene action: plabqtl sample_m Different genetic models, e.g. A vs. A+D vs. A+D+AA vs...., can be compared using statements, AA, and DD. The criteria R²(adj.) or AIC (Akaike information criterion) may be used to select between regression models (Hjorth 1994). These estimates and the corresponding estimates from resampling methods with 100 runs each are tabulated for our two-qtl example: Utz Introduction to PLABQTL 5

6 CIM analysis Median of R²(adj.)% in CV Model R²(adj.)% AIC BIC Calibr. Valid. A A+D 20.2* A+D+AA 20.1** A+D+AA+AD+DA+DD * see sample_c.qpt ** see sample_m.qpt with estimated genetic effects for the different models Model a1 d1 a2 d2 a1a2 a1d2 d1a2 d1d2 A -0.12** -0.15** A+D -0.11** ** A+D+AA -0.10** ** A+D+AA+AD+DA+DD -0.21** ** * *, ** significantly different from 0 at P=0.05 and 0.01 respectively R²(adj.), and R² even more, increases at calibration with CIM if more terms enter the model. But at validation, only the pure additive two-locus model is the best. The BIC, with a more stringent penalty than AIC, seems to correspond with the rankings from cross-validation. No indications for epistatic inheritance were present. In conclusion: We detected two mutual QTL at 1/26 and 2/28 with R²(adj.) = 20 % in the calibrating simultaneous fit. According to cross-validation results only 16 % of the total phenotypic variance may be explained by the two QTL whereby simple additive gene action may be sufficient to assume. Dividing this value by the heritability we get the explainable part of genetic variance. But heritability is unknown in this example. Problematic points in mapping QTL The analysis of QTL is in some sense soft and subjective. The interpretation must be cautious. Analyses with resampling can show the influence of sampling on findings. Points in the statistical analysis which require careful attention are a. choice of cofactors b. choice of LOD thresholds with cofactor selection c. choice between submodels of 1 and 2 loci: A, D, AA, AD, DD,... (see Zeng et al. 1999) d. unbiased estimates of R², positions and QTL effects (or elimination of overestimation due to model selection) e. effect of genotype x environment interactions on mapping Some other points are discussed on the internet page References Charcosset, A. and A. Gallais, 1996: Estimation of the contribution of quantitative trait loci Utz Introduction to PLABQTL 6

7 (QTL) to the variance of a quantitative trait by means of genetic markers. Theor.Appl. Genet. 93, Haley, C.S., and S.A. Knott, A simple regression method for mapping quantitative trait loci in line crosses using flanking markers. Heredity 69, Hjorth, J.S.U., 1994: Computer Intensive Statistical Methods. Chapmann&Hall Kearsey, M.J., and H.S. Pooni, 1996: The Genetical Analysis of Quantitative Traits. ChapmanHall, London. Lincoln, S.E., M.J. Daly, and E.S. Lander Constructing genetic linkage maps with MAPMAKER/EXP version 3.0: A tutorial and reference manual. Whitehead Institute for Biomedical Research, Cambridge, MA. Liu, B.-H Statistical Genomics, CRC Press, Boca Raton. Lynch, M., and B. Walsh, Genetics and Analysis of Quantitative Traits. Sinauer Associates, Inc., Sunderland, Massachusetts. Melchinger, A.E., H.F. Utz, and C.C. Schön, 1998: Quantitative trait locus (QTL) mapping using different testers and independent population samples in maize reveals low power of QTL detection and large bias in estimates of QTL effects. Genetics 149, Paterson, A.H. (ed.) Molecular Dissection of Complex Traits, CRC Press, Boca Raton Schön, C.C., A.E. Melchinger, J. Boppenmaier, E. Brunklaus-Jung, R.G. Herrmann, and J.F. Seitzer, RFLP mapping in maize. Quantitative trait loci affecting testcross performance of elite European flint lines. Crop Sci. 34: Utz, H.F., and A.E. Melchinger, Comparison of different approaches to interval mapping of quantitative trait loci. In: van Ooijen, J.W. and J. Jansen (eds.), Biometrics in Plant Breeding: Applications of Molecular Markers, Wageningen, Utz, H.F., and A.E. Melchinger, PLABQTL: A computer program to map QTL, Version 1.0, University of Hohenheim. Utz, H.F., and A.E. Melchinger, PLABQTL: A program for composite interval mapping of QTL. JQTL 2(1) Utz, H.F., Melchinger, A.E., and C.C. Schön, Bias and sampling error of the estimated proportion of genotypic variance explained by QTL determined from experimental data in maize using cross validation and validation with independent samples. Genetics 154, Xu, S A comment on the simple regression method for interval mapping. Genetics 141: Zeng, Z.-B., C.-H. Kao, and C.J. Basten, Estimating the genetic architecture of quantitative traits. Genet. Res., Camb. 74, Utz Introduction to PLABQTL 7

8 PLABQTL input files *.qin with data from MAPMAKER/QTL tutorial sample sample_s.qin: sample_c.qin: c Data of MAPMAKER tutorial c Data of MAPMAKER tutorial first c first convert load sample.qdt load sample.qdt out out c to select cofactors scan 2 c by stepwise regression: cov SEL scan 2 sample_t.qin: sample_p.qin: c Data of MAPMAKER tutorial c Data of MAPMAKER tutorial load sample.qdt load sample.qdt out out cov SEL c with all linked cofactors: c to conduct 1000 permutations: cov/+ SEL permut 1000 scan 2 scan 2 sample_d.qin:... c with hand-choosen cofactors: cov sample_v.qin: sample_m.qin: c Data of MAPMAKER tutorial c Data of MAPMAKER tutorial load sample.qdt load sample.qdt out out c to analyse with AA model: cov SEL AA c for 5-fold cross-validation: cov SEL cross scan 2 scan 2 Utz Introduction to PLABQTL 8

9 SIM sample_s CIM sample_c CIM(cov/+) sample_p CIM(cov...) sample_d Figure 2: LOD curves of MAPMAKER/QTL Tutorial sample, analysed with SIM and CIM procedures using PLABQTL (first row chromosome 1, second row chromosome 2) Utz Introduction to PLABQTL 9

Construction of a genetic map, mapping of major genes, and QTL analysis

Construction of a genetic map, mapping of major genes, and QTL analysis A. Touré a, B.I.G. Haussmann b, N. Jones c, H. Thomas d, and H. Ougham e a b c d IER, CRRA-Sotuba BP 261 Bamako, Mali, West Africa