PROC QTL A SAS PROCEDURE FOR MAPPING QUANTITATIVE TRAIT LOCI (QTLS)

Transcription

1 A SAS PROCEDURE FOR MAPPING QUANTITATIVE TRAIT LOCI (QTLS) S.V. Amitha Charu Rama Mithra NRCPB, Pusa campus New Delhi mithra.sevanthi@rediffmail.com Genes that control the genetic variation of quantitative traits are called quantitative trait loci (QTL) (Tanksley 1993). Finding the genome locations of the QTL and estimating the effects of the QTL using molecular markers as anchors is called QTL mapping (Tanksley 1993). Though the linkage between a genetic marker and a QTL was first demonstrated by associating the seed colour (marker) and seed size (QTL) in Phaseolus vulgaris (Sax 1923), non-availability of genetic markers remained one of the biggest practical hurdle for QTL detection (Thoday, 1961). This limitation was overcome by the construction of saturated linkage maps with molecular markers, allowing systematic genome-wide scans for QTLs influencing the expression of a quantitative trait (Paterson et al. 1988). From the single marker analysis (SMA) Sax (1923) employed to detect QTL in a segregating population, the QTL mapping procedures have come a long way now with development of large segregating (F 2 and BC) and immortal populations (RILs, DH and MAGIC) and the availability of sophisticated mapping procedures and software to implement them. QTL mapping almost exclusively uses the linear model to describe the relationship between the phenotypic value and the putative QTL. The most commonly used method is the maximum likelihood method. Logarithm of Odds (LOD) score or Likelihood Ratio Test (LRT) (Wilks 1938) is often used as the test statistic. There are at least dozens of software available to execute QTL analysis. QTL cartographer and Mapmaker/QTL version are the widely used ones. Why? However most of the availble software programmes do not handle marker data that exhibit segregation distortion. Segregation distortion is a ubiquitous phenomenon in the biosphere, which is responsible for deviation of the frequency of genotypes from the expected Mendelian ratio within segregating populations, which get fixed upon continuous selfing, thereby also affecting permanent mapping populations (Xu et al. 2008). Depending on the population under investigation, Mendelian ratio of a locus varies from 1:1 for a backcross to 1:2:1 for F 2 to 1:1:1:1 for a four-way cross. This phenomenon is actually encountered in mapping populations and caused by either gametic or zygotic effects (Li et al. 2005). Comparisons have shown that this phenomenon is more prevalent in RILS and DH than F2 mapping populations (Zhang et al. 2010). Loci exhibiting segregation distortion may not be common across populations (Yamagishi et al. 2010). Moreover, in some mapping populations such as RILs and F2, more often than not conscious or unconscious selection is exercised while sampling genotypes for phenotyping and genotyping. This selection, which may be very important for practical purposes, also brings in segregation distortion. Thus many polymorphic markers are excluded from the final analysis which shows segregation distortion either owing to genetic reasons or selection practiced, despite them being informative. For a long period of time, the effects of distorted markers on the result of QTL mapping were not known. Such loci or markers also cannot be handled by regular mapping procedures. For precaution, people simply discarded all the distorted markers in QTL

2 mapping. However, Xu (2008) reported that distorted markers can be safely used for QTL mapping with no detrimental effect on the result of QTL mapping. This finding can help researchers save tremendous resources by using all available markers, regardless whether they exhibit Mendelian segregation or not. If distorted markers are handled properly, they can be beneficial to QTL mapping and software programme (Hu and Xu 2010) handles such markers properly so that they can be employed for the QTL detection. Many commonly used software tools do not also handle data that are binary or discrete in nature, making it difficult to analyze threshold characters. Some traits have a discrete distribution, e.g., disease resistance traits, litter size, where the phenotype is measured by kind, e.g., affected and normal; or by classes e.g., 1, 2, 3 and 4 (Falconer 1960; Xu and Atchley 1996). Very few disease resistance traits are controlled by a single gene (Turnpenny and Ellard 2005) and litter size is certainly a quantitative trait, however, are controlled by multiple genes plus environmental effects. These traits, although phenotypically very simple, are genetically complicated. They are polygenic traits and thus are often defined as complex traits (Lander and Schork 2006). The way to handle these traits is to hypothesize an underlying continuously distributed liability under each discrete trait (Wright 1934). The connection between the unobserved liability and the observed phenotype is through a threshold. Below the threshold, the individual will have the normal phenotype. Above the threshold, it will show the abnormal (disease) phenotype. Using the threshold model, we can map QTL controlling the unobserved liability (Rao and Xu 1998; Xu et al. 2005; Xu and Atchley 1996). The QTL parameters are estimated in the scale of liability. mapping software also covers these kinds of complex traits, the only condition being the number of classes used should not exceed 10. What is Proc QTL? is a user defined SAS procedure for mapping quantitative trait loci. The current version of can handle the following mating designs: F 2, BC (backcross), FW (fourway cross), RIL (recombinant inbred lines) and DH (double haploid). It uses two major statistical methods to estimate QTL parameters, the maximum likelihood method (ML) and the Bayesian method. The maximum likelihood method is used for interval mapping while the Bayesian method is used for mapping multiple QTL. Ebayes method is used for mapping interactions between loci. More importantly it can handle marker data showing segregation distortion and also data that are in class intervals or binary in nature. It can handle the former under ML and the latter in any method, only requirement being declaration of the variable as class. This programme needs SAS environment for its execution. In a SAS enabled system, software can be downloaded and invoked. It needs two files for QTL detection like any other programme: one with phenotypic data of individuals along with their marker data across loci and another with the markers with their map positions. Map positions within a chromosome need to be cumulative. Markers have to be named as m1, m2, m3 to mn and the phenotypic variable as Y. Different statements required for executing this procedure (Table 1). Those statements that are marked in the table (**) are mandatory and others are used when required. For example, CLASS needs to be included in the script only when discrete traits are analyzed. METHOD has to be specified as ML or Bayes or Ebayes etc, otherwise method ML will be executed by default. For distorted markers, the method, ML /distortion has to be mentioned; even if one mentions distortion under methods it will not be executed.

3 Table 1: Statements required for procedure and their description Statement Description ** CLASS invokes the procedure declares classification (discrete) variables MODEL** defines the linear model to be fit for non-qtl effects, e.g., location and gender METHOD defines the method to be used for analysis; default is ML MARKER provides names of markers to be included in the analysis; default will consider all markers MATINGTYPE** define the type of line cross GENOTYPE** defines marker genotypes ESTIMATE** defines QTL effects (linear contrasts of genotypic values) RANGE specifies a region of the genome for analysis; default will scan the entire genome. WEIGHT declares a weight variable BY declare variables as subgroups for separate analysis (data must be sorted first) STEP Scanning interval in the genome in cm. The output data file contains the following information (Table 2). There may be little variation among methods with respect to the output parameters depending upon what they are intended for. Table 2: Variables in the output dataset Variables Description Trait The name of dependents variable specified in the model statement Chr Chromosome identification of the position scanned Marker The name of molecular marker variable described in the primary dataset Position Location of each assumed locus in the linkage map n_iter Number of iterations required for convergence conv_err Convergence error LRT Likelihood ratio test statistics Wald Wald test statistics Ve Residual error variance Intercpt The intercept or the mean of the dependent variable (trait) var_i The variance of the i-th user-defined QTL effect cov_i_j The covariance between the i-th and the j-th QTL effects intcpt_1 intcpt_n The intercept for ordinal data analysis. The first and last values are 1E10 and 1E10, respectively.

4 LRT_dist freq_aa freq_ab freq_bb The test statistics for segregation distortion analysis The estimated frequencies of genotypes AA, AB and BB for the locus scanned The tests statistics are Likelihood Ratio Test (LRT) and Wald statistic. It is better to use LRT than Wald statistic at least while analyzing distorted markers. Both of them essentially arrive at the same conclusion follow and the χ2 distribution but the Wald statistics are inflated than LRT. In plants LOD scores are the more common test statistics; however in animals LOD scores as well as LRT is used. Heritability estimates are not given in the output. Since genotype frequencies and estimates are availble from the output data set, one can directly calculate mean and variance from the phenotypic data and go for estimating heritability (R 2 ). A sample statement for proc qtl data=pridata map=map1 out=iarigb10 method='ml'/distortion step=5; model Y =; matingtype "RIL1"; Genotype A1A1='A' A2A2='B'; estimate "A"=1-1; run; For further reading and clarifications, the reader may download manual from the following site. Worked out example The following are the two data files required for QTL analysis. First one is the data on grain length obtained from 276 recombinant inbred lines (RILs) by continued selfing for six generations and their marker data (16 markers ) on chromosome one of rice. This data set is called the primary data set in QTL analysis. First two lines have the parental data and the rest are RILs. The second data set pertains to the genetic map indicating markers names, their position on the chromosome and the respective chromosomes. These two files need to be imported in SAS environment for further analysis after which is run. If these two files are named as pridata and map1 respectively, then the sample statements given above can be used as such. 1. Pridata(data file): Kindly note that the missing data is given as U and the markers are coded as either A or B since the population analyzed is homozygous and no heterozygotes are allowed in this data set. Y m 1 m 2 m 3 m 4 m 5 m6 m 7 m 8 m1 m9 0 m11 m1 m12 3 m1 4 m1 5 m A A A A A A A A A A A A A A A A 9.62 B B B B B B B B B B B B B B B B 9.56 B A A A A A A A A B B B B B B A B A A A A A A A A A A A A A B B 9.39 A B B B B B B B B A U U A A B A 9.09 B A A A A A A A A U A A A A A A 8.77 A A A B A B A A B A A A A A A A

5 8.68 B B B B U B A A A A A A A A A A 9.72 A B B B B B U A A B B B B B B B 9.49 A A B B B B B U B B B B B B B B B B B B B A A A B B B B B B B B 9.89 B B B B A A A A B A U B A A B A 9.38 A A A A A A A B A A A A A A B A 9.25 B B B B A A A A A B B B A A A B 9.38 B B B B A A A A A U B U A A B A 9.47 B A A B B B A B B A B U A A A B 8.64 A A U A A A A A A A B B A A A A 9.07 B A U B A B A B B U B B B B B B 9.63 B B U B B B A A B B A A A A A A 9.71 A A A A A A A A A B B B B B B B 9.24 B B U B A A A A A A A A A A A A 9.85 A A U A A B A A A A B B A A B B 9.58 B B U B A A A A A A B B A A B A 9.88 B B U U B B B B B U B B B A B B 8.50 B B B B B B A A A B B B B B B B U B U B B B B B B B B B B B B B 9.44 U B B B A A A A A B B B B A A A 8.96 B B B B B B U A A B B B A A A B 9.43 A A U A A A A A A A B B A A A A B B B B B B B A A B A A A B B B 9.75 A A A A A A A A A A A A A A A A 9.43 B B B B B A A A A B B B B B A A 9.84 B B U B B B U A A A A A A A A A 9.70 B B U B B B A A A A A A U A A B B B U B B A A A A A A A A A A A 9.54 A B B B B A A A A A A A A A A A 9.68 B B B A A A A A A B B B B B B B 9.59 A A A A A A A A A A A A A A A A 9.55 B B B B B A A A A B A A A A A A 9.26 A A A A A A A A B A A A B B B B A A A A A B A A U A A A A A A A 9.20 B B B B A A A A B A B U A A A A B A A A A A A A A A B U A A B B B B B B B B A B A B B B B B B B 9.77 B A A A A A A A A U U U A A A A 9.81 B B B B B A A A A A A U A A A A 9.00 B B B B B B A A A A A A A A A A 8.97 B B B B A A A A A B B B B B U B

6 9.57 B B B A B A B B B A A A A A A A B B B B B B A B B A A A A A A A A A A A B B B B A A A A A A A A 9.59 B B A A B B B B A B A A A A A A 9.63 B B B B B B B B B A B B B B B B 9.96 B B B B B B A A B A A A A A B B 9.23 A B B B B B B A A A A A A A A A 9.87 A A A B B A A A A A A A A A A A 9.39 B B B B B B A A A U A A A A A A B B B B A A A A A A A A A A A A 9.52 B B B B U B A A A A A A A A A A 8.93 B B B B U A A A A A A A A A A A 9.92 A A A A A A A A A A A A A A A B 9.53 A A A A A B A A A A A A A A A A 9.17 A A A A A A A A A U A A A A B B 9.82 B B B B B A A A A B U B A A A B A A U A B B A A B A B B B A B B A A A A A A A A B A A A A A A A 9.55 B B B B B B B A B A A A A A A A 8.86 B B A A A B A A A A A A A A A A 9.64 B A A B A B A B B A A A A A A A A A A B A B A U B A A A A A A A 9.50 A A A B A B A B A B B B A A A A 8.79 B A A B A B A B B B B B B B B B 8.77 B A A B B B A A A A B B B B A A 9.53 B A A B A B A B B A B U A A A A 9.48 B A A B A B A A B A A A U A A A 9.78 A A A B A B A B B A A A A A A A 8.92 B B A U A B A B B A A U A A A A A B B B B B B B B A A A A A B B 8.34 A A A B A B A B B A A A A A A A 9.52 A A A B A B A A B A B B A A B B 9.61 A A A U A B A A A A B U A A B A

7 10.97 B A A B A A B B A A A A A A A A B B B 9.44 U A A B A B A A A B B B B B B B B B B 9.47 B A A B A A A A B U B B B A B B B A B 9.57 B A A B A B A B B U B B B A A A A B A 8.74 B B B B B A B B B B B B A A A B B B B A A A B B A B B B A B B A A A A A A A A A B B A B A B B B A A A A A A A A A 9.31 U A B B A B A A A A B B B A B A A A A 9.51 U A B B B A A A A A A A A A A A A A A A A B B A B A A B A A A A A B A B B B B A B B B B A B B A A A A A B A B B B 9.83 B A A B A B A A A A A A A A B A B B B 9.01 U A A B U B A B B A A U B A B A B B B A A A A A A A A A B B B B B B B B A B 9.77 A B A B B A A A A A A A A A A A A A A 9.80 A A A A A B A A A A A A A A A A A A A 9.62 A A A A A B A B B A B B B B B B A A A 9.56 A A A A B B A B B A A A A A A A B B B 9.71 B B B B B A B U A A A A A A A A A A A 9.27 B B B B B A A U B A A B B B A A B B B 9.01 B B B B B B B B U A A A A A A A B B A 9.77 B B B B A A A A A B A A A A A A B A B 9.65 A B A A B A A A A A A A A A A A A A A 9.56 B B B B B B A B B B B B A A A A A B A 8.85 B A A A A B B B A B B B B B B B B B B A A A A B B B B A A A B B A A A A A A 9.82 A A U A A A U A A A A A A A A A B B B 8.85 B B A B B B A A A A A A B B B B A B A 9.27 B A A A A A A A A A A A A B B B U A A A A A B A B A A B A A A A A A A A A B 9.91 B B B B B B B A A A A A A A A A B B B 9.26 B A A A A A A A A A A A A U A A A A B 9.07 B A A A A A A A A A A A A A A A B B B 9.65 A A B B A A A A A B B B B B B B A A B 9.48 A B B B A A A A A A A A A A A A A A A 9.76 B B B B B B B B B A A A A A A A B B B B B B U U B A B B U B B A A B A A B B 8.89 B B B B B A B A A A A A A A B A A B A 9.03 A B U B B B B A B A A A A B B A B A B

8 10.67 A A A U A B U A B A A A A A A A A B A 9.98 A B B B B B A A A B B B B B B A B B B A B B B A A A A A A A A A A A A A B B B B B B U B U B B A A A A A A A B A A 8.63 A A A A B B B A A A A A B B B B A A A A B B B B B B B A U A A A A A A A U B A A B A A A B A A B B B A A U A B B B 9.67 A A B A A B A A A A A A A A A A B A B 9.58 B B B B B B B B B B B B B B B B B A B 9.30 A A A A A A A A A A A A A A A A A A A 9.77 A A B A A B B B A A A A A A A A A A A 9.45 B B B B B B B B A A A A A A A B A A A 9.26 A B B U A A U B A U U A A A A A A A A 8.88 B B B A A A U A U B A A A A A A A A A 9.41 A A A A A A A A B B B B B A U A B B B 9.51 A A A A A A U A A B B B B A B A B B B 9.92 B B B B B B U A B A A A A A A A A B B 9.48 A A A B A A A A A A A A A A A A A A A A A A A A B B B A B B B B B A A A B B 9.07 A A A B U A A A A A A A A A A A A A A 9.76 B B B A A A A A A A A A A A A A A A A 9.94 A A A B U A A A A A A A A A A A A A B 9.78 A B B B B B A A A A A A A A A B B B B B B B B B A A A A U A B U B B B A A A 8.78 A A A A A A B B A A A A A A A A B A B 9.53 B A A A A A U A A B B B B B B B A B B 9.28 A A A A B B B B B B B B B B B B B A B 9.02 B B A A A A B A A B A B B B B A B B B B A A A A A U A A A A A A A A A A A U 8.34 B A A A B A U A A A A A A A A B A B A B U B U U B B B A A A A A A A U A B B B B B B B B B B B A A A A A A B A A A A U A B A A A A A B B B B B B B A B B A A B B U B A A B B B B A A A A A A A 9.28 A A A A U B U B B A A A A A A A A A A 9.61 A A B B U B U B B A A A A A A A A A A B A B B B B B B B A A A A A A A A A A 9.49 B A B B A B B B B A A A A A A A A A B 9.22 B A A A A B B B B A A A A A A A B B B A A A A A B B U B A A A A A A A B B B B B B B B A B U B B B B B B A A A B B

9 9.41 B A A B U B B B B A A A A A A A A A A 9.32 A A A A A B B A B B B B A A A A B B B 9.92 B B B B B A B A A U B U A A A A A A A B A A B B B B A A B B U B A A B B A B B B B B A B B U A A B B B B B B B B B 9.66 B A A A A A B A A A A A A A U A A A A 9.60 A A A A A A B A A A A A A A A A A A A B B B B B B B A B A A A A A A B B B B 9.46 A A A A A A B A A U B B A A A A B B B 9.75 A A A A A A B A A U A A A A A A B B B 9.65 B A A B U B B B A A A A A B A A A A B 9.73 A A A B A B B B B A A A A A A A A A A 9.31 A B B B B B B B B A A A A A A B B B B B B B B A A B A A A B B B B B B A A A 9.75 B B B B B A B A A A A A A A A A B A B 9.80 B B B B B A U A A A A A U A A A A B B A A B B A B B B B U B B B B B B B A B 9.42 B B B B A A B A A A A A A A A A B B B 9.08 A A A B A A B A A A A A A A A A B A A 9.73 A A A A U A B U A B B B B A B B B B B 9.52 B B B B A U B U A A A A A A A A B B B 9.33 A A A B U B B U B A A A A A A A B A B A A A A A B B U A A A A B B B B B A A 9.56 B B B B B B B U B B B B B A B B B B B 9.13 A B B B B B B B A B A A A A A A A A A 9.36 A A A A A A A A B B B A A A A B A B U 9.64 A A A A A A A A A A B B B B B B B B B 9.74 B B B B B B A A U B B B B B B A A A A A B B B B A A A A A B A A A A B A A A 9.05 A U B B B B A A A A B A A A A B A A A 9.48 A A A A U B U A A A A A A A A B A A A 9.09 B A A A U B A B B B A A A A A B A A A A A U B A B A B A B A B B B B A A A A 9.60 A A B B U B A B B B A B B B B B A A A 9.53 A A A A B A A A A U B B A A B B A A A 9.87 B U A A A A A A A A B A A A A B B B B 9.54 A A A B B B B B B B B A A A A A B B B 9.67 B A A B B A A A A U B B B B B B B B B 9.51 B A A B A A A A A A B U A A A B B B B 9.49 B B U B B A A A A A A B B B B B A A A B A A B B B B B A U A A A A A B B A B

10 9.38 B B B B B B B B A B B B B B B B B B B 9.37 A A A A A A A A A B B A A A A B B A B A A A A U B B B U A B A U A U B A U A 9.29 B B B B A A A A A A A B A B B B B A A B B B B B B B A A A B A A A A B B B B 9.61 A B B B B A A A A U B A A A A B A A A 8.99 B U B B B A A A U A A B B B A A B A B B A B U B B A B B B B A A A A B A B U 9.74 B A A A A A B B B B B B U B B B B A B 9.65 B B B B B A A A A B A A A A A A A A A 9.83 A A U B B A A A A A A A A A A B U A A B A A B U B A B A B B A A B B B B A B 9.38 A A U U A A A A A A B A A A A B B B B 9.67 A A A A A A A A A B A A A A A B A A A 9.59 B B B B B B B B B A B B B B B B B B B 9.87 B B U B U B B B B A A A A A A A A A A B B U B B B B B B A A B B B B U U A B 8.81 B A U U B B A A B A B A A A A B B A B 9.42 B B U B B A A A A B B A A A A B A A A 9.50 B A A A A A A A A A B A A A A B A A A A B B B B B B A A B A A A A A B B A B 8.48 A B B B U B A B A A B B B B B B B B B 9.06 A A A A A A A A A A U A A A A B A B B 9.76 A A A A A A A A A A B B B B B B B A B 9.25 A A B B B B A A A A A A A A A B B A B 9.41 U A B B B B A A A B A A A A A A B A B 9.63 B A A A A A A A B A B A A A A A A A B 9.51 A B B B B A A A A A B A A A A B B B B 9.59 B B B B B B A A A A U A A A A U A A A 9.57 A B B A A A A A B B B B A A A U A A A A U B U A A A A A A B A A A A B A A B 9.72 A A B B B A A A A A A B A A A A A A A 8.30 B A B B A A A A A A U A U A A B A A A 9.06 B B U U B A A A A A A B B B B B A U A 8.47 B B B B B A A A A B A B B B B A A A A 8.54 B B B B B B A A A A B A A A A A B A A 9.69 B A A A A A A A A A B A A A A U B B B 9.92 B A A A A A A A A A A A A A A B A B B A A A A A A A A A A A A A A A B A A A 9.26 A B B B A A A A A U A A A A A U B A B U A B B U B A B B A A A A A A B A A B

11 8.55 A A A A A B B B B A A A B U B A B B B 9.22 U U B B A B A A A A A A A A A B B A B 9.36 A A B A A B A B B A A B B A B A A A B 8.63 B A A A A A A A A A A B B B B U A A A A B B B U B A B B U A A A A A B B B B 9.87 B B B B B B B B A B B A A A A U A A B B B U U B B B B B A B A A A A U B A B 9.16 B B B B B B A A A B B A A A A A A B A 9.55 B B B B B A A A A A B A A A A B B A B 9.22 B A B A A A A A A A A B B A A B A U A 9.45 B B B B B B B B B A A A A A B B B A A 9.64 A B B B B A A A A A B A A A B A A A A 9.13 A A A A B A A A A B B B U U B B B B B 9.56 A A A A U B A B B B A A A A A A B A B 9.75 B A A B U B A B A A B A A A A B A A A 9.84 U A A B A B A B B A B A A A A B A A A 8.60 A A U A B A A A A A B U A A A B A A B 9.67 A A A B B B A B B A U A A A A B B A A 8.85 U A U U B B A A A A B A A U A B A A U 9.74 A A A U A A A A A A B A A A A B A A A 9.21 B A A A A A A A A A A A A A A B B B B B B B B B A A A A A A A A A A A U B U A A A U B B U A U A B A A A A A A A B A B B B B B B B A A B U A A A A B B B 9.96 A B A A B A B A A B A A A A A U A U A U B B B B A B B B B A A A A A B A A A A A A A A A A A A U A A A A A B A A B 9.55 B U B B B A A A B B B B B B B B B U B A A A A A A A A A A B A A A A A A A A 8.39 A B B B B B B B B A U A A A A B B B B A B B B A B A B A A B A A A A B B A B 9.61 B A U B A B B B B A A A A A A A A A A B A U B A B A B B A A B B B B B A B B 9.96 A A B B B B A B A A A A A A A B B B U 9.23 A B B B B A B B A A B A A A A U A U A 2. map1(data file): Kindly note that the marker distances are cumulative and the first marker position is referred to as zero. marker distance chromosome m1 0 1 m

12 m m m m m m m m m m m m m m The output in the SAS log describes the data set and gives information on the missing percentage of markers. The result of the analysis can be exported to excel or doc file as per one s need. The SAS output is given below: Population Information: Sample size: 278 Number of non-qtl effects: 0 Number of markers: 16 Number of traits: 1 Mating type: Recombinant inbred line (Selfing) Marker Information: AA: 2533 BB: 1707 Number of missing marker genotypes: 208 Total number of marker genotypes: 4448 Missing marker proportion: 4.68% QTL Effect(s) defined: A : 1.00 AA BB

13 trait chr marker position n_iter conv_err LRT Wald ve intercpt A var_1 LRT_dist freq_aa freq_bb LRT_QS Y 1 m Y Y Y Y Y Y Y 1 m Y Y 1 m Y Y Y Y 1 m Y Y Y Y Y 1 m Y Y Y Y Y Y Y Y Y 1 m Y Y Y Y Y Y Y Y Y Y 1 m

14 Y Y Y Y Y 1 m Y Y Y Y 1 m Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y 1 m Y Y Y Y Y 1 m Y Y Y Y 1 m Y Y 1 m Y 1 m Y Y 1 m Y

15 Y Y Y Y Y 1 m The marker intervals having LRT scores higher than 10.2 (for α = at 1 d.f) are significant ones harbouring the QTLs and they are highlighted in the output.

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