QTL IciMapping is integrated software for linkage map construction and QTL detection. QEI mapping has been implemented in version 4.0 of the software as the MET functionality [37 ]. In this study, unlinked and linked QTL models were both considered to evaluate the efficiency of QEI mapping. The genome consisted of six chromosomes, each of 150 cM in length with 16 evenly distributed markers. Two environments were considered with equal heritability in the broad sense in both models. In the unlinked QTL model, five QTL were located on five chromosomes, and the broad sense heritability was 0.5 for both environments. QTL additive effects in the two environments were given in Table 3 , representing three QEI levels, i.e., strong interaction (Q2), environment-specific interaction (Q3 and Q4) and no interaction (Q1 and Q5).
Eight QTL effect scenarios were considered for two linked QTL (Table 4 ), i.e., Q1 and Q2, located at 25 and 55 cM on chromosome 1. These scenarios represented different QEI levels and linkage phases (coupling or repulsion phases). For example, Q1 and Q2 had strong QEI, and they were linked in the coupling phase in model L3, and in the repulsion phase in model L7. Three levels of heritability were considered, i.e., H2 = 0.1, H2 = 0.5 and H2 = 0.8.
One thousand DH populations, each of a size of 200, were generated for unlinked model (S3 File ) and for each effect scenario of the two linked QTL under each heritability level (S4 –S6 Files). The LOD threshold was set at 3.11 by empirical formula to ensure the genome-wide Type-I error rate (αg) to be less than 0.05. The scanning step was set at 1 cM. The two probabilities for entering and removing variables in stepwise regression were set at 0.001 and 0.002.
Detection power and FDR were used to evaluate the efficiency of QEI mapping. Each predefined QTL was assigned to a support interval of 10 cM centered at the predefined location. Power of each QTL was calculated as the percentage of the simulation runs having significant peaks higher than the LOD threshold in its support interval. QTL identified but out of this interval were treated as false positives. FDR was calculated as the ratio of the number of false positives to the total number of significant discovery [26 ,38 (link)]. For each genetic model, estimated positions and effects were calculated as the average values of all detected QTL.
Eight QTL effect scenarios were considered for two linked QTL (
One thousand DH populations, each of a size of 200, were generated for unlinked model (
Detection power and FDR were used to evaluate the efficiency of QEI mapping. Each predefined QTL was assigned to a support interval of 10 cM centered at the predefined location. Power of each QTL was calculated as the percentage of the simulation runs having significant peaks higher than the LOD threshold in its support interval. QTL identified but out of this interval were treated as false positives. FDR was calculated as the ratio of the number of false positives to the total number of significant discovery [26 ,38 (link)]. For each genetic model, estimated positions and effects were calculated as the average values of all detected QTL.
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