TABLE 7

Detection of QTL × E interaction in a barley dihaploid population scored over nine environments (for a QTL of chromosome 1 affecting ‘alpha amylase activity’; see Hayes et al. 1996)

kσj ≠ const 1σj = const 2
MGLOD(H2k/H1k) (df)2.954 (8)3.403 (8)
P0.0950.015
MALOD(H2k/H1k) (df)1.983 (2)1.817 (2)
P0.0100.015
MGLOD(H21/H22) (df)21.64 (8)
P0.000
MALOD(H21/H22) (df)20.25 (8)
P0.000
Embedded Image (df)0.971 (6)1.586 (6)
P0.600.29
  • We used the index k to denote two types of models corresponding to equal (k = 1) vs. nonequal (k = 2) residual variances across environments. Therefore, H11 and H12 hypotheses here assume the presence of a QTL effect with constant and varying residual variances, respectively. Correspondingly, H21 and H22 assume the presence of a QTL with varying effect and constant and varying residual variances, respectively. To test whether the two models, MA or MG, differ significantly, provided H2 {aj ≠ const} is true, both situations, i.e., with Embedded Image and Embedded Image , were considered using LOD score, Embedded Image (see the last section of the table).