In theory, one can use model selection ideas to find the best fit of one or more markers which explain the trait. In practice, it is wise to take advantage of the organization of markers into distinct linkage groups. Markers from distinct linkage groups are, by design, nearly uncorrelated. Therefore, they do not greatly affect each other's estimates of genotypic effect on agronomic traits. However, markers on the same linkage group are positively correlated, and hence their effects on a trait are much harder to distinguish. jans:1993 and others showed that there is only a modest loss of information if QTLs from other linkage groups are ignored. Mainly, these other markers help reduce the unexplained variation, making it easier to detect QTL effects.
Here is an analysis of two markers on the linkage group considered earlier. Note that both are very significant in the presence of the other. The R-Square is now 39.5%, which is 10% than either marker on its own. The overall F Value is 29.75. Thus there is evidence to support two QTL on this linkage group. Further, it is more appropriate to examine them together than one at a time. That is, the effect of each genotype is assessed after adjusting for the other, using the Type III approach.
Type Mean
Source DF III SS Square F Value Pr > F
WG6B10 1 0.0954 0.0954 9.16 0.0032
ACA1 1 0.2066 0.2066 19.83 0.0001
Error 91 0.9479 0.0104
Corrected Total 93 1.5678
R-Square C.V. Root MSE TRAIT Mean
0.396 7.67 0.102 1.331
Marker Type lsmean stderr
WG6B10 M 1.367 0.018
S 1.293 0.015
ACA1 M 1.386 0.015
S 1.275 0.018
Notice how the least squares means for marker WG6B10 adjusted for the other marker differ from those presented in the previous section. This is due to missing data and to linkage between these two markers. A test for epistasis found no evidence for interaction (p=0.31).
While it is possible to consider all possible combinations (45) of two markers out of 10 in this linkage group, the task is tedious. It gets even worse when one considers a whole genome, consisting of 5 to 25 linkage groups. In addition, there are problems of detection if QTL are far from markers, as noted earlier. Instead, it is probably better to consider an approach which incorporates information about linkage, as is done in the next two sections.