The consequences of using inadequate testers in the simplified triple test-cross

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Abstract
The genetical consequences of common alleles in the L1 and L2 testers of a simplified version of the triple test-cross which is applicable to populations of inbred lines are examined. The test for epistasis under these circumstances becomes ambiguous and can spuriously detect non-allelic interactions when they may not exist although it still provides a test for epistasis and the adequacy of the testers simultaneously. The tests of significance and the estimates of additive variation are biased to an extent related to the dominance and dominance additive effects of the common loci while the significance and estimates of dominance variation are deflated because they reflect the dominance effects at the non-common loci only. The covariance of sums and differences is also underestimated for the same reasons. These expectations are illustrated by analysing the 190 simplified triple test-crosses that could be extracted from a 20 20 diallel set of crosses between pure-breeding lines of Nicotiana rustica.