title: The efficiency  and optimal size of triple test cross designs for detecting epistatic variation.
abstract: The triple test cross and two of its associate designs have been compared for their theoretical and practical efficiency in detecting epistatic variation. The comparisons are made on the basis of optimal experimental sizes required for each of these tests to detect a modest level of epistasis significantly (P less than or equal to 0-05) and with a reasonable certainty (95 per cent). The experimental sizes are determined for various combinations of heritability, dominance ratio and gene association and for both duplicate and complementary epistasis. Two versions of the test epistasis designed by Kearsey and Jinks (1968). Test 1a and Test 1b, do not differ much in their theoretical efficiency for detecting epistasis and the optimal experimental sizes required by them to detect non-allelic interactions significantly are largely impraticable except when dominance and heritability are high and the degree of association is 50 per cent or more. Both the tests require much smaller experiments to detect duplicate epistasis than complementary epistasis of the same magnitude and this difference is more pronounced for lower levels of heritability and dominance. The theoretical efficiency of Test 2 (given by Jinks, Perkins and Breese, 1969), however, does not vary with the type of epistasis but the sensitivity of the test is inversely related to the degree of gene association between the tester parents. The practical implications of the present investigation are discussed and the validity of some of the most important theoretical predictions and assumptions are tested on a triple test cross involving 80 inbred lines of Nicotiana rustica.
mesh_terms: D003433:Crosses, Genetic; D005787:Gene Frequency; D014644:Genetic Variation; D008954:Models, Biological; D011156:Population Density