Experimental designs for population hybridization studies

In this investigation, experimental designs were developed for population hybridization studies. The objective of all of these designs was to obtain information about

(i) the general combining ability of populations,

(ii) the specific combining ability of population crosses,

(iii) the general combining ability of individuals, and

(iv) the specific combining ability of individual crosses.

These concepts were first introduced by Hinkelmann (1974) in relationship to the two-level diallel mating design.

With m populations, P₁, P₂, …, P_m, and n individuals for the ith population, I_il, I_i₂, …, I_in (i = 1, 2, …, m), to be evaluated, the two-level diallel mating design consists of

(i) m(m-1)/2 population crosses P_ixP_j where i<j, and

(ii) n² individual crosses I_ikx_jl for each population cross P_ixP_j.

When the offspring from this design are grown in a randomized block environmental design, the blocks will be of size m(m-1)n²/2. Even for moderate values of m and n the required block size may be far too large. Three methods are proposed that will either reduce the block size or the size of the total experiment or both. These are obtained by

(i) using an incomplete environmental design to grow the offspring from the complete diallel cross,

(ii) selecting only a sample of the m(m-1)n²/2 total crosses, either at the population level or at the individual level, to be tested,

(iii) selecting only a sample of the m(m-1)n²/2 crosses to be tested and using an incomplete environmental design.

Two modifications of the two-level diallel cross were suggested that would include intrapopulation crosses. First the two-level diallel mating design to which, for each population P_i, n(n-1)/2 intrapopulation crosses, I_ik x I_il (k < l), were added, was investigated. This augmented design has the advantage that the general and specific combining ability of the populations and individuals can be measured on the basis of intrapopulation and interpopulation crosses. In addition this design allows the experimenter to test for population heterosis.

The second modification suggested was to use pollen bulk as the male parent. In this mating design n females from each of m populations are fertilized with pollen bulk from each of them populations. Besides including intrapopulation crosses as a control, this design also reduces the number of crosses to be made and tested. The two-level diallel cross with intrapopulation crosses added makes mn(mn-1)/2 crosses. Using pollen bulk as the male parent reduces the number of crosses to be tested to m²n.

For all cases considered, the construction and analysis of appropriate mating and environmental designs have been given.