The Partial Diallel Cross

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Abstract
The diallel cross, which is composed of all possible single crosses among a group of inbred lines, is a common plan of investigation in plant and animal breeding. It can be used to estimate general and specific combining abilities and variances, to estimate components of genotypic variation and to estimate yielding capacities of multi-way crosses. With n lines it does however involve n(n-l)/2 crosses, even if maternal effects can be ignored. Breeding programs can easily lead to 50 inbred lines which merit examination, so the diallel cross becomes unfeasible. This paper deals with sampling of the complete diallel cross table in a specific way, namely (1) arrange the lines in random order (2) obtain the crosses of line i with lines k + i, k + i + 1, ..., k + i - 1 + s where k = (n + 1 - s)/2 is an integer and all numbers above n are reduced by a multiple of n so as to be between 1 and n. Each line is crossed then with s lines and s = n - 1 corresponds to the complete diallel cross. This partial diallel cross is considered in the following respects: (1) estimation of variance components (2) comparing the yielding capacities of all possible crosses and (3) estimation of general combining abilities. The efficiency of the plan with regard to each of these aspects is evaluated and discussed. It is shown to be more efficient than some other possible plans under some circumstances''.

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