**Functions for diallel cross data**

Diallel cross is a widely used genetic design that is made of all possible crosses (combinations) among a set of parents (inbreds or varieties). Diallel cross data are used to study the inheritance of a trait among the set of parents. For quantitative traits, general and specific combining ability (GCA and SCA) often are the statistics used to characterize the parents and their combinations.

A diallel cross dataset is a two-way table, each parent being both an entry and a tester. The parent per se values are the diagonal elements of the two-way table. The following can be achieved through GGE biplot analysis of a diallel cross dataset:

**Evaluation of parents as entries**

- To rank parents based on their combining ability (F1 performance) with a given parent
- To show the relative combining ability of a parent with other parents
- To rank parents based on general combining ability (GCA) (mean of its F1's)
- To visualize both the general (GCA) and specific (SCA) combining ability of the parents
- To show the best mating partner of each parent
- To show the best (F1) combinations
- To identify heterotic groups

**Evaluation of parents as testers**

- To show relationship among parents when used as testers
- To show discriminating ability and representativeness of the parents as testers
- To rank parents relative to the "ideal" tester

**Note**: If you are only interested in understanding the entry-by-tester interactions, i.e., biplot based on double-centered data, should be used. However, I don't see how such analysis can be of any value.