Optimal Allocation in Designs for Assessing Heterosis From cDNA Gene Expression Data

Heterosis is defined as the superiority of a hybrid cross over its two parents. Plant and animals breeders have long been exploiting heterosis, but the causes of this phenomenon are as yet only partly understood. Recently, chip technology has opened up the opportunity to study heterosis at the gene expression level. This article considers the cDNA chip technology, which allows assaying two genotypes simultaneously on the same chip. Heterosis involves the response of at least three genotypes (two parents and their hybrid), so a chip or microarray constitutes an incomplete block, which raises a design problem specific to heterosis studies. The question to be answered is how genotype pairs should be allocated to chips. We address this design problem for two types of heterosis: midparent heterosis and better-parent heterosis. The general picture emerging from our results is that most of the resources should be allocated to parent-hybrid pairs, while chips with parent-parent pairs or hybrid-reciprocal pairs should be used sparingly or not at all.