Transformation of QTL genotypic effects to allelic effects

The genotypic and allelic effect models are equivalent in terms of QTL detection in a simple additive model, but the QTL allelic model has the advantage of providing direct information for marker-assisted selection. However, the allelic matrix is four times as large as the genotypic IBD matrix, causing computational problems, especially in genome scans examining multiple positions. Transformation from genotypic to allelic effects, after estimating the genotypic effects with a smaller IBD matrix, can solve this problem. Although the validity of transformation from genotypic to allelic effects has been disputed, this work proves that transformation can successfully yield unique allelic effects when genotypic and allelic IBD matrixes exist.