Genet. Sel. Evol. 36 (2004) 621-642
DOI: 10.1051/gse:2004021

Identification of gametes and treatment of linear dependencies in the gametic QTL-relationship matrix and its inverse

Armin Tuchscherer, Manfred Mayer and Norbert Reinsch

Forschungsinstitut für die Biologie landwirtschaftlicher Nutztiere, Forschungsbereich Genetik und Biometrie, Wilhelm-Stahl-Allee 2, 18196 Dummerstorf, Germany

(Received 29 December 2003; accepted 14 June 2004)

Abstract - The estimation of gametic effects via marker-assisted BLUP requires the inverse of the conditional gametic relationship matrix G. Both gametes of each animal can either be identified (distinguished) by markers or by parental origin. By example, it was shown that the conditional gametic relationship matrix is not unique but depends on the mode of gamete identification. The sum of both gametic effects of each animal - and therefore its estimated breeding value - remains however unaffected. A previously known algorithm for setting up the inverse of G was generalized in order to eliminate the dependencies between columns and rows of G. In the presence of dependencies the rank of G also depends on the mode of gamete identification. A unique transformation of estimates of QTL genotypic effects into QTL gametic effects was proven to be impossible. The properties of both modes of gamete identification in the fields of application are discussed.

Key words: marker assisted selection / best linear unbiased prediction / linkage analysis / gametic relationship matrix

Correspondence and reprints: reinsch@fbn-dummerstorf.de

© INRA, EDP Sciences 2004