The effect of the H(−1) scaling factors τ and ω on the structure of H in the single-step procedure

BACKGROUND: The single-step covariance matrix H combines the pedigree-based relationship matrix [Formula: see text] with the more accurate information on realized relatedness of genotyped individuals represented by the genomic relationship matrix [Formula: see text] . In particular, to improve convergence behavior of iterative approaches and to reduce inflation, two weights [Formula: see text] and [Formula: see text] have been introduced in the definition of [Formula: see text] , which blend the inverse of a part of [Formula: see text] with the inverse of [Formula: see text] . Since the definition of this blending is based on the equation describing [Formula: see text] , its impact on the structure of [Formula: see text] is not obvious. In a joint discussion, we considered the question of the shape of [Formula: see text] for non-trivial [Formula: see text] and [Formula: see text] . RESULTS: Here, we present the general matrix [Formula: see text] as a function of these parameters and discuss its structure and properties. Moreover, we screen for optimal values of [Formula: see text] and [Formula: see text] with respect to predictive ability, inflation and iterations up to convergence on a well investigated, publicly available wheat data set. CONCLUSION: Our results may help the reader to develop a better understanding for the effects of changes of [Formula: see text] and [Formula: see text] on the covariance model. In particular, we give theoretical arguments that as a general tendency, inflation will be reduced by increasing [Formula: see text] or by decreasing [Formula: see text] .