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

MARTINI, JOHANNES W. R.; SCHRAUF, MATIAS F.; GARCIA-BACCINO, CAROLINA A.; PIMENTEL, EDUARDO C. G.; MUNILLA, SEBASTIAN; ROGBERG-MUÑOZ, ANDRES; CANTET, RODOLFO J. C.; REIMER, CHRISTIAN; GAO, NING; WIMMER, VALENTIN; SIMIANER, HENNER

Genetics Selection Evolution

BioMed Central

Año: 2018 vol. 50

Background: The single-step covariance matrix H combines the pedigree-based relationship matrix A with themore accurate information on realized relatedness of genotyped individuals represented by the genomic relationshipmatrix G. In particular, to improve convergence behavior of iterative approaches and to reduce inflation, two weights and have been introduced in the definition of H−1, which blend the inverse of a part of A with the inverse of G .Since the definition of this blending is based on the equation describing H−1, its impact on the structure of H is notobvious. In a joint discussion, we considered the question of the shape of H for non-trivial and .Results: Here, we present the general matrix H as a function of these parameters and discuss its structure and properties.Moreover, we screen for optimal values of and with respect to predictive ability, inflation and iterations upto 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 and on the covariance model. In particular, we give theoretical arguments that as a general tendency, inflation will bereduced by increasing or by decreasing .