Generalized gametic relationships for flexible analyses of parent-of-origin effects

A class of epigenetic inheritance patterns known as genomic imprinting allows alleles to influence the phenotype in a parent-of-origin-specific manner. Various pedigree-based parent-of-origin analyses of quantitative traits have attempted to determine the share of genetic variance that is attributable to imprinted loci. In general, these methods require four random gametic effects per pedigree member to account for all possible types of imprinting in a mixed model. As a result, the system of equations may become excessively large to solve using all available data. If only the offspring have records, which is frequently the case for complex pedigrees, only two averaged gametic effects (transmitting abilities) per parent are required (reduced model). However, the parents may have records in some cases. Therefore, in this study, we explain how employing single gametic effects solely for informative individuals (i.e., phenotyped individuals), and only average gametic effects otherwise, significantly reduces the complexity compared with classical gametic models. A generalized gametic relationship matrix is the covariance of this mixture of effects. The matrix can also make the reduced model much more flexible by including observations from parents. Worked examples are present to illustrate the theory and a realistic body mass data set in mice is used to demonstrate its utility. We show how to set up the inverse of the generalized gametic relationship matrix directly from a pedigree. An open-source program is used to implement the rules. The application of the same principles to phased marker data leads to a genomic version of the generalized gametic relationships.