AN EXTENSION OF THE CONCEPT OF PARTITIONING HEREDITARY VARIANCE FOR ANALYSIS OF COVARIANCES AMONG RELATIVES WHEN EPISTASIS IS PRESENT

Abstract

It is convenient, for purposes of description and analysis, to consider the phenotypic expression of a characteristic as a sum of an hereditary or geno- typic value and of an environmental value, If the actual joint results deviate from this linear description (i.e., if interaction effects exist) the breeder or geneticist must exercise caution in extrapolating from his results because in this case the hereditary and environmental values are defined specifically in terms of each other (NELDER1950). For some characteristics a transformation of scale may help in coming closer to additivity (WRIGHT1950). With this linear description, the total or phenotypic variance may be con- sidered to consist of the hereditary, environmental and interaction variances, and also of covariance terms if the components are correlated in their occur- rence. The covariance between heredities and environments is often a trouble- some feature in human and livestock populations. For example, where dairy cattle are fed in proportion to their production, the better genotypes are pro- vided better environments. However, in designed experiments correlation in occurrence can, for the most part, be avoided by randomization devices. FISHER(1918) partitioned the phenotypic variance further by subdividing the hereditary variance into an additive portion resulting from average effects of genes, a portion resulting from dominance effects (allelic interactions) of genes and a portion resulting from epistatic effects (non-allelic interactions) of genes. FISHEsRhowed the distribution of the additive and dominance por- tions in correlations between various relatives in a randomly mating popula- tion. The present paper shows the subdivision of the epistatic variance into components and gives the distribution of these epistatic components in the covariances or correlations between relatives.