A DeFries and Fulker regression model for genetic nonadditivity

Parameter estimates from the DeFries and Fulker [(DF) Behav. Genet. 15:462-473, 1985] regression method can be greater than unity or less than zero. This occurs when the monozygotic correlation is greater than twice the dizygotic correlation. Sensible values can be obtained in these cases by fitting a constrained DF model that estimates genetic and nonshared environmental variance components only. In this article I demonstrate that the original Df model yields positively biased heritability estimates and negatively biased estimates of shared environmentality when data are significantly influenced by genetic nonadditivity. The magnitude of the bias is algebraically expressed. I then describe a simple regression equation that provides unbiased estimates of the standardized additive and dominance genetic variance components. Results of a study of 6 million twin pairs from the Monte Carlo Twin Registry demonstrate that the DF additive and dominance genetic parameter estimates are virtually identical to those obtained by maximum-likelihood procedures. Finally, I derive the expectations for the constrained DF model and show that the genetic parameter estimates from this model are negatively biased estimates of broad-sense heritability.