The detection of sex-differences in environmental and genetic effects on BMI leads to questions regarding the nature of these differences. Speculation might suggest that the somewhat lower male heritability estimate may be due to the fact that males are less accurate in their self-report of height and weight than are females. With additional information, such as test-retest data, this hypothesis could be rigorously tested. The sex-dependency of genetic dominance is similarly curious. It may be that the common environment in females exerts a greater influence on BMI than in males, and, consequently, masks a genetic dominance effect. Alternatively, the genetic architecture may indeed be different across the sexes, resulting from sex differences in selective pressures during human evolution. Again, additional data, such as that from reared together adopted siblings, could be used to explore these alternative hypotheses.
One sex-limitation model that we have not considered, but which is
biologically reasonable, is that the across-sex correlation between
additive genetic effects is the same as the across-sex correlation
between the dominance genetic effects.
Fitting a model of this type involves a non-linear constraint which
can easily be specified in Mx.