An exact expression for the joint probability density function of the
phenotypic and genotypic values is examined for the ratio-defined char
acter in which two component characters are assumed to follow a bivari
ate normal law and to have positive values. An approximation to the fu
nction is derived in terms of parameters of two component characters.
A nonlinear approximation to the true regression function of the genot
ypic value on the phenotypic value is obtained. Similar approximations
to the regression functions of the genotypic values of two component
characters on the phenotypic value of the ratio-defined character are
also given. An example is used to discuss the validity of the given ap
proximations and to illustrate the geometric shapes of the regression
functions.