1998 Volume 69 Issue 5 Pages 417-423
Of ratio traits, there exists a trait whose numerator is also contained in the denominator as its one component. This type of trait may be called a proportion-defined trait or simply a proportion trait. In this paper, the truncation point for a proportion-defined trait is investigated, assuming that its component traits follow normality and have positive values and supposing a proportion of population selected truncatedly. A formula for the point is expressed in terms of phenotypic parameters such as coefficients of variation and correlation for component traits and the truncation value corresponding to a given proportion of population selected of the standard normal distribution. It is considered that the validity of the formula requires the fulfilled assumption of small coefficients of variation or curtailed normality for component traits. Using the formula and its approximation based on the assumption of normality, the discrepancy between the truncation value and the approximate value is evaluated deterministically. The degree of the discrepancy is shown to be affected by the values of phenotypic parameters, especially by the relative magnitude of coefficients of variation, for component traits. It is suggested that the geometric shape of the intrinsic distribution of the proportion trait is changeable: that is, symmetric, skewed to the right, or to the left.
