Further examination on the truncation point in truncation selection for proportion-defined trait

For truncation selection on a proportion‐defined trait, an approximate expression for the true truncation point is currently available, which has been derived assuming that the component traits follow a curtailed normal distribution. This note deterministically examines the validity of the approximate expression in some details. We show that the value defined by the approximate expression is equivalent to that derived from an approximation to the true probability density function for the proportion trait of concern. We also show that the validity of the approximate expression is definitely dependent on the magnitude of the lower limit in the definite integral involved in the true probability density function for the proportion trait. We reveal some properties of the lower limit concerning its maximum and minimum. We indirectly assess the adequacy of the approximate expression under the settings of the altered coefficients of variation for the component traits and the changed correlation between them. The results indicate that the true value of the truncation point can be numerically represented quite sufficiently by the approximate expression, when the coefficients of variation are approximately below 25% and the positive correlation is not extremely high.