Final answer:
Falconer's formula for broad sense heritability uses correlation values rather than the coefficient of determination (r²) because it estimates the total genetic variation.
Step-by-step explanation:
Falconer's formula for broad sense heritability is used in quantitative genetics to estimate the total heritability of a trait, including all genetic factors. This formula does not use r2, the coefficient of determination, because heritability estimates aim to account for the entire genetic variation, including additive, dominance, and epistatic variances, not just the proportion of variation.
In statistical terms, r2 reflects the explained variance in a regression analysis, which indicates the extent to which changes in one variable explain the variation in another variable. The key difference here lies in the distinction between explained variation and total genetic variation.
Subtracting the correlation values, rather than r2 values, from 1 provides a measurement that encompasses the entire genetical variance instead of just the variance directly attributed to the linear relationship between variables, represented by a regression line.