Additivity of Variances
traits A and B contribute to a combined
trait A+B. The
contributions of the two loci are (1) approximately equal (means
53 & 59) and (2) independent (A & B are not correlated).
Then, the phenotypic value
of the combined trait is simply the sum of the two
contributing loci, and the variance of A+B is the sum of the
variances of A & B separately.
The result is not particularly sensitive to small differences
in the relative contribution
of traits. In the second data set, B contributes only 33% of the value of A to the combined trait, but the variances
The result is more sensitive to non-independence of the contribution of
traits. In the third data set, the second trait is perfectly
correlated with A by
the addition of 10 units. (Note that the variances of A and A' are identical).
However, the variance of the combined trait is much greater
than the sum of the contributing traits. (This is an extreme
of variance is a crucial assumption of many
biological experiments and analyses, especially Analysis of Variance (ANOVA) and Heritability studies.