Variance: A measure of dispersion

In order to understand the heritability calculations, it is important to think about how variation among a group of individuals can be measured. We will defer the hard statistical formulations for your biometry course and just stick with the basic idea.

In figure 4 below, we can see the distribution of seed protein in the F1 and F2 populations of soybean. Both populations have the same mean or average. The F2 population has many plants with higher or lower protein levels. In contrast, the F1 population has most of its plants with a protein level near the average. We can quantify this dispersion around the mean in each population by measuring the variance of each population. The variance is a measure without units. It simply measures the relative amount of variation.

Fig. 4: F2 has the same mean as the F1 but it has a larger variance or dispersion around the mean then the F1. There are also larger numbers of F2s. (Image credit: D. Lee)

Heritability Calculations:

(Image credit: D. Lee)

If the hard working undergraduate student had also collected seed yield on these same F2 plants and parent lines, they might have expected the following result:

(Image credit: D. Lee)

This tells us that seed yield is more highly influenced by environment than is seed protein. We can speculate this is because the plant processes that govern seed yield involve many more variables than the processes controlling seed protein. If Dr. Graef selects the highest yielding F2 plant and the highest seed protein F2, he is more likely to get high protein offspring from the high protein selection than high yielding offspring from the high yielding selection.