A graduate student is studying a population of bluebonnets along a roadside. The plants in this population are genetically variable. She counts the seeds produced by 100 plants and measures the mean and variance of seed number. The variance is 20 and the average seed number is 25. Selecting one plant, the graduate student takes cuttings from it and cultivates these cuttings in the greenhouse, eventually producing many genetically identical clones of the same plant. She then transplants these clones into the roadside population, allows them to grow for one year, and then counts the number of seeds produced by each of the cloned plants. The graduate student finds that the variance of seed number among these cloned plants is 5 and the average seed production is 15. What is the broad-sense heritability of seed number for the roadside population of bluebonnets?

The phenotypic variation (VP) in quantitative genetics refers to the combined influence of the genotype (VG) and the environment (VE). The equation is VP = VG + VE

Heritability predicts that how much of the phenotypic variation can be illustrated by genetic-environmental or genetic effects. The broad-sense heritability (H2) refers to the inclusion of all the probable sources of genetic variation (dominance, additive, paternal, and maternal effects).

H2 + VG / VP --------- (1)

The roadside population is genetically variable and as a consequence, the variance must be a combination of genetic and environmental components. The VP here is 20.

VP = VG + VE

20 = VG + VE -------- (2)

In the identical population, the variance must be environmental as all the individuals are of same genotype and thus VG must be 0. Here, the VP is 5.

VP = VG + VE

5 = 0 + VE

Thus, VE = 5

Now substitute, the value of VE = 5 in equation (2)

Thus, 20 = VG + 5

VG = 20-5

VG = 15

Now put the values of VG and VE of the roadside population in equation 1:

H2 = VG/VP

H2 = 15/20 = 0.75

Thus, the broad-sense heritability of seed number of the roadside population of bluebonnets is 0.75.