In a natural population of outbreeding plants, the variance of the total number of seeds per plant is 16. From the natural population, 20 plants are taken into the laboratory and developed into separate true-breeding lines by self-fertilization—with selection for high, low, or medium number of seeds—for 10 generations. The average variance in the tenth generation in each of the 20 sets is about equal and averages 5.8 across all the sets. Estimate the broad-sense heritability for seed number in this population.

To estimate the broad-sense heritability for seed number in this population, we can use the formula:

H^2 = Vg / Vp

Where:
H^2 is the broad-sense heritability
Vg is the genetic variance
Vp is the phenotypic variance

First, let's calculate the genetic variance (Vg). We know that the average variance in the tenth generation in each of the 20 sets is 5.8. Since we are looking at broad-sense heritability, we need to account for both additive genetic variance (Va) and non-additive genetic variance (Vd). Assuming the non-additive genetic variance is negligible, we can approximate Vg as Vg = Va.

Therefore, Vg = 5.8

Next, we need to calculate the phenotypic variance (Vp). We know that the variance of the total number of seeds per plant in the natural population is 16. Since we are selecting for high, low, or medium number of seeds in the laboratory, the phenotypic variance will change due to artificial selection.

We can estimate the phenotypic variance (Vp) as the sum of the genetic variance (Vg) and the environmental variance (Ve). In the natural population, the plants are outbreeding, so we can assume that the environmental variance is the same as the phenotypic variance before selection.

Vp = Ve + Vg

Since the selection is being done for 10 generations, we can assume that the environmental variance remains constant and is equal to the original phenotypic variance in the natural population.

Vp = Ve + Vg = 16 + 5.8 = 21.8

Finally, we can estimate the broad-sense heritability (H^2) by dividing the genetic variance (Vg) by the phenotypic variance (Vp).

H^2 = Vg / Vp = 5.8 / 21.8 ≈ 0.266

Therefore, the broad-sense heritability for seed number in this population is approximately 0.266, or 26.6%.