Final answer:
The genotypic variance in the F2 offspring from the cross of F1 progeny with phenotypic variances of 54 mm² is 38 mm².
This is calculated based on the increase in phenotypic variance from the F1 to the F2 generation, which is due to genetic factors as environmental variance is constant.
Therefore, the correct answer is: option "38 mm^2".
Step-by-step explanation:
To calculate the genotypic variance (σ2G) in the offspring, we can make use of the information provided from parental (P1 and P2) and F1 progeny.
The phenotypic variance among the F1 progeny is the result of genotypic variance plus environmental variance (Vp = Vg + Ve), where environmental variance (Ve) is assumed to be the same across the experiments.
Here's how the calculation can be done:
Since P1 and P2 are pure-breeding lines, their phenotypic variance (Vp) is equal to their genotypic variance (Vg).
The average genotypic variance of the parents (Vg of P1 and P2) is calculated as the average of their Vp, which equals 60 mm².
The F1 progeny have a Vp of 54 mm². Assuming Ve remains constant and it can be ignored, the Vg for F1 can be assumed to be close to 54 mm².
A cross between two F1 progeny results in offspring with a Vp of 92 mm².
To find the genotypic variance of the F2 generation, we use the equation Vp = Vg + Ve, but because the Ve is constant, the increase in Vp from F1 to F2 must be due to an increase in Vg.
So, the increase in phenotypic variance from F1 to F2 is 92 mm² - 54 mm² = 38 mm², which represents the genotypic variance due to segregation and recombination.
Therefore, the genotypic variance in the F2 offspring is 38 mm².