Question

A fish with a 6 cm long tail and a fish with a 30 cm long tail are bred. All of the F1s have tails that are 18 cm. The F1s were interbred and out of 256 F2 offspring, 1 had a 6 cm tail and 1 had a 30 cm tail. All other F2s had tails that ranged in length from 6 to 30 cm in 3 cm intervals. Given these numbers, you suspect that in these fish, tail length is inherited via polygenic quantitative alleles.

A) How many gene pairs are involved in inheritance of tail length?

B) How many F2 individuals would you predict to have a 9 cm long tail?

Answer 1

A) Four gene pairs are involved. As question says 256 offsprings are produced in F2, so 256 is a square root of 16. Total 16 gamets are produced by a single parent and in total 32 from both the parents.

B) Four offspring will show 9 cm long tail. 'Abcd', 'aBcd', 'abCd' and 'abcD' when crossed with 'abcd' gamets will produce 9 cm long tail. Because each recessive gene contributes 0.75(6*8) cm length tail and dominant alleles contributes 3.75 (30*8) cm length of tail. So total 8 alleles are involved than 7 are recessive and one is dominant than only it will give a sum of 9 cm. Therefor only the above possible pair contributes such pair. Hence four offspring will be of 9 cm tail size.

You can make square punnet chart to conform the resultd for tetrahybrid F2 cross.

Also, as given in question each offspring will range by 3 cm interval, that is not possible according to me.