Assume plant height is controlled by 4 gene pairs a and a b
Assume plant height is controlled by 4 gene pairs (a+ and a-, b+ and b-, c+ and c-, d+ and d-) which independently assort. The alleles also are additive and are equal in their effects, A tall plant that is homozygous for all contributing alleles (+) is mated to a short plant that is homozygous for noncontributing alleles (-). The F1 offspring are self mated to produce a F2 generation. Assuming there are no environmental affects:
a) What proportion of the F2 progeny will be the same phenotype as the short P1 parent?
b) How many phenotypes will there be in the F2 generation?
Solution
Answer:
a) Only 1
b) 256
See below
| a+a+b+b+c+c+d+d+ | 
| a+a+b+b+c+c+d-d+ | 
| a+a+b+b+c-c+d+d+ | 
| a+a+b-b+c+c+d+d+ | 
| a+a+b+b+c-c+d-d+ | 
| a+a+b-b+c-c+d+d+ | 
| a+a+b-b+c+c+d-d+ | 
| a+a+b-b+c-c+d-d+ | 
| a-a+b+b+c+c+d+d+ | 
| a-a+b+b+c+c+d-d+ | 
| a-a+b+b+c-c+d+d+ | 
| a-a+b-b+c+c+d+d+ | 
| a-a+b+b+c-c+d-d+ | 
| a-a+b-b+c-c+d+d+ | 
| a-a+b-b+c+c+d-d+ | 
| a-a+b-b+c-c+d-d+ | 
| a+a+b+b+c+c+d+d- | 
| a+a+b+b+c+c+d-d- | 
| a+a+b+b+c-c+d+d- | 
| a+a+b-b+c+c+d+d- | 
| a+a+b+b+c-c+d-d- | 
| a+a+b-b+c-c+d+d- | 
| a+a+b-b+c+c+d-d- | 
| a+a+b-b+c-c+d-d- | 
| a-a+b+b+c+c+d+d- | 
| a-a+b+b+c+c+d-d- | 
| a-a+b+b+c-c+d+d- | 
| a-a+b-b+c+c+d+d- | 
| a-a+b+b+c-c+d-d- | 
| a-a+b-b+c-c+d+d- | 
| a-a+b-b+c+c+d-d- | 
| a-a+b-b+c-c+d-d- | 
| a+a+b+b+c+c-d+d+ | 
| a+a+b+b+c+c-d-d+ | 
| a+a+b+b+c-c-d+d+ | 
| a+a+b-b+c+c-d+d+ | 
| a+a+b+b+c-c-d-d+ | 
| a+a+b-b+c-c-d+d+ | 
| a+a+b-b+c+c-d-d+ | 
| a+a+b-b+c-c-d-d+ | 
| a-a+b+b+c+c-d+d+ | 
| a-a+b+b+c+c-d-d+ | 
| a-a+b+b+c-c-d+d+ | 
| a-a+b-b+c+c-d+d+ | 
| a-a+b+b+c-c-d-d+ | 
| a-a+b-b+c-c-d+d+ | 
| a-a+b-b+c+c-d-d+ | 
| a-a+b-b+c-c-d-d+ | 
| a+a+b+b-c+c+d+d+ | 
| a+a+b+b-c+c+d-d+ | 
| a+a+b+b-c-c+d+d+ | 
| a+a+b-b-c+c+d+d+ | 
| a+a+b+b-c-c+d-d+ | 
| a+a+b-b-c-c+d+d+ | 
| a+a+b-b-c+c+d-d+ | 
| a+a+b-b-c-c+d-d+ | 
| a-a+b+b-c+c+d+d+ | 
| a-a+b+b-c+c+d-d+ | 
| a-a+b+b-c-c+d+d+ | 
| a-a+b-b-c+c+d+d+ | 
| a-a+b+b-c-c+d-d+ | 
| a-a+b-b-c-c+d+d+ | 
| a-a+b-b-c+c+d-d+ | 
| a-a+b-b-c-c+d-d+ | 
| a+a+b+b+c+c-d+d- | 
| a+a+b+b+c+c-d-d- | 
| a+a+b+b+c-c-d+d- | 
| a+a+b-b+c+c-d+d- | 
| a+a+b+b+c-c-d-d- | 
| a+a+b-b+c-c-d+d- | 
| a+a+b-b+c+c-d-d- | 
| a+a+b-b+c-c-d-d- | 
| a-a+b+b+c+c-d+d- | 
| a-a+b+b+c+c-d-d- | 
| a-a+b+b+c-c-d+d- | 
| a-a+b-b+c+c-d+d- | 
| a-a+b+b+c-c-d-d- | 
| a-a+b-b+c-c-d+d- | 
| a-a+b-b+c+c-d-d- | 
| a-a+b-b+c-c-d-d- | 
| a+a+b+b-c+c-d+d+ | 
| a+a+b+b-c+c-d-d+ | 
| a+a+b+b-c-c-d+d+ | 
| a+a+b-b-c+c-d+d+ | 
| a+a+b+b-c-c-d-d+ | 
| a+a+b-b-c-c-d+d+ | 
| a+a+b-b-c+c-d-d+ | 
| a+a+b-b-c-c-d-d+ | 
| a-a+b+b-c+c-d+d+ | 
| a-a+b+b-c+c-d-d+ | 
| a-a+b+b-c-c-d+d+ | 
| a-a+b-b-c+c-d+d+ | 
| a-a+b+b-c-c-d-d+ | 
| a-a+b-b-c-c-d+d+ | 
| a-a+b-b-c+c-d-d+ | 
| a-a+b-b-c-c-d-d+ | 
| a+a+b+b-c+c+d+d- | 
| a+a+b+b-c+c+d-d- | 
| a+a+b+b-c-c+d+d- | 
| a+a+b-b-c+c+d+d- | 
| a+a+b+b-c-c+d-d- | 
| a+a+b-b-c-c+d+d- | 
| a+a+b-b-c+c+d-d- | 
| a+a+b-b-c-c+d-d- | 
| a-a+b+b-c+c+d+d- | 
| a-a+b+b-c+c+d-d- | 
| a-a+b+b-c-c+d+d- | 
| a-a+b-b-c+c+d+d- | 
| a-a+b+b-c-c+d-d- | 
| a-a+b-b-c-c+d+d- | 
| a-a+b-b-c+c+d-d- | 
| a-a+b-b-c-c+d-d- | 
| a+a+b+b-c+c-d+d- | 
| a+a+b+b-c+c-d-d- | 
| a+a+b+b-c-c-d+d- | 
| a+a+b-b-c+c-d+d- | 
| a+a+b+b-c-c-d-d- | 
| a+a+b-b-c-c-d+d- | 
| a+a+b-b-c+c-d-d- | 
| a+a+b-b-c-c-d-d- | 
| a-a+b+b-c+c-d+d- | 
| a-a+b+b-c+c-d-d- | 
| a-a+b+b-c-c-d+d- | 
| a-a+b-b-c+c-d+d- | 
| a-a+b+b-c-c-d-d- | 
| a-a+b-b-c-c-d+d- | 
| a-a+b-b-c+c-d-d- | 
| a-a+b-b-c-c-d-d- | 
| a+a-b+b+c+c+d+d+ | 
| a+a-b+b+c+c+d-d+ | 
| a+a-b+b+c-c+d+d+ | 
| a+a-b-b+c+c+d+d+ | 
| a+a-b+b+c-c+d-d+ | 
| a+a-b-b+c-c+d+d+ | 
| a+a-b-b+c+c+d-d+ | 
| a+a-b-b+c-c+d-d+ | 
| a-a-b+b+c+c+d+d+ | 
| a-a-b+b+c+c+d-d+ | 
| a-a-b+b+c-c+d+d+ | 
| a-a-b-b+c+c+d+d+ | 
| a-a-b+b+c-c+d-d+ | 
| a-a-b-b+c-c+d+d+ | 
| a-a-b-b+c+c+d-d+ | 
| a-a-b-b+c-c+d-d+ | 
| a+a-b+b+c+c+d+d- | 
| a+a-b+b+c+c+d-d- | 
| a+a-b+b+c-c+d+d- | 
| a+a-b-b+c+c+d+d- | 
| a+a-b+b+c-c+d-d- | 
| a+a-b-b+c-c+d+d- | 
| a+a-b-b+c+c+d-d- | 
| a+a-b-b+c-c+d-d- | 
| a-a-b+b+c+c+d+d- | 
| a-a-b+b+c+c+d-d- | 
| a-a-b+b+c-c+d+d- | 
| a-a-b-b+c+c+d+d- | 
| a-a-b+b+c-c+d-d- | 
| a-a-b-b+c-c+d+d- | 
| a-a-b-b+c+c+d-d- | 
| a-a-b-b+c-c+d-d- | 
| a+a-b+b+c+c-d+d+ | 
| a+a-b+b+c+c-d-d+ | 
| a+a-b+b+c-c-d+d+ | 
| a+a-b-b+c+c-d+d+ | 
| a+a-b+b+c-c-d-d+ | 
| a+a-b-b+c-c-d+d+ | 
| a+a-b-b+c+c-d-d+ | 
| a+a-b-b+c-c-d-d+ | 
| a-a-b+b+c+c-d+d+ | 
| a-a-b+b+c+c-d-d+ | 
| a-a-b+b+c-c-d+d+ | 
| a-a-b-b+c+c-d+d+ | 
| a-a-b+b+c-c-d-d+ | 
| a-a-b-b+c-c-d+d+ | 
| a-a-b-b+c+c-d-d+ | 
| a-a-b-b+c-c-d-d+ | 
| a+a-b+b-c+c+d+d+ | 
| a+a-b+b-c+c+d-d+ | 
| a+a-b+b-c-c+d+d+ | 
| a+a-b-b-c+c+d+d+ | 
| a+a-b+b-c-c+d-d+ | 
| a+a-b-b-c-c+d+d+ | 
| a+a-b-b-c+c+d-d+ | 
| a+a-b-b-c-c+d-d+ | 
| a-a-b+b-c+c+d+d+ | 
| a-a-b+b-c+c+d-d+ | 
| a-a-b+b-c-c+d+d+ | 
| a-a-b-b-c+c+d+d+ | 
| a-a-b+b-c-c+d-d+ | 
| a-a-b-b-c-c+d+d+ | 
| a-a-b-b-c+c+d-d+ | 
| a-a-b-b-c-c+d-d+ | 
| a+a-b+b+c+c-d+d- | 
| a+a-b+b+c+c-d-d- | 
| a+a-b+b+c-c-d+d- | 
| a+a-b-b+c+c-d+d- | 
| a+a-b+b+c-c-d-d- | 
| a+a-b-b+c-c-d+d- | 
| a+a-b-b+c+c-d-d- | 
| a+a-b-b+c-c-d-d- | 
| a-a-b+b+c+c-d+d- | 
| a-a-b+b+c+c-d-d- | 
| a-a-b+b+c-c-d+d- | 
| a-a-b-b+c+c-d+d- | 
| a-a-b+b+c-c-d-d- | 
| a-a-b-b+c-c-d+d- | 
| a-a-b-b+c+c-d-d- | 
| a-a-b-b+c-c-d-d- | 
| a+a-b+b-c+c-d+d+ | 
| a+a-b+b-c+c-d-d+ | 
| a+a-b+b-c-c-d+d+ | 
| a+a-b-b-c+c-d+d+ | 
| a+a-b+b-c-c-d-d+ | 
| a+a-b-b-c-c-d+d+ | 
| a+a-b-b-c+c-d-d+ | 
| a+a-b-b-c-c-d-d+ | 
| a-a-b+b-c+c-d+d+ | 
| a-a-b+b-c+c-d-d+ | 
| a-a-b+b-c-c-d+d+ | 
| a-a-b-b-c+c-d+d+ | 
| a-a-b+b-c-c-d-d+ | 
| a-a-b-b-c-c-d+d+ | 
| a-a-b-b-c+c-d-d+ | 
| a-a-b-b-c-c-d-d+ | 
| a+a-b+b-c+c+d+d- | 
| a+a-b+b-c+c+d-d- | 
| a+a-b+b-c-c+d+d- | 
| a+a-b-b-c+c+d+d- | 
| a+a-b+b-c-c+d-d- | 
| a+a-b-b-c-c+d+d- | 
| a+a-b-b-c+c+d-d- | 
| a+a-b-b-c-c+d-d- | 
| a-a-b+b-c+c+d+d- | 
| a-a-b+b-c+c+d-d- | 
| a-a-b+b-c-c+d+d- | 
| a-a-b-b-c+c+d+d- | 
| a-a-b+b-c-c+d-d- | 
| a-a-b-b-c-c+d+d- | 
| a-a-b-b-c+c+d-d- | 
| a-a-b-b-c-c+d-d- | 
| a+a-b+b-c+c-d+d- | 
| a+a-b+b-c+c-d-d- | 
| a+a-b+b-c-c-d+d- | 
| a+a-b-b-c+c-d+d- | 
| a+a-b+b-c-c-d-d- | 
| a+a-b-b-c-c-d+d- | 
| a+a-b-b-c+c-d-d- | 
| a+a-b-b-c-c-d-d- | 
| a-a-b+b-c+c-d+d- | 
| a-a-b+b-c+c-d-d- | 
| a-a-b+b-c-c-d+d- | 
| a-a-b-b-c+c-d+d- | 
| a-a-b+b-c-c-d-d- | 
| a-a-b-b-c-c-d+d- | 
| a-a-b-b-c+c-d-d- | 
| a-a-b-b-c-c-d-d- | 






