Answer:
- Red = 27/256
- Pink = 117/256
- White = 112/256
Explanation:
<u>Available data</u>:
- Four diallelic genes: A, B, C, D
- AA and Aa allows the conversion of P0 tp P1, while aa does not
- BB and Bb allows the conversion of P1 tp P2, while bb does not
- CC and Cc allows the conversion of P2 tp P3, while cc does not
- DD and Dd inhibit the action of allele C (P2 to P3), while dd does not
This is:
In the presence of the dominant alleles A, B, and C, the three might occur:
Po (white 0) ----> P1 (White 1) ----> P2 (Pink)----> P3 (Red)
A B C
In the presence of the recessive alleles a, b or c, the three reactions or some of them might not occur ( the X represents the inhibition of the reaction):
Po (white 0) --X--> P1 (White 1) --X--> P2 (Pink)--X--> P3 (Red)
a b c
In the presence of allele D, the last reaction is not possible, because D inhibits the action of C
P2 (Pink) --X-->P3 (Red)
C + D
- So, in order to get Red flowers we must have the next genotype:
A-B-C-dd (The three reactions can occur, and D must be absent)
- To get Pink flowers we must have the next genotypes:
A-B-C-D- (D Inhibits C, hence it inhibits the third reaction) or A-B-ccD- or A-B-ccdd (cc does not allow the third reaction to happen, independently of the D gene presence
- To get White flowers we must have the next genotypes:
aaB-C-D-,aabbC-D-, aaB-ccD-, aabbccD-, aabbccdd, aaB-C-dd, aaB-ccdd, aabbC-dd, A-bbC-D-, A-bbccD-, A-bbC-dd, A-bbccdd
(aa must be present to get a white0 flower, or bb must be present to get a white1 flower)
In the proposed problem, we have that the parental are AAbbCCDD and aaBBccdd, so we can tell that the whole F1 progeny will be heterozygous for the four genes, this is AaBbCcDd.
Knowing that these four genes assort independently, then we can infer that the F2 will have the next genotypic proportions for each gene:
- AA + Aa=3/4
- aa= 1/4
- BB + bb= 3/4
- bb = 1/4
- CC + Cc = 3/4
- cc= 1/4
- DD + Dd =3/4
- dd= 1/4
So, to get each of the mentioned genotypes for each trait, we must multiply their respective genotypic proportions, like this:
- Red: A- x B- x C- x dd: 3/4 x 3/4 x 3/4 x 1/4 = 27/256
- Pink: A- x B- x C- x D-: 3/4 x 3/4 x 3/4 x 3/4 = 81/256
A- x B- x cc x D-: 3/4 x 3/ x 1/4 x 3/4 = 27/256
A- x B- x cc x dd: 3/4 x 3/4 x 1/4 x 1/4= 9/256
By summing these proportions, we can get the proportion of all the pink flowers: 27/256 + 81/256 + 27/256 + 9/256= 117/256
- White: To get the proportion of white flowers, you can repeat the same multiplications as before for each possible white genotype and then sum the results, as we did for pink flowers. Or you can extract from the total number of flowers (256), the amounts of red and pink flowers (27 and 117). This is: 256 - (27 + 117) = 112.
Then 112/256 is the proportion of white flowers.
