Answer and Explanation:
<u>Complete question:</u>
"What is the expected proportion of progeny with the following broad genotypes each having a distinct phenotype in a typical Mendelian dihybrid cross:A_B_ : A_bb : aaB_ : aabb. Be able to derive the above ratios directly by studying alleles for one gene at a time (individual Punnett) and applying the product rule.
Example: (1 AA: 2Aa: 1aa) (1BB : 2Bb: 1bb) Suppose you want to know the proportion of A_B_ among the total progeny, you may first estimate which genotypes represent A_ and which genotypes represent B_. Clearly AA and Aa for the first genotype A_. And BB and Bb for the second genotype".
<u>Answer</u>:
In a typical Mendelian dihybrid cross, we have:
Parental) AaBb x AaBb
Gametes) AB Ab aB ab
AB Ab aB ab
Punnet Square) AB Ab aB ab
AB AABB AABb AaBB AaBb
Ab AABb AAbb AaBb Aabb
aB AaBB AaBB aaBB aaBb
ab AaBb Aabb aaBb aabb
F1 phenotypic frequencies)
9/16 A-B-
3/16 aaB-
3/16 A-bb
1/16 aabb
But if you do not want to do the dihybrid cross, you might just perform the cross for each gene and then apply the product rule. This is:
Parental) Aa x Aa
Gametes) A a A a
Punnet Square) A a
A AA Aa
a Aa aa
F1 genotypic frequencies)
1/4 AA
2/4 Aa
1/4 aa
F1 phenotypic frequencies)
3/4 A-
1/4 aa
Parental) Bb x Bb
Gametes) B b B b
Punnet Square) B b
B BB Bb
b Bb bb
F1 genotypic frequencies)
1/4 BB
2/4 Bb
1/4 bb
F1 genotypic frequencies)
3/4 B-
1/4 bb
To estimate the progeny phenotypic proportions (A-B-, aaB-, AAB-, aabb), from the genotypic proportions of progeny, you can sum the genotypic frequency of homozygote plus heterozygote, to get the proportions A- and B-.
Aa=2/4
A- = AA+Aa= 1/4 + 2/4 = 3/4
Bb= 2/4
B- = BB + Bb = 1/4 + 2/4 = 3/4
Then multiply these proportions to get the progeny proportions, like this:
A-B-= (AA+Aa) x (BB + Bb) = 3/4 x 3/4 = 9/16
A-bb = (AA + Aa) x bb = 3/4 x 1/4 = 3/16
aaB- = aa x (BB + Bb) = 1/4 x 3/4 = 3/16
aabb = aa x bb = 1/4 x 1/4 = 1/16
Note: You can get the same results using directly the phenotypic proportions of each cross.
