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Genetics · Problem type
Expected counts for a modified dihybrid ratio
Use this for “A 9:3:4 cross gives 160 offspring. How many are expected in each class?”
Chart
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N
Offspring
example
ratio
Modified ratio
example
s₁
Boxes of 16 in class 1
worked out (not typed)
s₂
Boxes of 16 in class 2
worked out (not typed)
s₃
Boxes of 16 in class 3
worked out (not typed)
E₁
Expected in class 1
worked out (not typed)
E₂
Expected in class 2
worked out (not typed)
E₃
Expected in class 3
worked out (not typed)
Formulas
s₁
=
class
1
of
ratio
9 = class 1 of 9:3:4
s₂
=
class
2
of
ratio
3 = class 2 of 9:3:4
s₃
=
class
3
of
ratio
4 = class 3 of 9:3:4
E₁
=
N
×
s₁
16
90
=
160
×
9
16
E₂
=
N
×
s₂
16
30
=
160
×
3
16
E₃
=
N
×
s₃
16
40
=
160
×
4
16
Assumptions
•
Both parents are AaBb, and the two genes assort independently: 16 equally likely boxes.
•
Epistasis merges the 9:3:3:1 classes into a modified ratio whose parts still add to 16.
•
Each class’s expected count is the offspring times its boxes out of 16.
•
A ratio with two classes leaves class 3 empty: 0 boxes.
Step-by-step
WE KNOW
N = 160, ratio: 9:3:4
FIND
boxes of 16 in class 1 (s₁), boxes of 16 in class 2 (s₂), boxes of 16 in class 3 (s₃), expected in class 1 (E₁), expected in class 2 (E₂), expected in class 3 (E₃)
Step 1 · Find boxes of 16 in class 1 (s₁)
Use s₁ = class 1 of ratio
Class 1 of 9:3:4 takes 9 of the 16 boxes.
s₁
=
9
Step 2 · Find boxes of 16 in class 2 (s₂)
Use s₂ = class 2 of ratio
Class 2 of 9:3:4 takes 3 of the 16 boxes.
s₂
=
3
Step 3 · Find boxes of 16 in class 3 (s₃)
Use s₃ = class 3 of ratio
Class 3 of 9:3:4 takes 4 of the 16 boxes.
s₃
=
4
Step 4 · Find expected in class 1 (E₁)
Use E₁ = N × s₁ ÷ 16
The offspring split like the 16 boxes: take this class’s share of them.
E₁
=
160
×
9
16
E₁
=
1,440
16
E₁
=
90
Step 5 · Find expected in class 2 (E₂)
Use E₂ = N × s₂ ÷ 16
The offspring split like the 16 boxes: take this class’s share of them.
E₂
=
160
×
3
16
E₂
=
480
16
E₂
=
30
Step 6 · Find expected in class 3 (E₃)
Use E₃ = N × s₃ ÷ 16
The offspring split like the 16 boxes: take this class’s share of them.
E₃
=
160
×
4
16
E₃
=
640
16
E₃
=
40
Check
Put the numbers back in. Both sides should match.
9 = 9 ✓
3 = 3 ✓
4 = 4 ✓
90
=
160
×
9
16
✓
30
=
160
×
3
16
✓
40
=
160
×
4
16
✓
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Mode of inheritance from a pedigree
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