SME
Grade 9 Science · Problem type
Codominance
Use this for “A roan bull and a white cow: how many calves in 4 are roan?”
Diagram
0 of 4 red, 2 of 4 roan, 2 of 4 white.
Codominance: the heterozygote shows both colors.
This is an example. Choose your own values to start a new problem.
a
Cᴿ alleles in the first parent
example
c
Cᴿ alleles in the second parent
example
R
Boxes of 4 red
worked out (not typed)
N
Boxes of 4 roan
worked out (not typed)
W
Boxes of 4 white
worked out (not typed)
Formulas
R
=
a
×
c
0 = 1 × 0
N
=
a
×
(2
−
c
)
+
c
×
(2
−
a
)
2 = 1 × (2 − 0) + 0 × (2 − 1)
W
=
(2
−
a
)
×
(2
−
c
)
2 = (2 − 1) × (2 − 0)
Assumptions
•
Cattle coat: CᴿCᴿ is red, CᵂCᵂ white, and CᴿCᵂ roan, red and white hairs side by side.
•
Both alleles show in full in the heterozygote: codominance, not a blend as in pink snapdragons.
•
A parent is written by its count of Cᴿ alleles: 2 (red), 1 (roan) or 0 (white).
Step-by-step
WE KNOW
a = 1, c = 0
FIND
boxes of 4 red (R), boxes of 4 roan (N), boxes of 4 white (W)
Step 1 · Find boxes of 4 red (R)
Use R = a × c
A calf is red with a Cᴿ from each parent: one parent’s Cᴿ times the other’s.
R
=
1
×
0
R
=
0
Step 2 · Find boxes of 4 roan (N)
Use N = a × (2 − c) + c × (2 − a)
A calf is roan with Cᴿ from one parent and Cᵂ from the other, either way round: both colors show.
N
=
1
×
(2
−
0)
+
0
×
(2
−
1)
N
=
2
Step 3 · Find boxes of 4 white (W)
Use W = (2 − a) × (2 − c)
A calf is white with a Cᵂ from each parent.
W
=
(2
−
1)
×
(2
−
0)
W
=
2
Check
Put the numbers back in. Both sides should match.
0 = 1 × 0 ✓
2 = 1 × (2 − 0) + 0 × (2 − 1) ✓
2 = (2 − 1) × (2 − 0) ✓
Topic check
See what you know: 5 questions on this topic
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