SME
Grade 9 Science · Biology
Mendelian and non-Mendelian inheritance
Use this for “Two RrYy pea plants are crossed. What share of offspring are round and yellow?” with a dihybrid Punnett square.
Diagram
RrYy × RrYy: 9:3:3:1 of 16 boxes (round yellow, round green, wrinkled yellow, wrinkled green).
This is an example. Choose your own values to start a new problem.
a
R alleles in the first parent
example
c
R alleles in the second parent
example
b
Y alleles in the first parent
example
e
Y alleles in the second parent
example
tR
Boxes of 4 with round seeds
worked out (not typed)
tY
Boxes of 4 with yellow seeds
worked out (not typed)
D
Round yellow, boxes of 16
worked out (not typed)
F
Round green, boxes of 16
worked out (not typed)
S
Wrinkled yellow, boxes of 16
worked out (not typed)
N
Wrinkled green, boxes of 16
worked out (not typed)
Formulas
tR
=
4
−
(2
−
a
)
×
(2
−
c
)
3 = 4 − (2 − 1) × (2 − 1)
tY
=
4
−
(2
−
b
)
×
(2
−
e
)
3 = 4 − (2 − 1) × (2 − 1)
D
=
tR
×
tY
9 = 3 × 3
F
=
tR
×
(4
−
tY)
3 = 3 × (4 − 3)
S
=
(4
−
tR)
×
tY
3 = (4 − 3) × 3
N
=
(4
−
tR)
×
(4
−
tY)
1 = (4 − 3) × (4 − 3)
Assumptions
•
Pea seeds: R (round) is dominant to r (wrinkled), and Y (yellow) is dominant to y (green).
•
The two genes are on different chromosomes, so they sort independently into the gametes.
•
Each parent’s 4 gametes (some may repeat) are equally likely, so each of the 16 boxes is 1/16.
•
The product rule: the chance of both traits is the one-gene chances multiplied.
Step-by-step
WE KNOW
a = 1, c = 1, b = 1, e = 1
FIND
boxes of 4 with round seeds (tR), boxes of 4 with yellow seeds (tY), round yellow, boxes of 16 (D), round green, boxes of 16 (F), wrinkled yellow, boxes of 16 (S), wrinkled green, boxes of 16 (N)
Step 1 · Find boxes of 4 with round seeds (tR)
Use tR = 4 − (2 − a) × (2 − c)
Only boxes with a recessive allele from both parents lack the round trait; the rest of the 4 show it.
tR = 4 − (2 − 1) × (2 − 1)
tR = 4 − 1
tR = 3
Step 2 · Find boxes of 4 with yellow seeds (tY)
Use tY = 4 − (2 − b) × (2 − e)
Only boxes with a recessive allele from both parents lack the yellow trait; the rest of the 4 show it.
tY = 4 − (2 − 1) × (2 − 1)
tY = 4 − 1
tY = 3
Step 3 · Find round yellow, boxes of 16 (D)
Use D = tR × tY
The genes sort independently, so multiply: round in tR of 4 and yellow in tY of 4.
D
=
3
×
3
D
=
9
Step 4 · Find round green, boxes of 16 (F)
Use F = tR × (4 − tY)
Round in tR of 4 times green, the other 4 − tY of 4.
F
=
3
×
(4
−
3)
F
=
3
Step 5 · Find wrinkled yellow, boxes of 16 (S)
Use S = (4 − tR) × tY
Wrinkled, the other 4 − tR of 4, times yellow in tY of 4.
S
=
(4
−
3)
×
3
S
=
3
Step 6 · Find wrinkled green, boxes of 16 (N)
Use N = (4 − tR) × (4 − tY)
Neither dominant trait: wrinkled times green.
N
=
(4
−
3)
×
(4
−
3)
N
=
1
Check
Put the numbers back in. Both sides should match.
3 = 4 − (2 − 1) × (2 − 1) ✓
3 = 4 − (2 − 1) × (2 − 1) ✓
9 = 3 × 3 ✓
3 = 3 × (4 − 3) ✓
3 = (4 − 3) × 3 ✓
1 = (4 − 3) × (4 − 3) ✓
Topic check
See what you know: 5 questions on this topic
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