Working out a dihybrid cross
A dihybrid cross follows two genes at once. If they are on different chromosomes they are inherited independently, so you can cross each gene on its own and multiply the probabilities.
Rules
- Independent assortment: genes on different chromosomes are sorted independently
- Product rule: P(A_ and B_) = P(A_) × P(B_)
- AaBb × AaBb: 9 : 3 : 3 : 1
- AaBb makes 4 gametes (AB, Ab, aB, ab), AaBbCc 8 = 2³
- aabb from AaBb × AaBb: 1/4 × 1/4 = 1/16
Your turn
Three problems on this topic. Type probabilities as a percentage number, e.g. 18.75.
Task
Three independently inherited genes, each dominant-recessive. The cross is AaBbCc × AaBbCc. How many different gametes does AaBbCc make? What is the probability that an offspring is dominant in all three traits, and recessive in all three?
Number of different gametes of AaBbCc
Dominant in all three in %
Recessive in all three in %
Probabilities as a percentage number (25 or 18.75), rounded to 2 decimal places; allele frequencies as a decimal (0.02).
Worked example
Two independently inherited genes: A (round) dominant over a (wrinkled) and B (yellow) dominant over b (green). The cross is AaBb × AaBb. Find the probability of offspring dominant in both traits, recessive in both, and with genotype AaBb.
Worked solution
- 1.Gene A on its own: Aa × Aa → dominant 3/4, recessive 1/4, Aa 1/2
- 2.Gene B on its own: Bb × Bb → dominant 3/4, recessive 1/4, Bb 1/2
- 3.Independent genes: multiply the probabilities (product rule)
- 4.Both dominant: 3/4 × 3/4 = 56.25%; both recessive: 1/4 × 1/4 = 6.25%; AaBb: 1/2 × 1/2 = 25%
Typical mistake: Drawing a 16-box Punnett square and miscounting. Faster and safer: cross each gene on its own and multiply the probabilities.
Three independently inherited genes, each dominant-recessive. The cross is AaBbCc × aabbcc. How many different gametes does AaBbCc make? What is the probability that an offspring is dominant in all three traits, and recessive in all three?
Worked solution
- 1.Gametes: each heterozygous gene doubles the options, 2³ = 8 (ABC, ABc, AbC, Abc, aBC, aBc, abC, abc)
- 2.Each gene Aa × aa: dominant 1/2, recessive 1/2
- 3.All dominant: (1/2)³ = 1/8 = 12.5%; all recessive: (1/2)³ = 1/8 = 12.5%
Typical mistake: Adding the probabilities of the three genes instead of multiplying them. For independent genes the product rule applies.
Common questions
Do I always have to draw a 16-box Punnett square?
No. Cross each gene on its own and multiply. It is faster and you will not miscount.
When does independent assortment not apply?
When the genes lie close together on the same chromosome (linkage). Then they are usually inherited together.