How the 9:3:3:1 Dihybrid Ratio Is Derived
The 9:3:3:1 ratio comes from combining two independent 3:1 monohybrid ratios: multiplying (3:1) by (3:1) gives 9 (both dominant) : 3 (first dominant, second recessive) : 3 (first recessive, second dominant) : 1 (both recessive).
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Starting point: two separate 3:1 ratios
In a TtYy x TtYy cross, gene T/t on its own gives a 3:1 ratio (3 dominant : 1 recessive), and gene Y/y on its own also gives a 3:1 ratio. Because the two genes assort independently (Mendel's second law), the combined ratio is found by multiplying the two ratios together, treating each fraction of one gene's outcome as independent of the other.
Multiplying the ratios
| 3/4 Y_ (dominant) | 1/4 yy (recessive) | |
|---|---|---|
| 3/4 T_ (dominant) | 9/16 T_Y_ | 3/16 T_yy |
| 1/4 tt (recessive) | 3/16 ttY_ | 1/16 ttyy |
Matching the fractions to the Punnett square
- 9/16 show both dominant traits (e.g. round and yellow), 9 of the 16 boxes.
- 3/16 show the first dominant trait and second recessive trait (round, green), 3 of the 16 boxes.
- 3/16 show the first recessive trait and second dominant trait (wrinkled, yellow), 3 of the 16 boxes.
- 1/16 show both recessive traits (wrinkled, green), 1 of the 16 boxes.
Why this shortcut works
The multiplication shortcut works because independent assortment means the probability of inheriting a particular combination of alleles from two different genes equals the probability of inheriting each allele separately, multiplied together. This avoids drawing the full 16-box grid when only the ratio is needed.
Worked problem 1 (easy): fraction showing both recessive traits
In a TtYy x TtYy cross, find the fraction of offspring that show both recessive traits (wrinkled and green). Take each gene on its own: the chance of tt is 1/4 and the chance of yy is 1/4.
Multiplying the two independent fractions gives 1/4 x 1/4 = 1/16. So 1/16 of the offspring are wrinkled and green, which matches the final '1' in the 9:3:3:1 ratio.
Worked problem 2 (medium): predicting the ratio of TtYy x Ttyy
Use the multiplication method for a TtYy x Ttyy cross. Gene T/t is Tt x Tt, giving 3/4 round : 1/4 wrinkled.
Gene Y/y is Yy x yy, giving 1/2 yellow : 1/2 green.
So the phenotype ratio is 3 round yellow : 3 round green : 1 wrinkled yellow : 1 wrinkled green. Multiplying the separate ratios gives the answer without drawing a 16-box grid.
| 1/2 yellow (Y_) | 1/2 green (yy) | |
|---|---|---|
| 3/4 round (T_) | 3/8 round yellow | 3/8 round green |
| 1/4 wrinkled (tt) | 1/8 wrinkled yellow | 1/8 wrinkled green |
Worked problem 3 (SPM level): turning the ratio into offspring counts
A TtYy x TtYy cross produces 160 offspring. Predict how many fall into each phenotype class.
Each class is a fraction of 16, so multiply each fraction by 160.
The expected numbers are 90 round yellow : 30 round green : 30 wrinkled yellow : 10 wrinkled green. Real results vary a little around these figures because fertilisation is random, but with a large total the counts sit close to the predicted ratio.
| Phenotype class | Fraction | Expected number |
|---|---|---|
| Round yellow (T_Y_) | 9/16 | 90 |
| Round green (T_yy) | 3/16 | 30 |
| Wrinkled yellow (ttY_) | 3/16 | 30 |
| Wrinkled green (ttyy) | 1/16 | 10 |
Practice problems
Work out each one using the multiplication method, then check the answers below.
- 1. What fraction of a TtYy x TtYy cross is round and green (T_yy)?
- 2. Using the multiplication method, what phenotype ratio results from a TtYy x ttYy cross?
- 3. In 240 offspring of a TtYy x TtYy cross, how many are expected to be wrinkled and yellow (ttY_)?
Answers
Common mistakes
Source:SRC-DSKP-EN
Frequently asked questions
Where does the 9:3:3:1 ratio come from?
Why do you multiply the two 3:1 ratios instead of adding them?
Does the dihybrid cross always give a 9:3:3:1 ratio?
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