Setting it up
- Write the alleles each parent can pass on. An Aa parent gives A or a.
- Put one parent's alleles along the top and the other's down the side.
- Fill each box with the allele from its column and its row.
One gene: Aa × Aa
The four boxes are AA, Aa, Aa and aa, a genotype ratio of 1 : 2 : 1. If A is dominant, three of the four show the dominant trait, a phenotype ratio of 3 : 1. Each box is a probability for each child, not a promise about a family of four.
Two genes: AaBb × AaBb
Each parent can pass on AB, Ab, aB or ab, so the square is 4 × 4 with 16 boxes. When the genes sort independently and both show simple dominance, the phenotypes come out 9 : 3 : 3 : 1.
From families to populations
Hardy-Weinberg does the same for a whole population. If p and q are the frequencies of A and a, the genotypes are expected at p², 2pq and q². If 16% of people are aa, q = 0.4, p = 0.6 and 48% are carriers (Aa).
Calculators
The Punnett Square Calculator draws the square for any cross and gives the ratios. The Hardy-Weinberg Calculator gives allele frequencies from genotype counts and tests whether a population is in equilibrium.
Traits on the X chromosome
For a recessive trait on the X chromosome, such as red-green color blindness, cross a carrier mother (XAXa) with an unaffected father (XAY):
| XA | Y | |
|---|---|---|
| XA | XAXA | XAY |
| Xa | XAXa | XaY |
No daughters are affected, but half are carriers. Each son has a 1 in 2 chance of being affected.
Other patterns
- Incomplete dominance. Crossing red and white snapdragons gives pink flowers. Crossing two pinks gives red, pink and white in a 1 : 2 : 1 ratio, because each genotype has its own look.
- A test cross. To find out whether a dominant-looking parent is AA or Aa, cross it with aa. Any recessive offspring show that the parent is Aa.
Several children
Each child is a separate event, so multiply the chances. For two Aa parents, the chance that two children are both aa is ¼ × ¼ = 1/16.