Dihybrid crosses

A dihybrid cross follows the inheritance of two genes at once. When both parents are heterozygous for two genes on different chromosomes, each parent produces four different gametes, all equally likely, the Punnett square has 16 boxes, and the offspring phenotypes come out in the ratio 9 : 3 : 3 : 1.

What is a dihybrid cross?

A monohybrid cross follows one gene, such as flower colour. A dihybrid cross follows two, such as flower colour and height. AQA's A-level specification asks you to use fully labelled genetic diagrams to interpret, or predict, the results of monohybrid and dihybrid crosses involving dominant, recessive and codominant alleles.

The simple ratios only work if the two genes are on different chromosomes. Then, in meiosis, the alleles of one gene sort into gametes independently of the alleles of the other. This is independent assortment: every combination of alleles is equally likely to end up in a gamete.

How to do a dihybrid cross

Suppose that in a plant, tall (T) is dominant to short (t), and purple flowers (P) are dominant to white (p), with the two genes on different chromosomes. Cross two plants that are heterozygous for both: TtPp × TtPp.

1. Write the parents' genotypes and phenotypes: TtPp (tall, purple) × TtPp (tall, purple).
2. Work out the gametes. Each gamete gets one allele of each gene. Pair each height allele with each colour allele: TP, Tp, tP, tp. A quick way is the FOIL method used for expanding brackets: first, outer, inner, last.
3. Draw a 4 × 4 Punnett square with one parent's gametes across the top and the other's down the side.
4. Fill in the 16 offspring genotypes, keeping the alleles of each gene together.
5. Count the phenotypes and write the ratio.

Counting the boxes: 9 have at least one T and one P (tall, purple), 3 have at least one T but pp (tall, white), 3 are tt with at least one P (short, purple), and 1 is ttpp (short, white).

Why the ratio is 9 : 3 : 3 : 1

Because the genes assort independently, you can treat them as two separate monohybrid crosses and multiply. Tt × Tt gives ¾ tall and ¼ short; Pp × Pp gives ¾ purple and ¼ white. So:

• Tall and purple: ¾ × ¾ = 9/16
• Tall and white: ¾ × ¼ = 3/16
• Short and purple: ¼ × ¾ = 3/16
• Short and white: ¼ × ¼ = 1/16

This shortcut is quicker than a full Punnett square, and it works for any cross between unlinked genes. The ratio is an expected probability: in a real batch of offspring, the numbers will only be close to it.

Other dihybrid ratios

Example: a test cross

A tall, purple plant of unknown genotype is crossed with a short, white plant (ttpp), and 80 seeds grow into roughly equal numbers of all four phenotypes, about 20 each. The short, white parent can only give tp gametes, so the offspring show exactly which gametes the other parent made. Four kinds in equal numbers means it made TP, Tp, tP and tp equally, so it was TtPp.

Try one: work out the chance of an offspring phenotype, then press Mark to check your answer in the Genetics and DNA course.

Testing a dihybrid cross with chi-squared

AQA's specification includes using the chi-squared test to check how well observed phenotype ratios fit expected ones. OpenStax Biology gives these F2 results from a pea cross for two genes: 2706 tall and inflated pods, 930 tall and constricted, 888 dwarf and inflated, and 300 dwarf and constricted, 4824 plants in all.

χ² = 0.021 + 0.719 + 0.301 + 0.007 = 1.05. With four categories there are 4 − 1 = 3 degrees of freedom, and the critical value at the 0.05 probability level is 7.82. Since 1.05 is smaller, the difference between observed and expected is not significant: the results fit a 9 : 3 : 3 : 1 ratio, as expected for two unlinked genes.

When the ratio isn't 9 : 3 : 3 : 1

• Autosomal linkage: if the two genes are close together on the same chromosome, they tend to be inherited together and don't assort independently. You get more of the parental combinations and fewer recombinants. See autosomal linkage.
• Epistasis: one gene can mask or change the effect of the other, merging phenotype classes into ratios such as 9 : 3 : 4 or 12 : 3 : 1.
• Chance: with small numbers of offspring, the observed ratio can differ from the expected one just by chance. The chi-squared test tells you whether a difference is big enough to matter.

Common mistakes

• Putting two alleles of the same gene in a gamete. A gamete has one allele of each gene: Tp, never TT or Pp.
• Only listing two gametes. A double heterozygote makes four kinds of gamete, in equal numbers.
• Writing genotypes in a messy order. Keep alleles of the same gene together, capital first: TtPp, not TPtp.
• Expecting 9 : 3 : 3 : 1 from every cross. It only comes from two heterozygotes with unlinked genes and complete dominance.
• Treating the ratio as exact. It is a probability. Real numbers vary, which is why we use chi-squared.

Try crosses of your own in the genetics cross lab, or check a Punnett square with the Punnett square calculator guide. For practice in a short timed paper, try today's A-level Biology: Year 2 paper.

Read next

Biology · Genetics and inheritancePunnett square calculator: monohybrid and dihybridMake a Punnett square for any monohybrid or dihybrid cross, with genotype and phenotype ratios, the chance of each outcome and worked examples.