11 min readPathway sheet1-mark MCQ, a 3-mark cross, or a 5-mark answer with a Punnett square, plus the seed-ratio spotting in practicals; also a NEET favourite

Dihybrid cross and the law of independent assortment

When two pairs of traits are crossed, each pair separates on its own. This independent assortment gives the 9:3:3:1 F2 ratio and new trait combinations.

Dihybrid F2 phenotypes9 round yellow : 3 round green : 3 wrinkled yellow : 1 wrinkled green

Dihybrid F2 genotypes9 genotypes in the ratio 1:2:1:2:4:2:1:2:1

n heterozygous gene pairsGamete types = 2ⁿ; F2 phenotypes = 2ⁿ (with full dominance); F2 genotypes = 3ⁿ

Dihybrid test crossRrYy × rryy gives 1:1:1:1

The law of independent assortment

Mendel next crossed plants that differed in two characters: seed shape and seed colour. Round (R) is dominant over wrinkled (r), and yellow (Y) over green (y). The law of independent assortment says: when two pairs of traits are combined in a hybrid, segregation of one pair is independent of the other pair. So an F1 plant RrYy makes four kinds of gametes, RY, Ry, rY and ry, in equal numbers (1/4 each). Random fusion of these gametes gives 16 combinations in F2. Two of the F2 classes, round green and wrinkled yellow, are new combinations not seen in either parent.

The dihybrid cross from P to F2

1
P: RRYY (round yellow) × rryy (wrinkled green).
2
Gametes: RY from one parent, ry from the other.
3
F1: RrYy, all round yellow.
4
F1 gametes: RY, Ry, rY, ry, each 1/4.
Independent assortment
5
F2: a 4 × 4 Punnett square with 16 boxes.
6★
F2 phenotypes: 9 round yellow (R_Y_) : 3 round green (R_yy) : 3 wrinkled yellow (rrY_) : 1 wrinkled green (rryy).
A blank (_) means either allele

★ key step

The 9:3:3:1 ratio is two 3:1 ratios combined

Problem

Show that the dihybrid F2 ratio is made of two separate 3:1 ratios. Then find what fraction of F2 seeds are RrYy.

Working

Seed shape alone: round : wrinkled = (9 + 3) : (3 + 1) = 12 : 4 = 3 : 1.
Seed colour alone: yellow : green = (9 + 3) : (3 + 1) = 12 : 4 = 3 : 1.
Independent events multiply: (3 round : 1 wrinkled) × (3 yellow : 1 green) = 9 : 3 : 3 : 1.
From Rr × Rr, the chance of Rr is 1/2. From Yy × Yy, the chance of Yy is 1/2.
Chance of RrYy = 1/2 × 1/2 = 1/4, that is 4 of the 16 boxes.

Answer

9 : 3 : 3 : 1 = (3 : 1) × (3 : 1); 1/4 of F2 seeds are RrYy.

Activity: Mendelian ratios with seeds of different colours

This models how gametes fuse at random. Seeds of two colours stand for two alleles.

1
Take two beakers. Label one male gametes and the other female gametes.
2
Put 50 yellow and 50 green seeds (for example maize or pea) in each beaker and mix well. Yellow stands for the dominant allele Y, green for y. Each beaker is like a Yy parent.
3
Without looking, pick one seed from each beaker and write the pair: YY, Yy or yy.
4
Put the seeds back so the numbers stay equal. Repeat at least 64 times.
5
Count each kind of pair and work out the ratios.
6★
Record: about 1 YY : 2 Yy : 1 yy, and about 3 'yellow' : 1 'green'. With a second pair of beakers holding large and small seeds, picking from all four gives close to 9 : 3 : 3 : 1.
7
In the spotting test you may get a tray of pea seeds or a maize cob. Count each type of seed and say whether the ratio is near 3 : 1 or 9 : 3 : 3 : 1.

★ key step

How to draw the dihybrid Punnett square

Write P: Round yellow (RRYY) × Wrinkled green (rryy); gametes RY and ry in circles; F1: Round yellow (RrYy).
List the four F1 gametes in circles: RY, Ry, rY, ry.
Draw a 4 × 4 grid. Write the four male gametes across the top and the four female gametes down the side.
Fill all 16 boxes, writing the R alleles first and then the Y alleles, e.g. RRYy.
Mark each phenotype class (for example with a tick or shading) and count them.
Write below: 9 round yellow : 3 round green : 3 wrinkled yellow : 1 wrinkled green.

In real life

Breeders combine two useful traits, such as disease resistance from one rice variety and high yield from another. Independent assortment is why some F2 plants carry both traits together.

Exam angle

2 marks: “State the law of independent assortment.” When two pairs of traits are combined in a hybrid, the segregation of one pair of characters is independent of the other pair.

3 marks: “A pea plant with round yellow seeds (RrYy) is crossed with a plant with wrinkled green seeds (rryy). Work out the offspring and their ratio. What is this cross called?” Gametes RY, Ry, rY, ry × ry. Offspring RrYy (round yellow), Rryy (round green), rrYy (wrinkled yellow), rryy (wrinkled green) in the ratio 1 : 1 : 1 : 1. It is a dihybrid test cross.

5 marks: “Explain the law of independent assortment with a dihybrid cross. Draw the F2 Punnett square.” State the law; P RRYY × rryy; F1 RrYy; four gametes in equal numbers; 4 × 4 Punnett square; 9 : 3 : 3 : 1; new combinations round green and wrinkled yellow.

Remember it

9 + 3 + 3 + 1 = 16 boxes. Only 1 box in 16 shows both recessive traits.