Mendel's Dihybrid Cross and Independent Assortment for CBSE Class 10

In his monohybrid experiments, Gregor Mendel proved that individual traits (like plant height) segregate cleanly without blending. But in real life, living organisms do not inherit traits one at a time; an organism inherits thousands of traits simultaneously. This led Mendel to ask a deeper question: Are different physical traits linked together during inheritance, or are they inherited independently of one another? For instance, are yellow seeds always tied to round shapes, or can a plant inherit round green seeds or wrinkled yellow seeds?

To answer this, Mendel conducted his famous Dihybrid Cross, tracking two different pairs of contrasting characters simultaneously. In CBSE Class 10 Science, Chapter 8 (Heredity), the dihybrid cross and the famous $9 : 3 : 3 : 1$ phenotypic ratio form the foundation of Mendel's Third Law: The Law of Independent Assortment.

What You Will Learn

• Definition of a Dihybrid Cross
• Selection of traits: Seed Shape (Round $R$ vs. Wrinkled $r$) and Seed Colour (Yellow $Y$ vs. Green $y$)
• Parental genotypes: Pure Round Yellow ($RRYY$) $\times$ Pure Wrinkled Green ($rryy$)
• The $F_1$ generation and the four gamete combinations ($RY, Ry, rY, ry$)
• Construction and analysis of the 16-box Punnett Square
• The $F_2$ Phenotypic Ratio: $\mathbf{9 : 3 : 3 : 1}$
• Formal statement of Mendel's Law of Independent Assortment
• High-yield board exam numerical questions and common traps

1. What is a Dihybrid Cross?

Definition

A breeding cross between two parent organisms that differs in two pairs of contrasting characters simultaneously is called a dihybrid cross.

The Two Selected Traits in Pea Plants:

1. Seed Shape:
   • Dominant allele: Round ($R$)
   • Recessive allele: Wrinkled ($r$)
2. Seed Colour:
   • Dominant allele: Yellow ($Y$)
   • Recessive allele: Green ($y$)

2. The Dihybrid Cross Step-by-Step

    Parental Generation (P):    Round Yellow (RRYY)   ×   Wrinkled Green (rryy)
                                        |                         |
    Gametes:                           (RY)                      (ry)
                                        \                       /
    F1 Generation:                              RrYy
                                         (All are ROUND YELLOW!)
                                                 ↓
                                      Selfing: RrYy × RrYy
                                                 ↓
    F2 Generation:                     16-Box Punnett Square
                                  Phenotypic Ratio = 9 : 3 : 3 : 1

1. The Parental Cross ($P$):

• Pure-breeding Round Yellow parent: genotype $RRYY$ (produces gametes carrying $RY$).
• Pure-breeding Wrinkled Green parent: genotype $rryy$ (produces gametes carrying $ry$).
• When crossed, the resulting $F_1$ generation inherits $R$ and $Y$ from one parent, and $r$ and $y$ from the other.

2. The $F_1$ Generation:

• Genotype of all $F_1$ plants: $RrYy$ (Heterozygous for both genes).
• Phenotype of all $F_1$ plants: $100\%$ Round Yellow Seeds.
• Reason: Round ($R$) dominates wrinkled ($r$), and Yellow ($Y$) dominates green ($y$).

3. Gamete Formation in the $F_1$ Hybrid ($RrYy$)

When the $F_1$ plant ($RrYy$) undergoes meiosis to form gametes, the segregation of the seed shape alleles ($R$ and $r$) is completely independent of the segregation of the seed colour alleles ($Y$ and $y$):

• Allele $R$ can pair with either $Y$ or $y \implies$ Gametes $RY$ and $Ry$
• Allele $r$ can pair with either $Y$ or $y \implies$ Gametes $rY$ and $ry$

Thus, the $F_1$ plant produces four distinct types of gametes in equal proportions ($25\%$ each): $\mathbf{RY, \quad Ry, \quad rY, \quad ry}$

4. The 16-Box Punnett Square ($F_2$ Generation)

Self-pollinating the $F_1$ generation ($RrYy \times RrYy$) combines these 4 gametes from the male parent with the same 4 gametes from the female parent, yielding $16$ possible genetic combinations:

5. The $F_2$ Phenotypic Classes and Ratio

When we inspect the physical appearance of the 16 combinations:

1. Round Yellow Seeds (Parental Combination):
   • Must have at least one $R$ and one $Y$ ($R\_Y\_$).
   • Total count = $9$
2. Round Green Seeds (New Recombinant Combination):
   • Must have at least one $R$ and two recessive $y$ alleles ($R\_yy$).
   • Total count = $3$
3. Wrinkled Yellow Seeds (New Recombinant Combination):
   • Must have two recessive $r$ alleles and at least one $Y$ ($rrY\_$).
   • Total count = $3$
4. Wrinkled Green Seeds (Parental Combination):
   • Must have two recessive $r$ alleles and two recessive $y$ alleles ($rryy$).
   • Total count = $1$

The Master Phenotypic Ratio of a Dihybrid Cross:

$\mathbf{9 \text{ Round Yellow} : 3 \text{ Round Green} : 3 \text{ Wrinkled Yellow} : 1 \text{ Wrinkled Green}}$ $\mathbf{\text{Dihybrid Phenotypic Ratio} = 9 : 3 : 3 : 1}$

Important: <u>The appearance of entirely NEW combinations—Round Green ($3$) and Wrinkled Yellow ($3$)—that were not present in either of the original pure parents proved conclusively that seed shape and seed colour are NOT tied together! They assort completely independently.</u>

6. Mendel's Third Law: The Law of Independent Assortment

From the $9:3:3:1$ dihybrid cross results, Mendel formulated his Third Law:

Formal Statement

When two pairs of traits are combined in a hybrid, the segregation and inheritance of one pair of characters is completely independent of the segregation and inheritance of the other pair of characters during gamete formation.

Each pair of alleles sorts into gametes independently, producing equal numbers of parental and recombinant combinations.

7. Summary and Examination Tips

Exam Tip: In numerical board questions: If 1600 pea seeds are obtained in the $F_2$ generation of a dihybrid cross:

• Round Yellow $= \frac{9}{16} \times 1600 = \mathbf{900}$
• Round Green $= \frac{3}{16} \times 1600 = \mathbf{300}$
• Wrinkled Yellow $= \frac{3}{16} \times 1600 = \mathbf{300}$
• Wrinkled Green $= \frac{1}{16} \times 1600 = \mathbf{100}$

Common Mistake: Writing gametes with two of the same letter (like $RR$ or $YY$). A gamete must contain one allele of EACH gene pair (e.g., $RY, Ry, rY, ry$). A gamete can NEVER be $RR$ or $yy$!