Step 1: Understanding the Concept:
Gregor Mendel, the father of modern genetics, conducted experiments on garden pea plants ({Pisum sativum}) to understand the patterns of inheritance. A dihybrid cross is an experiment where two different pairs of contrasting traits are studied simultaneously. For example, Mendel looked at seed shape (Round vs. Wrinkled) and seed color (Yellow vs. Green) at the same time. These experiments were designed to determine if different traits are inherited together as a "package" or if they are inherited separately. The mathematical outcome of these crosses provided the evidence for his third fundamental law.
Step 2: Detailed Explanation:
Let's trace the dihybrid cross mentioned in the question:
- Parental Generation (P): Mendel crossed a homozygous dominant plant (RRYY: Round and Yellow seeds) with a homozygous recessive plant (rryy: Wrinkled and Green seeds).
- \(F_{1}\) Generation: All the offspring were heterozygous (RrYy). Phenotypically, they were all Round and Yellow because Round (R) is dominant over Wrinkled (r), and Yellow (Y) is dominant over Green (y).
- \(F_{2}\) Generation: When the \(F_{1}\) plants were self-pollinated (\(RrYy \times RrYy\)), Mendel observed four different phenotypes in the following ratio:
1. 9 Round, Yellow (Parental phenotype)
2. 3 Round, Green (New recombinant phenotype)
3. 3 Wrinkled, Yellow (New recombinant phenotype)
4. 1 Wrinkled, Green (Parental phenotype)
The appearance of "recombinant" types (Round-Green and Wrinkled-Yellow) is the most significant observation. It proved that the Round trait doesn't always have to stay with the Yellow trait. The allele for seed shape segregated into the gametes completely independently of the allele for seed color.
Mathematically, the 9:3:3:1 ratio is simply the product of two independent 3:1 monohybrid ratios:
\[ (3 \text{ Round} : 1 \text{ Wrinkled}) \times (3 \text{ Yellow} : 1 \text{ Green}) = 9:3:3:1 \]
This led to the formulation of the Law of Independent Assortment, which states that when two pairs of traits are combined in a hybrid, the segregation of one pair of characters is independent of the other pair during gamete formation. This law is generally true for genes located on different chromosomes or very far apart on the same chromosome.
Step 3: Final Answer:
The 9:3:3:1 dihybrid ratio provides the classic experimental evidence for Mendel's Law of Independent Assortment.