How do Mendel’s experiment show that traits are inherited independently?

Mendel demonstrated that traits are inherited independently by performing a dihybrid cross, in which he crossed pea plants differing in two contrasting characteristics: plant height (tall vs. short) and seed shape (round vs. wrinkled).

1. F1 Generation:

• He crossed a pure-breeding tall plant with round seeds ($TTRR$) and a short plant with wrinkled seeds ($ttrr$).
• The resulting $F_1$ progeny were all tall with round seeds ($TtRr$). This showed that tallness ($T$) and round shape ($R$) are dominant traits.

1. F2 Generation:

• When the $F_1$ plants were self-pollinated to produce the $F_2$ generation, they did not just produce the parental combinations. Instead, they produced four distinct phenotypes in a ratio of approximately $9:3:3:1$:
• Parental combinations: Tall-Round ($9$) and Short-Wrinkled ($1$)
• New combinations (Recombinants): Tall-Wrinkled ($3$) and Short-Round ($3$)

1. Conclusion:

• The appearance of completely new combinations (such as tall plants with wrinkled seeds and short plants with round seeds) proves that the trait for plant height and the trait for seed shape are inherited completely independently of each other. The factors (genes) controlling these traits assort independently during gamete formation.