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Question
How do Mendel's experiment show that traits are inherited independently?
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Solution 1
Mendel carried out dihybrid crosses by crossing two pea plants differing in contrasting traits of two characters. For example, he crossed a pea plant having yellow colour and round seed characters with another pea plant bearing green colour and wrinkled seed characters. In the F2 generation, he obtained pea plants with two parental and two recombinant phenotypes as yellow round and green wrinkled (parental) and yellow wrinkled and green round (recombinant). This indicated that traits separated from their original parental combinations and got inherited independently.

Solution 2
Mendel crossed pure-breeding tall plants with round seeds and pure-breeding short plants with wrinkled seeds. The plants of the F1 generation were all tall with round seeds, indicating that the traits of tallness and round seeds were dominant. Self-breeding of F1 yielded plants with characters of 9 tall round seeded, 3 tall wrinkled seeded, 3 short round seeded, and 1 short wrinkled seeded. Tall wrinkled seeded and short round seeded plants are new combinations which can develop only when the traits are inherited independently.
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