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

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In a dihybrid cross, Mendel selected two pairs of contrasting characters of pea plants and they were crossed. The resultant cross showed the segregation of the traits of both the parents which indicated that the traits were inherited independently. 

Explanation: Mendel selected pea plants (Pisum sativum) with dihybrid seed characteristics such as yellow coloured, round seeds and green coloured, wrinkled seeds. The plants with yellow coloured round seeds were crossed with green coloured wrinkled seeds. 

After the cross, in f2 generation, the offspring obtained were with both the parental traits and with two recombinant phenotypes such as yellow round and green wrinkled (the parental trait) and another recombinant phenotype with green round and yellow wrinkled. Thus, in the f2 generation, all the characters were inherited and the characters were round yellow, round green, wrinkled yellow and wrinkled green. The obtained traits or characteristics of the phenotypes obtained in the f2 generations indicates original parental combinations are separated which in the process gets inherited independently by the offspring in the in the next generations. 

Diagrammatic illustration:

Round yellow : 9 

Round green : 3 

Wrinkled yellow : 3 

Wrinkled green : 1

Therefore, phenotypic ratio = 9:3:3:1

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