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How did Mendel derive the Law of Segregation and Independent Assortment from his experiments?

Answer
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Hint: George Mendel conducted his research on the common garden pea plant Pisum Sativum over a period of eight years. After That, he presented the results of his experiments together with “Mendel’s Law”. Mendel conducted the experiment on seven characters individually by crossing a variety carrying a particular trait of character.

Complete answer:
Mendel gave the laws of inheritance based on his extensive research conducted by him over a period of eight years.
Mendel’s Law of Inheritance:-
-Law of dominance
-Law of segregation
-Law of independent Assortment.

LAW OF SEGREGATION:-
-Mendel demonstrated that a hybrid between two different varieties possess both types of parental factor, which subsequently separate in the gametes.
-When Mendel crossed a pure tall pea plant with a pure dwarf plant, he found out all the plants in F1 generation were tall as the gene (i.e. factor) for tallness was dominant. It is a type of monohybrid cross as we are only observing one trait i.e. height of the plant.
-When F1 plants are crossed with each other the plants of the F2 generation were found to be both tall and dwarf in the ratio 3:1. Mendel concluded that the Dwarf factor or gene was not lost in F1 generation.
-He assumed that each trait is carried out by two factors or alleles like the tall plant has factors TT and the dwarf plant had factors Tt and these factors segregate during the time of gamete formation. He concluded that plants which are tall can be pure i.e. have the factors TT or can be impure Tt. And the dwarf plant has the factors tt. When any individual produces gamete, the allele segregates; so each gamete receives only one member of the pair of alleles and the paired condition is restored by random fusion during fertilization.

LAW OF INDEPENDENT ASSORTMENT:-
-Mendel extended his work by crossing two factors i.e. dihybrid cross.
-A cross between plants producing round and yellow seeds and plants producing wrinkled and green seeds. The F1 generation was all yellow and round seeded which suggests that yellow and round are the dominant characters. When F1 generation was self crossed, the gametes carried all the possible combinations of the unit factors.
The resulting progeny was as followed:
9/16 yellow round; 3/16 yellow wrinkled; 3/16 green round; 1/16 green wrinkled. The resultant ratio becomes 9:3:3:1 of mendel's dihybrid cross.

Note: George Mendel was born in 1822 in Czech republic. He performed his first set of hybridization with a pea plant in 1856. He continued his research throughout his life. . Unfortunately he died in 1884 without getting any recognition of his work. It was years later when three different researchers De Varies, Correns and Tschermark obtained results like Mendel. Mendel's Paper finally got recognition after 34 years in around 1900 A.D.