State the law of independent assortment. Write schematic representation of dihybrid cross.

Explanation

Mendel proposed his second law namely the law of independent assortment this law states that the inheritance of genes of each pair in a dihybrid during gamete formation is independent of the other
When two pairs of traits are combined in a hybrid, segregation of one pair of characters is independent of the other. Law of independent assortment can be studied by means of dihybrid cross (eg) between pure breeding pea plants having yellow round seed (YYRR) and pure breeding pea plant having green wrinkled seed (yyrr). the plants of first filial or `F_(1)` generation have all yellow and round seeds (YrRr). At the time of gamete formation according to the law of segregation each parent produce one gamete YR and yr. the `F_(1)` generation shows one contrasting dominant character.
On self - breeding, the resultant second filial or `F_(2)` generation show four types of gametes, `YR, Yr, yR, yr`. Fusion occurs between any two of these gametes, thus 16 combination were possible in a `9: 3: 3: 1` phenotypic ratio.
The genotypic ratio shall be `1:2: 2:4:1:2:1 : 2: 1.` This experiment clearly shows that the genes for the seed characters are assorted independently of each other and the presence of one factor does not contaminate the other.
The dihybrid cross can be schematically represented as follows :


`{:("yellow round",:,"yellow wrinkled",:,"green round",:,"green wrinkled"),(" 9",:," 3",:," 3",:," 1"):}`
Thus, the phenotypic ratio of the dihybird cross is `9:3:3:1`. The genotypic dihybrid cross is `9:3:3:1`. The genotypic ratio of this `F_(2)` generation ratio of this `F_(2)` generation can be represented as follows.
`{:("Yellow"),("Round 9"):}{:("YYRR (homozygous yellow, homozygous round) = 1"),("YYRr (homozygous yellow, heterozygous round) = 2"),("YyRR (heterozygous yellow, homozygous round) = 2"),("YyRr (heterozygous yellow, heterozygous round) = 4"):}`
`{:("Yellow"),("Wrinkled 3"):}{:("YYrr (homozygous yellow, wrinkled) = 1"),("Yyrr (heterozygous yellow, wrinkled) = 2"):}`
`{:("Green"),("Round 3"):}{:("yyRR (green, homozygous round) = 1"),("yyRr (green, heterozygous round) = 2"):}`
`{:("Green"),("Wrinkled 1"):}{:(),("yyrr (green, wrinkled) = 1"):}`
Therefore, the genotypic ratio is
`{:(ul(1 : 2 : 2 : 4),:," "ul(1 : 2),:," "ul(1 : 2),:," "ul(1)),(" "darr,:," "darr,:," "darr,:," "darr),(" 9",:," 3",:," 3",:," 1"):}`