State the law Independent Assortment and how it is derived ?

Explanation

Law of Independent Assortment states that when two pairs of traits are combined in a hybrid, segregation of one pair of characters is independent of the other pair of characters at the time of gamete formation.
= It also get randomly rearranged in the offsprings producing both parental and new combinations of characters.
= In the dihybrid cross, the phenotypes round yellow, wrinkled yellow, round green and wrinkled, green appeared in the ratio 9:3:3 : 1.
= Such a ratio was observed for several pairs of characters that Mendel studied.
= The ratio of 9 : 3:3:1 can be derived as a combination series of 3 yellow, 1 green with 3 round : 1 wrinkled.
= This derivation can be written as follows: (3 round : 1 wrinkled] [3 yellow : 1 green) = 9 round, yellow : 3 wrinkled yellow, 3 round Green : 1 wrinkled green.
= Based upon such observation on dihybrid crosses (crosses between plants differing in two traits) Mendel proposed a second set of generalisations that we call Mendel.s law of Independent Assortment.
= The Punnett Square can be effectively used to understand the independent segregation of the two pairs of genes during meiosis and the production of eggs and pollen in the F RrYy plant.
= Consider the segregation of one pair of genes R and r.
= Fifty percent of the gametes have the gene .R. and the other 50% have .r..
= Now besides each gamete having either R or r it should also have the allele Y or y.
= The important thing to remember here is that segregation of 50% R and 50% r is independent from the segregation of 50% Y and 50% y.
= Therefore, 50% of the r bearing gametes has Y and the other 50% has .y.
= Similarly 50% of the .R. bearing gametes has Y and the other 50% has .y .
= Thus there are four genotypes of gametes (four types of pollen and four types of eggs.
= The four genotypes of gametes are RY, Ry, ry, ry each with a frequency of 25% or 1/4th of the total gamete produced.
= When you write down the four types of eggs and pollen on the two sides of a Punnett Square it is very easy to derive the composition of the zygotes that give rise to the F, plants.