# 5.3.1 Law of Independent Assortment

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 observations 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 law 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’.

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 F1 RrYy plant. Consider the segregation of one pair of genes R and r. Fifty per cent of the gametes have the gene R and the other 50 per cent 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 per cent R and 50 per cent r is independent from the segregation of 50 per cent Y and 50 per cent y. Therefore, 50 per cent of the r bearing gamete has Y and the other 50 per cent has y. Similarly, 50 per cent of the R bearing gamete has Y and the other 50 per cent has y. Thus there are four genotypes of gametes (four types of pollen and four types of eggs).

The four types are RY, Ry, rY and ry each with a frequency of 25 per cent or ¼th of the total gametes 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 F2 plants.

Although there are 16 squares how many different types of genotypes and phenotypes are formed? Note them down in the format given. Can you, using the Punnett square data work out the genotypic ratio at the F2 stage and fill in the format given? Is the genotypic ratio also 9:3:3:1?