Mendel made crosses between pea plants differing in two characters such as texture of seed and colour of cotyledons. Such a cross in which inheritance of two characters is considered is called a dihybrid cross.
First of all Mendel crossed a pea plant that was breeding true for round seeds with a plant that bred true for wrinkled seeds. The Fl indicated that roundness was dominant over wrinkled texture of seedcoat. Similarly, by another cross he could determine that yellow colour of cotyledons was dominant over green. He now used as male parent a plant which bred true for both round and yellow characters and crossed it with a female parent that bred true for wrinkled green. As expected from the results of his single crosses, the Fl was round yellow.
When he selfed the F1 hybrids, the F2 progeny showed all the parental characters in different combinations with each other. Thus plants with round yellow seeds, round green seeds, wrinkled yellow seeds and wrinkled green seeds all appeared in the ratio 9:3:3:1. Reciprocal cross in which the female parent was round yellow and male parent wrinkled green gave the same results.
Mendel applied the principle of a monohybrid cross and argued that in the dihybrid cross the true breeding round yellow parent must be homozygous RRYY, and the wrinkled green parent rryy. Since each character is determined be two factors, in a dihybrid cross there must be four factors present in each parent. Likewise the Fl hybrid must be RrYy. But the question remained as to how did the four different combinations of parental phenotypes appear in the progeny? Mendel argued that the pair of factors for roundness must be behaving independently of the pair of factors for yellow colour of seeds. In other words, one factor for a character must be passing independently of a factor for another character. Thus in the F1 hybrids, R and r pass into different gametes. Now the probability of an R gamete formed is one-half, and of r gamete also one-half. Similar probabilities exist for Y and y gametes. It follows that the probability that R and Y should go to the same gamete is one-fourth, as also of R and y, r and Y, and r and y. Therefore, gametes containing factors RY, Ry, rY and ry should form in equal proportions.
The Fl hybrid producing the four types of gametes mentioned above was selfed. The results expected in the F2 progeny can be predicted by making a checkerboard or a Punnett Square. Gametes produced by one parent are plotted on top of the checkerboard, and gametes
of the other parent on the side. The sixteen squares of the checkerboard are filled up by making various possible combinations of male and female gametes during fertilisation. The phenotypes read out from the checkerboard indicate a 9 : 3 : 3 : 1 ratio exactly as observed by Mendel.
As in the case of the monohybrid cross, Mendel verified his results by performing the test cross. He crossed the F1 hybrid heterozygous for both characters with a double recessive parent (r/7,y) which should produce only one type of gamete ry. The uniformity in the gametes of the recessive parent determines the differences in the types of gametes produced by the heterozygous parent. Now the hybrid RrYy produces gametes carrying RY, Ry, rY and ry with equal frequency. It follows that during fertilisation if all these four types of gametes unite with ry gamete of the recessive parent, the resulting progeny should show all the four combinations of characters also in equal proportions. Indeed, Mendel observed the test cross progeny to consist of Round Yellow, Round Green, Wrinkled Yellow and Wrinkled Green plants in the ratio 1:1:1:1.
From the results of his dihybrid crosses, Mendel realised the following facts. At the time of gamete formation the segregation of alleles R and r into separate gametes occurs independently of the segregation of alleles Y and y. That is why the resulting gametes contain all possible combinations of these alleles, i.e. RY, Ry, rY, ry. In this way Mendel proved that when two characters are considered in a cross, there is independent assortment of genes for each character, and this became the Law of Independent Assortment.