During self-fertilization or inbreeding of the F₁ dihybrids to produce an F2 generation, these male and female gametes can form maximum to dihybrid unions as shown in the Punnet’s Checker-board (Figure 7.3). These can be grouped into four kinds on the basis of phenotypic appearance. i.e. yellow round, yellow wrinkled, green round and green wrinkled in the ratio of 9:3:3:1 respectively. This is called the Phenotypic dihybrid ratio.

In Figure 7.3, the 16 squares of the checker board are serially numbered for convenience. The squares represent the 16 possible combinations of the gametes which might result. The genotypes and the phenotypes of the F₂ offspring are shown in the sixteen squares. A count of these squares shows the four kinds of phenotypes and their ratio in the F₂ generation.

In the actual dihybrid cross of the above type, Mendel obtained a total of 556 seeds in the F2 generation. The actual number of seeds of each type was as follows.

This gives approximately 9:3:3:1 ratio. Thus the actual results agree completely with the theoretical expectations.

Multiplication rule states that the probability of two or more independent events occurring together is the product of their individual probabilities.

In the above mentioned dihybrid cross, the gene for shape (round/wrinkled) and the gene for color (yellow/green) are present together but are sorted independently (law of independent assortment).

The multiplication rule applies to the probabilities of the phenotypes. For each gene, the monohybrid phenotypic ratio is 3:1 or ¾ : ¼

Thus, for the color gene the monohybrid phenotypic the ratio is 3 yellow : 1 green or ¾ yellow  : ¼ green. And, for the shape gene, it is 3 Round :1 wrinkled or ¾ Round : ¼ wrinkled.

Therefore, in the dihybrid cross, the total probability of the F_{1 phenotypes will be the product of the two monohybrid ratios.}

This is calculated as follows:

Gene for        Gene for        Probabilities
shape              color            of Phenotypes

Table of Contents

7.0 Introduction
7.1 Gregor Mendel
7.2 Mendel's Experiment on Sweet Pea
7.3 Terminology Used
7.4 Law of Dominance
7.5 Monohybrid Ratio
7.6 Law of Segregation
7.7 Dihybrid Ratio
7.8 Law of Independent Assortment
7.9 Test Cross or Back Cross
7.10 The Concept of "Factor"

Chapter 8

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