Genetics - A. V. Sivolob 2008

Formal Genetics: Patterns of Trait Inheritance
Mendel's Laws
Dihybrid and Polyhybrid Crosses

In his experiments, Mendel also analyzed the inheritance of two pairs of contrasting traits simultaneously: such crosses are called dihybrid crosses, and individuals heterozygous for two genes at the same time are termed dihybrids. Mendel crossed pea strains with yellow and smooth seeds with plants having green and wrinkled seeds. All first-generation hybrids produced yellow and smooth peas: the yellow color, as in the previous example, dominated over the green, and the smooth shape over the wrinkled one. Keeping A/a to designate the color alleles, let us denote the seed shape alleles as B (smooth) and b (wrinkled). Following self-pollination of the first-generation hybrids, a 9 : 3 : 3 : 1 phenotypic ratio was observed—it turned out that 9/16 of the progeny possessed two dominant traits simultaneously (yellow and smooth seeds), two groups of 3/16 exhibited only one of the two dominant traits (yellow and wrinkled, green and smooth), and 1/16 of the individuals displayed both recessive traits.

If we assume (as Mendel did) that the two genes inherit independently, dihybrid crosses can be considered as two independent Monohybrid Crosses. According to Mendel's second law, the color segregation In the second generation is 3/4A_ : 1/4aa, and the shape segregation is likewise 3/4B_ : 1/4bb. Using the well-known product rule of probability (the probability of two independent events occurring simultaneously is equal to the product of the probabilities of each of those events), we can calculate the aforementioned segregation ratio:

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Applying the product rule and knowing the segregation ratios in a monohybrid cross, one can calculate the proportions of both phenotypic and genotypic classes in polyhybrid crosses (Table 3.1).

Table 3.1. Selected parameters of segregation in polyhybrid crosses

Cross

Number of allele pairs by which parents differ

Number of gamete types produced by the heterozygote

Number of F2 phenotypic classes under complete dominance

Number of F2 genotypic classes

Proportion of F2 individuals homozygous for all genes

Monohybrid

1

2

2

3

1/4

Dihybrid

2

4

4

9

1/16

Trihybrid

3

8

8

27

1/64

Polyhybrid

n

2n

2n

3n

1/4n

Having analyzed the results of dihybrid crosses, Mendel formulated the postulate of independent assortment of traits, which subsequently became known as Mendel's third law.



Last update: 11/08/2026

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