Topic Content:
- Mendel’s Second Law (Law of Independent Assortment)
- Describe a Dihybrid Cross Example in Pea Plants
- Summary
What is Mendel’s Second Law?
Mendel’s Second Law – Law of Independent Assortment – states that when more than one pair of traits are involved in sexual reproduction for the formation of an offspring, each pair segregate independently from the other (just as a pair of homologous chromosomes separate) only one entering each gamete.
The segregation of one gene pair occurs independently of any other gene parent. In other words the alleles of two (or more) different genes get sorted into gametes independently of one another.
Dihybrid Cross Example in Pea Plants:
The parent genotypes in a dihybrid cross are both heterozygous for two genes. Let’s take a look at an example in pea plants;
Gene 1:
- The first Gene is for seed colour and has two alleles, a dominant allele that results in a yellow seed colour (Y) and a recessive allele that results in a green pea colour (y).
- The homozygous dominant (YY) and heterozygote genotypes (Yy) result in yellow seeds.
- The homozygous recessive genotype (yy) results in green seeds.
Gene 2:
- The second gene is for seed shape and has two alleles, a dominant allele that results in a round seed shape (R) and a recessive allele that results in a wrinkled seed shape (r).
- The homozygous dominant (RR) and heterozygote genotypes (Rr) result in a round shape.
- The homozygous recessive genotype (rr) results in a wrinkled shape.
This is illustrated below:

Mendel first crossed pure-bred pea plants having round and yellow seeds (RRYY) with pure-bred pea plants having wrinkled and green seeds (rryy) and found that only round yellow seeds (RrYy) were produced in the F1 generation.
In a dihybrid cross, the gametes can only receive one of each allele (or one of each letter). The parent with round yellow seeds can only form two types of gametes, RY and RY, while the parent with wrinkled green seeds can only form two types of gametes, ry and ry, as seen below.
If for example the genotye of a parent is RRYy, the two possible gametes will be RY and Ry, it can never be RR or Yy.

We can then draw a punnet square to understand how they can be fused and produce offspring. Because each parent produces 2 gametes there are 2 columns and 2 rows making 4 squares in the Punnett square.

As you can see the F1 generation will all have round and yellow seeds (RrYy)
They will have round and yellow seeds because:
- the yellow-seed allele is dominant (Y) and the green-seed allele is recessive (y).
- the round shape allele is dominant (R) and the wrinkled shape allele is recessive (r).
Next, the F1 Generation were self-pollinated (RrYy × RrYy) to produce the F2 offspring.
Let’s look at the possible gametes of only one F1 parent. Remember, in a dihybrid cross, the gametes can only receive one of each letter (or one of each allele) as shown below:

Therefore, after crossing RrYy × RrYy, the possible gametes for Parent 1 is 4 combinations, RY, Ry, rY and ry and for Parent 2 it is also 4 possible combinations RY, Ry, rY and ry.
We can then set up a Punnett square with this information. Because each parent produces 4 gametes there are 4 columns and 4 rows making 16 squares in the Punnett square.

The phenotypic ratio of the dihybrid cross is significant which is 9 : 3 : 3 : 1 as follows:
- 9 Round and Yellow (1, 2, 3, 4, 5, 7, 9, 10, 13)
- 3 Round and green (6, 8, 14)
- 3 wrinkled and Yellow (11, 12, 15)
- 1 wrinkled and green (16)
i.e. \(\frac{9}{16}\) Round and Yellow, \(\frac{3}{16}\) Round and green
\(\frac{3}{16}\) wrinkled and Yellow, \(\frac{1}{16}\) wrinkled and green

Summary:

Mendel’s law of independent assortment states that each character behaves as a separate unit and is inherited independently of the other.