Law of Independent Assortment

According to this law, during the process of recombination and then separation, no allele influences the likelihood that another allele will be packaged in the same gamete.

Summarize the law of independent assortment

Mendel performed his dihybrid cross with homozygous dominant yellow round pea seeds and crossed them to homozygous recessive green wrinkled peas. The dominant seeds were dominant for both color and shape, as yellow is dominant to green, and round is dominant over wrinkled. Their genotypes?

(Parental generation 1) P1: Dominant for color and shape: YYRR.

(Parental generation 2) P2: Recessive for color and shape: yyrr.

From the outcome of this cross, Mendel observed that all the plants produced from this cross, called the F1 generation, were yellow and round. We can deduce their genotypes ourselves via combinations of possible gametes from their parents.

As we know, one allele per gene is packaged into a gamete. So the gametes produced by P1 and P2 must have one color allele and one shape allele in their gametes. Because both peas are homozygotes, they only have the possibility of distributing one type of gamete to their offspring: YR for the yellow, round peas, and yr for the green wrinkled peas.

Thus every cross of P1 x P2 must be the following: YR x yr

This gives the following genotype in every F1: YyRr.

F1 plants are considered dihybrids. Di - means two, Hybrid - here means heterozygous. These plants are heterozygous for two different genes.

Dihybrid cross: F1 x F1 - an example of the law of independent assortment

Here's where it gets interesting. Mendel took two F1 plants and crossed them to each other. This is called a dihybrid cross, when two dihybrids for identical genes are crossed together.

Mendel saw that the P1 x P2 cross had only led to one phenotype, a yellow round pea (F1), but he had the hypothesis that this F1 x F1 cross would lead to four distinct phenotypes! And if this hypothesis held true, it would support his law of independent assortment. Let's see how.

F1 x F1 = YyRr x YyRr

There are four possible gametes from F1 parents, considering one allele for color and one allele for shape must be present per gamete:

YR, Yr, yR, yr.

We can make from these a massive Punnett square. Because we're examining two different genes, the Punnett square has 16 boxes, instead of the normal 4. We can see the possible genotypic outcome from each cross.

Figure 2. Dihybrid cross for pea color and shape.

The Punnett square shows us the genotype, and thus the phenotype. Just as Mendel suspected, there were four different phenotypes: 9 yellow and round, 3 green and round, 3 yellow and wrinkled, and 1 green and wrinkled.

The ratio of these phenotypes is 9:3:3:1, which is a classic ratio for a dihybrid cross. 9/16 with dominant phenotype for traits A and B, 3/16 with dominant for trait A and recessive for trait B, 3/16 recessive for trait A and dominant for trait B, and 1/16 recessive for both traits. The genotypes we see from the Punnett square, and the ratio of phenotypes they lead to, are both indicative of Mendel's law of independent assortment, and here's how.

If every trait assorts independently to find the probability of a dihybrid phenotype, we should simply be able to multiple the probabilities of two phenotypes of different traits. To simplify this, let's use an example: The probability of a round, green pea should be the probability of a green pea X the probability of a round pea.

To determine the probability of obtaining a green pea, we can do an imaginary monohybrid cross (Fig. 3): Cross two homozygotes for different colors to see the color and proportion of colors in their offspring, first with P1 x P2 = F1:

YY x yy = Yy.

Then, we can follow this up with an F1 x F1 cross, to see the outcome of the F2 generation:

Figure 3. Monohybrid cross outcomes.

Yy and yY are the same, so we get the following proportions: 1/4 YY, 2/4 Yy (which = 1/2 Yy) and 1/4 yy. This is the monohybrid genotypic cross ratio: 1:2:1

To have a yellow phenotype, we can have the YY genotype OR the Yy genotype. Thus, the probability of yellow phenotype is Pr (YY) + Pr (Yy). This is the sum rule in genetics; whenever you see the word OR, combine these probabilities by addition.

Pr (YY) + Pr (Yy) = 1/4 + 2/4 = 3/4. Probability of a yellow pea is 3/4, and probability of obtaining the only other color, green is 1/4 (1 - 3/4).

Figure 4. Monohybrid crosses for pea shape and color.

We can go through the same process for pea shape. From the monohybrid cross ratio, we can expect that from the cross Rr x Rr, we will have 1/4 RR, 1/2 Rr, and 1/4 rr offspring.

Thus the probability of obtaining a round pea is Pr (round pea) = Pr (RR) + Pr (Rr) = 1/4 + 1/2 = 3/4.

Now back to our original hypothesis. If the law of independent assortment is true, we should be able to find, by probabilities, the same percentage of green, round peas as Mendel found from his physical experiments. If the alleles from these different genes for color and shape assort independently, they should mix and match evenly to allow for predictable mathematical proportions.

How do we determine the probability of a pea that is BOTH green AND round? This requires the product rule, a rule in genetics that states to find the probability of two things occurring in the same organism at the same time, you must multiply the two probabilities together. Thus:

Pr (round and green) = Pr (round) x Pr (green) = 3/4 x 1/4 = 3/16.

What proportion of the peas in Mendel's dihybrid cross were green and round? 3 out of 16! Thus the law of independent assortment is supported.

The difference between the law of segregation and the law of independent assortment

The law of segregation and the law of independent assortment apply in similar instances, for example, during gametogenesis, but they are not the same thing. You could say that the law of independent assortment fleshes out the law of segregation.

The law of segregation explains how alleles are packaged into different gametes, and the law of independent assortment states that they are packaged irrespective of other alleles on other genes.

The law of segregation looks at one allele with respect to the other alleles of that gene. Independent assortment, on the other hand, looks at one allele with respect to other alleles on other genes.

Gene linkage: An exception to the law of independent assortment

Some alleles on different chromosomes do not sort independently, irrespective of which other alleles are packaged with them. This is an example of gene linkage, when two genes tend to be present in the same gametes or organisms more than what should occur by random chance (which are the probabilities we see in Punnett squares).

Usually, gene linkage occurs when two genes are located very close to one another on a chromosome. In fact, the closer two genes are, the more likely they are to be linked. This is because, during gametogenesis, it is harder for recombination to occur between two genes with close loci. So, there's reduced breakage and reassortment between those two genes, which leads to a higher chance that they are inherited together in the same gametes. This increased chance is gene linkage.