Question

What indication do we get by the reappearance of dwarf plants in F$_2$ generation?

Answer 1

According to the law of segregation, the genes segregate separately from each other. Moreover, the filial 2 generation or the F$_2$ generation is the second generation of progeny. Also, the recessive gene does not express itself in the presence of a dominant gene.

Complete answer: Let us look at a monohybrid cross.
Consider two monohybrid homozygous parents. The dominant parent would be with the genotype $AA$ and the recessive parent would have the genotype $aa$. On performing the cross between these two parents the Filial 1 generation would be as follows –

Now from the above cross, it can be inferred that the monohybrid parents segregate into the homozygous gametes. These gametes then fuse together to form the heterozygous offspring or the Filial 1 generation. Hence, from the above cross, we can infer that all the offspring produced are Heterozygous $Aa$. Now to obtain the Filial 2 generation, a cross between any two plants of the Filial 1 generation is carried out. The cross will be as follows –

From the above cross, we can see that along with the Heterozygous offspring, the homozygous offspring also appear. It is interesting to note that the recessive offspring has appeared again. This means that the reappearance of dwarf plants in F$_2$ generation has occurred. This is because of the law of segregation and the law of independent assortment.
According to the law of segregation, the gametes segregate, separately, irrespective of their type. This means that each allele in a monohybrid cross is made up of two types of genes. These genes segregate separately and then form two gametes from a single allele. The male and female gametes that fuse together to form the zygote. In the case of the first filial generation, all the gametes formed are heterozygous. So, all of them express the dominant trait. This is because of the law of Independent assortment which states that the recessive gene can only express itself when it is independent or in homozygous form. In the case of the heterozygous condition, the expression is as per the dominant allele. Now in the filial 2 generation, due to the segregation of gametes, two homozygous recessive genes fuse and form the zygote. Since, both the genes are recessive so the expression is that of the recessive gene and a dwarf plant reappears.

Note: In a monohybrid cross, $25\%$ of the offspring produced are dwarf plants. This is because the probability of a dwarf plant is $\dfrac{1}{4}$. This can be seen from the cross of the Filial 2 generation. Out of the 4 plants produced from the two alleles of the parents, 1 offspring is dwarf. So, this corresponds to the $25\%$ of the total population of offspring.