Question

What will be the number of genotypes in ${{F}_{2}}$ generation if a character is controlled by 4 pairs of polygenes?
A) 16
B) 9
C) 25
D) 61
E) 81

Answer 1

Polygene is a group of genes that produces a specific phenotype or trait when expressed together but their individual effect is too small to be observed. This type of trait is called a polygenic trait.

Complete answer:
Let us first discuss the basic monohybrid cross between the parents. The P is the parental generation of a cross. ${{F}_{1}}$ is the first filial generation produced from a cross between parents.
${{F}_{2}}$is the second filial generation of individuals which arises as a result of interbreeding among ${{F}_{1}}$ generations.

Genotype is an organism’s set of heritable genes that can be passed from parents to offspring. The combination of alleles that an individual poses for a specific gene is their genotype.
Examples of genotype include:

hair/ eye colour
Shoe size
Height

Coming to the numerical part, A pair of genes (Aa) contains only one pair of heterozygotes. Second pair of genes (Bb) contains one pair of heterozygotes. Similarly, four pairs of genes will contain four heterozygotes.

Heterozygotes are represented as “N”
General formula for number of genotypes is: ${{3}^{n}}$
For four pair of polygenes, ${{3}^{n}}={{3}^{4}}$
$3\times 3\times 3\times 3=81$

Therefore, the number of genotypes would be 81 in four pairs of polygenes.Option “E” is the correct answer.

Note: There are three types of genotypes: homozygous dominant, homozygous recessive and heterozygous.
i) Homozygous dominant: Here both the alleles are the same and they are dominant.
ii) Homozygous recessive: Here both the allele are the same and they are both recessive.
iii) Heterozygous: Here both the alleles are different.