Question
Explain the inheritance of one gene by Punnett Square ?
✓
Answer
$\rightarrow$ Punnett Squre:
$\rightarrow$ The production of gametes by the parents, the formation of the zygotes, the $F,$ and $F_2$ plants can be understood from a diagram called Punnett Square $($By Reginald $C.$ Punnett).
$\rightarrow$ It is a graphical representation to calculate the probability of all possible genotypes of offspring in a genetic cross.
$\rightarrow$ The Punnett Square shows,
$TT$ $\rightarrow$ Tall $($Male$)$ $(♂)$
$tt$ $\rightarrow$ Dwarf $($Female$)$ $(♀)$
Produced Gametes $(T, t)$
$Tt\rightarrow$ $F$ Progeny $($self$-$pollinated$)$
$\rightarrow$ The $F_1$ plant of the genotype $Tt$ when self$-$ pollinated, produces gametes of the genotype $T$ and $t$ in equal proportion.
$\rightarrow$ When fertilisation takes place, the pollen grains of genotype $T$ have a $50$ per cent chance to pollinate eggs of the genotype $T,$ as well as of genotype $t.$
$\rightarrow$ Also pollen grains of genotype $t$ have a $50$ per cent chance of pollinating eggs of genotype $T,$ as well as of genotype $t.$ As a result of random fertilisation, the resultant zygotes can be of the genotypes $TT, Tt$ or $ tt.$
$\rightarrow$ From the Punnett square it is easily seen that $1/4^{th}$ of the random fertilisations lead to $TT, 1/2$ lead to $Tt $ and $1/4^{th}$ to $tt.$
$\rightarrow$ Though the $F_1$ have a genotype of $Tt,$ but the phenotypic character seen is 'tail'.
$\rightarrow$ At $F_2$, $3/4$ of the plants are tall, where some of them are $TT$ while others are $Tt.$
$\rightarrow$ Externally it is not possible to distinguish between the plants with the genotypes $TT$ and $Tt.$ Hence, within the genotypic pair $Tt$ only
one character $' \ T\ '$ tall is expressed.
$\rightarrow$ Hence the character $T$ or 'tall' is said to dominate over the other allele or 'dwarf character.
$\rightarrow$ It is thus due to this dominance of one character over the other that all the $F_1$ are tall $($though the genotype is $Tt)$ and in the $F_2$ $3/4$ of the plants are tall $($though genotypically $1/2$ are $Tt$ and only $1/4th$ are $TT).$
$\rightarrow$ The $ 1/4 1/2 1/4$ ratio of $TT \ Tt: tt$ is mathematically condensable to the form of the binomial expression $(ax + by)^2,$ that has the gametes bearing genes $T$ or $t$ in equal frequency of $1/2.$ The expression is expanded as given below:
$\rightarrow$ $(1/2T + 1/2t)^2= (1/2T + 1/2t) \times (1/2T + 1/2t)$
$= 1/4 \ TT + 1/2 \ Tt + 1/4 \ tt$
$\rightarrow$ Mendel self$-$pollinated the $F_2$ plants and found that dwarf $F_2$ plants continued to generate dwarf plants in $F_3$ and $F_4$ generations. He concluded that the genotype of the dwarfs was homozygous $- tt.$
$\rightarrow$ The production of gametes by the parents, the formation of the zygotes, the $F,$ and $F_2$ plants can be understood from a diagram called Punnett Square $($By Reginald $C.$ Punnett).
$\rightarrow$ It is a graphical representation to calculate the probability of all possible genotypes of offspring in a genetic cross.
$\rightarrow$ The Punnett Square shows,
$TT$ $\rightarrow$ Tall $($Male$)$ $(♂)$
$tt$ $\rightarrow$ Dwarf $($Female$)$ $(♀)$
Produced Gametes $(T, t)$
$Tt\rightarrow$ $F$ Progeny $($self$-$pollinated$)$
$\rightarrow$ The $F_1$ plant of the genotype $Tt$ when self$-$ pollinated, produces gametes of the genotype $T$ and $t$ in equal proportion.
$\rightarrow$ When fertilisation takes place, the pollen grains of genotype $T$ have a $50$ per cent chance to pollinate eggs of the genotype $T,$ as well as of genotype $t.$
$\rightarrow$ Also pollen grains of genotype $t$ have a $50$ per cent chance of pollinating eggs of genotype $T,$ as well as of genotype $t.$ As a result of random fertilisation, the resultant zygotes can be of the genotypes $TT, Tt$ or $ tt.$
$\rightarrow$ From the Punnett square it is easily seen that $1/4^{th}$ of the random fertilisations lead to $TT, 1/2$ lead to $Tt $ and $1/4^{th}$ to $tt.$
$\rightarrow$ Though the $F_1$ have a genotype of $Tt,$ but the phenotypic character seen is 'tail'.
$\rightarrow$ At $F_2$, $3/4$ of the plants are tall, where some of them are $TT$ while others are $Tt.$
$\rightarrow$ Externally it is not possible to distinguish between the plants with the genotypes $TT$ and $Tt.$ Hence, within the genotypic pair $Tt$ only
one character $' \ T\ '$ tall is expressed.
$\rightarrow$ Hence the character $T$ or 'tall' is said to dominate over the other allele or 'dwarf character.
$\rightarrow$ It is thus due to this dominance of one character over the other that all the $F_1$ are tall $($though the genotype is $Tt)$ and in the $F_2$ $3/4$ of the plants are tall $($though genotypically $1/2$ are $Tt$ and only $1/4th$ are $TT).$
| Genotypic ratio | $3 : 1 ($Tall: Dwarf$)$ |
| Phenotypic ratio | $1:2:1 \ (TT: Tt: tt)$ |
$\rightarrow$ $(1/2T + 1/2t)^2= (1/2T + 1/2t) \times (1/2T + 1/2t)$
$= 1/4 \ TT + 1/2 \ Tt + 1/4 \ tt$
$\rightarrow$ Mendel self$-$pollinated the $F_2$ plants and found that dwarf $F_2$ plants continued to generate dwarf plants in $F_3$ and $F_4$ generations. He concluded that the genotype of the dwarfs was homozygous $- tt.$
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