Punnett Square

Punnett Square:

• In a genetic cross the genotypes and phenotypes of offspring, resulting from combining gametes during fertilization can be easily understood with the help of a diagram called Punnett’s Square.
• It was developed by a British geneticist, Reginald C. Punnett.
• It is a graphical representation to calculate the probability of all possible genotypes of offspring in a genetic cross.
• The possible gametes are written on two sides, usually the top row and left columns.
• All possible combinations are represented in boxes below in the squares, which generates a square output form.
• The Punnett Square shows the parental tall TT (male) and dwarf tt (female) plants, the gametes produced by them, and the F₁ Tt progeny. The F₁ plants of genotype Tt are self-pollinated.
• The symbols ♀ and ♂ are used to denote the female (eggs) and male (pollen) of the F₁ generation, respectively.
• The F₁ plant of the genotype Tt when self-pollinated, produces gametes of the genotype T and t in equal proportion.
  

  A Punnett square used to understand a typical monohybrid cross conducted by Mendel between true-breeding tall plants and true-breeding dwarf plants

• From Punnett Square, it can be observed that:
  a) 1/4^th of the random fertilisations lead to TT,
  b) 1/2 of the random fertilisations lead to Tt, and
  3) 1/4^th of the random fertilisations lead to tt.
• Though the F₁ has a genotype of Tt, the phenotypic character seen is ‘tall’.
• At F₂, 3/4^th of the plants are tall, where some of them are TT while others are Tt. Externally it is not possible to distinguish between the plants with the genotypes TT and Tt.
• Hence, within the genopytic pair Tt, only one character ‘T’ tall is expressed. Hence the character T or ‘tall’ is said to dominate over the other allele t or ‘dwarf’ character which is a recessive character.
• It is thus due to this dominance of one character over the other that all the F₁ are tall (though the genotype is Tt) and in the F₂ 3/4^th of the plants are tall (though genotypically 1/2 are Tt and only 1/4^th are TT).
  
• 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 the equal frequency of `1/2`. The expression is expanded as given below:
  `(1/2 "T" + 1/2"t")^2 = (1/2"T" + 1/2"t") × (1/2"T" + 1/2"t") = 1/4 "TT" + 1/2 "Tt" + 1/4 "tt"`
• Mendel self-pollinated F₂ plants and he found that F₂ plants continued to generate dwarf plants in F₃ and f₄ generations.