Genetics is the study of heredity and the variation of inherited characteristics. While the physical transmission of DNA occurs via chromosomes during meiosis and fertilization, the expression of those genes follows specific mathematical probabilities. The IGCSE 0654 Extended syllabus requires students to move beyond defining genetic terms and practically apply them using a visual model: the Punnett square.

Before constructing a Punnett square, one must understand the Law of Segregation.

• In a diploid organism, every trait is governed by two alleles (one from each parent).
• During meiosis, these alleles separate. Consequently, each haploid gamete (sperm or egg) carries only one allele for every gene.

A Punnett square is a grid used to calculate the expected genotypic and phenotypic ratios of offspring from a specific cross. Let us examine a monohybrid cross (involving a single trait) between two heterozygous parents.

Let T represent the dominant allele for Tallness.

Let t represent the recessive allele for Shortness.

The Cross: Tt (Tall) $\times$ Tt (Tall)

Step 1: Gamete Formation

Determine the alleles each parent can produce:

• Parent 1 (Tt) can produce sperm carrying T or t.
• Parent 2 (Tt) can produce eggs carrying T or t.

Step 2: The Grid

Place the gametes of one parent across the top and the other down the side.

Step 3: Analysis of Results

The four inner squares represent the statistical probability of the offspring's genotypes.

1. Genotypic Ratio: The ratio of the actual genetic makeup.

• 1 TT (Homozygous Dominant)
• 2 Tt (Heterozygous)
• 1 tt (Homozygous Recessive)
• Ratio = 1 : 2 : 1

1. Phenotypic Ratio: The ratio of the observable physical traits.

• Because T is dominant, both TT and Tt will be Tall (1 + 2 = 3).
• Only tt will be Short (1).
• Ratio = 3 : 1 (Tall to Short)

It is crucial to understand that a Punnett square does not dictate exact numbers; it dictates probability. A 3:1 ratio does not mean that out of four children, exactly three will be tall and one will be short. It means that for every single fertilization event, there is a 75% chance of the offspring being tall and a 25% chance of it being short. In small sample sizes, the actual results may deviate significantly from the expected ratio due to chance.

The Punnett square is an elegant tool that bridges the gap between the microscopic events of meiosis and macroscopic observable traits. By mapping out the possible combinations of haploid gametes, scientists and breeders can predict inheritance patterns, making it a foundational technique in both classical genetics and modern agriculture.