Investigate the inheritance of patterns including but not limited to: predicting genotypic and phenotypic ratios using Punnett squares and probability rules

What this dot point is asking

NESA wants you to use Punnett squares and probability rules to predict the genotypic and phenotypic ratios of offspring from a given parental cross. This is a calculation skill, and Punnett squares appear in almost every HSC Biology exam.

The answer

Gregor Mendel's experiments on pea plants in the 1860s established three core laws of inheritance.

1. Law of Segregation. Each parent contributes one of two alleles for each gene to its offspring, randomly.
2. Law of Independent Assortment. Alleles for different genes segregate independently (assuming they are on different chromosomes).
3. Law of Dominance. When two different alleles are present, the dominant allele determines the phenotype; the recessive allele is masked.

Key terminology

• Gene: a section of DNA that codes for a trait.
• Allele: a version of a gene (e.g. A or a).
• Genotype: the alleles an individual has (e.g. AA, Aa, aa).
• Phenotype: the observed trait (e.g. tall, short).
• Homozygous: two identical alleles (AA or aa).
• Heterozygous: two different alleles (Aa).
• Dominant: the allele expressed when heterozygous (capital letter).
• Recessive: the allele masked when heterozygous (lowercase letter).

Setting up a Punnett square

A Punnett square predicts the possible genotypes and phenotypes of offspring from a given parental cross.

Step 1. Identify the parental genotypes.
Step 2. Write the possible gametes from each parent across the top and down the side.
Step 3. Fill in each cell with the combined genotype.
Step 4. Read off the genotypic ratio.
Step 5. Convert to phenotypic ratio using the dominance rules.

Standard monohybrid cross: Aa × Aa

• Genotypic ratio: 1 AA : 2 Aa : 1 aa
• Phenotypic ratio: 3 dominant : 1 recessive

This is the canonical 3:1 ratio Mendel observed.

Test cross: Aa × aa

• Genotypic ratio: 1 Aa : 1 aa
• Phenotypic ratio: 1 dominant : 1 recessive

A test cross with a homozygous recessive individual is used to determine whether a dominant-phenotype individual is homozygous (AA) or heterozygous (Aa).

Dihybrid cross: AaBb × AaBb

When tracking two independent genes, set up a 4 × 4 Punnett square with the four possible gametes from each parent (AB, Ab, aB, ab).

The classic phenotypic ratio is 9:3:3:1 (9 dominant for both : 3 dominant for A only : 3 dominant for B only : 1 recessive for both).

Probability rules

When tracking multiple events:

• Multiplication rule (independent events): P(A AND B) = P(A) × P(B). E.g. probability that two consecutive children are both affected = 1/4 × 1/4 = 1/16.
• Addition rule (mutually exclusive events): P(A OR B) = P(A) + P(B). E.g. probability that a child is either homozygous dominant OR heterozygous = 1/4 + 1/2 = 3/4.

Common Punnett-square traps

Wrong gametes. Each parent contributes only ONE allele per gene to each gamete. A heterozygous parent (Aa) produces TWO types of gametes (A and a), not four (AA, Aa, Aa, aa).

Failing to simplify ratios. 2:2 is the same as 1:1. 4:2 is the same as 2:1. Markers reward simplified ratios.

Confusing genotype and phenotype. Genotype = letters (AA, Aa, aa). Phenotype = trait (purple, white).

Independent probability for separate children. Each child is an independent event. The "probability the next child is affected" does not depend on the previous children. 1/4 each time.

Capitalisation matters. A means dominant, a means recessive. Be consistent. Markers often use unfamiliar letters (e.g. R/r for red, h/H for hairy); follow the question's convention.

In one sentence

Mendelian inheritance uses Punnett squares to predict offspring genotypes and phenotypes from given parental crosses, producing the canonical 3:1 ratio for a heterozygous monohybrid cross and 9:3:3:1 for a heterozygous dihybrid cross, with the multiplication rule applied for independent events across multiple offspring.