Apply Mendel's laws of segregation and independent assortment to predict the outcomes of monohybrid and dihybrid crosses using Punnett squares, and explain the purpose of a test cross

What this dot point is asking

QCAA wants you to use Punnett squares to predict the outcomes of monohybrid and dihybrid crosses, state and apply Mendel's two laws, and design and interpret a test cross. Genetics calculation problems are core marks every year.

The answer

Gregor Mendel worked out the basic rules of inheritance in pea plants in the 1860s without knowing about DNA, chromosomes or genes. His laws still describe single-gene inheritance accurately and form the foundation of every genetics problem.

Vocabulary

• Gene. A heritable factor (a stretch of DNA) that codes for a particular trait.
• Allele. An alternative form of a gene (for example T for tall, t for short).
• Genotype. The combination of alleles an individual carries (TT, Tt or tt).
• Phenotype. The observable trait (tall or short).
• Homozygous. Both alleles the same (TT or tt).
• Heterozygous. Two different alleles (Tt).
• Dominant. An allele that is expressed in the phenotype of a heterozygote. Written with a capital letter.
• Recessive. An allele whose phenotype is only seen in the homozygote. Written with a lowercase letter.

Mendel's laws

Law of segregation. Each individual has two alleles for each gene; the two alleles separate during meiosis so that each gamete carries only one. This is the chromosomal behaviour of homologous chromosomes separating in anaphase I.

Law of independent assortment. Alleles for different genes segregate into gametes independently of one another, provided the genes are on different chromosomes (or far enough apart on the same chromosome to recombine freely). This is the chromosomal behaviour of independent metaphase I alignment.

Monohybrid crosses

A monohybrid cross follows one gene with two alleles.

Heterozygous x heterozygous. Tt x Tt.

Genotype ratio: 1 TT to 2 Tt to 1 tt.
Phenotype ratio: 3 tall to 1 short.

Heterozygous x homozygous recessive. Tt x tt.

Phenotype ratio: 1 tall to 1 short.

Dihybrid crosses

A dihybrid cross follows two genes simultaneously. The dihybrid ratio is the product of the two monohybrid ratios.

Heterozygous at both loci x heterozygous at both loci. TtYy x TtYy.

Each parent produces four gamete types in equal proportions: TY, Ty, tY, ty. A 4 by 4 Punnett square gives 16 boxes, and the phenotype ratio is:

• 9 with both dominant traits (TY, tall yellow)
• 3 with one dominant and one recessive (T_yy, tall green)
• 3 with the other one dominant and one recessive (ttY_, short yellow)
• 1 with both recessive (ttyy, short green)

The classic 9:3:3:1 ratio.

The mathematical shortcut: probability of being tall (3/4) times probability of being yellow (3/4) = 9/16 tall yellow, and so on. Use the product rule when the genes are independent and the sum rule when combining mutually exclusive outcomes.

The test cross

When an organism shows the dominant phenotype, its genotype could be either homozygous dominant (TT) or heterozygous (Tt). A test cross distinguishes them.

Method. Cross the unknown with a homozygous recessive individual (tt). The recessive partner contributes only t gametes, so any t in the offspring must come from the unknown parent.

Possible outcomes.

• If the unknown is TT: all offspring are Tt, and all show the dominant phenotype.
• If the unknown is Tt: half the offspring are Tt (dominant) and half are tt (recessive). A roughly 1:1 phenotype ratio.

A single recessive offspring is enough to conclude the unknown is heterozygous. The more offspring observed, the more confident you can be that an apparent "all dominant" result is genuine.

Test crosses are still used in plant and animal breeding to confirm whether a desirable individual is homozygous (will breed true) or heterozygous.

Pedigree and probability work

A Punnett square gives probabilities for each offspring. For two independent events use the product rule (multiply probabilities); for either of two mutually exclusive outcomes use the sum rule (add probabilities). For example, the probability that a TtYy x TtYy cross gives an offspring that is both homozygous recessive at both loci is 1/4 x 1/4 = 1/16. The probability that it shows at least one recessive trait is 1 minus the probability of showing both dominants = 1 minus 9/16 = 7/16.

Examples in context

Example 1. Saltwater crocodile colour at Australia Zoo. Saltwater crocodile skin colour at Australia Zoo segregates Mendelianly: a dominant dark-pigment allele (D) produces standard dark skin, while the homozygous recessive (dd) produces the rare leucistic pale phenotype. Crossing two heterozygous Dd parents yields offspring in the classical ratio: 1 DD : 2 Dd : 1 dd, with phenotypic ratio 3 dark : 1 pale. A test cross of an unknown dark animal to a dd parent reveals genotype: all dark offspring indicate DD; a mix of dark and pale (1:1) indicates Dd. Australia Zoo's breeding records can illustrate independent assortment when colour and a second trait (such as scale-pattern) segregate independently.

Example 2. Cane-toad poison-gland trait in northern Queensland. Two genes in cane toads can be modelled Mendelianly: large-gland (G dominant) and skin-spot pattern (S dominant). A dihybrid cross GgSs $\times$ GgSs produces the 9:3:3:1 ratio (9 large-gland-spotted, 3 large-gland-plain, 3 small-gland-spotted, 1 small-gland-plain). Researchers at the University of Queensland comparing front-line invasion populations with long-established populations have documented allele-frequency shifts of G across the cane-toad range, consistent with selection at the gland locus. While the actual genetics are polygenic, the simplified two-gene model is QCAA-standard for explaining independent assortment, gametes (GS, Gs, gS, gs) and the Punnett-square 4 by 4 grid.

Try this

Q1. State Mendel's law of segregation and law of independent assortment, and explain the chromosomal basis for each. [3 marks]

• Cue. Segregation: alleles separate during meiosis. Independent assortment: alleles of different genes assort independently if on different chromosomes.

Q2. A heterozygous Rr (round, dominant) pea plant is crossed with a homozygous rr (wrinkled). Predict the offspring genotype and phenotype ratios and identify this as a test cross. [3 marks]

• Cue. 1 Rr : 1 rr genotype; 1 round : 1 wrinkled phenotype. Test cross reveals heterozygosity.

Q3. Refer to a dihybrid cross AaBb $\times$ AaBb. (a) List the gametes each parent produces. (b) Predict the phenotypic ratio assuming complete dominance and independent assortment. (c) Justify whether linkage between A and B would alter this ratio. [2+2+2 marks]

• Cue. (a) AB, Ab, aB, ab. (b) 9:3:3:1. (c) Yes; linkage reduces recombinants and shifts ratios.