predicted genetic outcomes of a monohybrid cross and a monohybrid test cross

What this dot point is asking

VCAA wants you to predict the offspring of a monohybrid cross (one gene at a time) using a Punnett square, and explain how a test cross with a homozygous recessive parent reveals the unknown genotype of a parent showing the dominant phenotype.

The answer

Setting up a monohybrid cross

A monohybrid cross considers one gene with two alleles.

Steps:

1. Identify the alleles and their relationship (dominant/recessive, codominant, etc.).
2. Assign genotypes to the parents.
3. List the gametes each parent can produce (each gamete carries one allele, from meiosis).
4. Draw a Punnett square with one parent's gametes across the top and the other's down the side.
5. Fill the cells with the genotype produced by each combination.
6. Count genotypes and phenotypes for the ratio.

Mendel used the conventional capital and lowercase letters for dominant and recessive alleles (P, p). For codominance, use superscripts (IA, IB, i). For sex-linked, use the chromosome (X-H, X-h, Y).

The four basic monohybrid crosses (autosomal dominant pattern)

Using P (purple, dominant) and p (white, recessive).

1. Homozygous dominant times homozygous recessive (PP times pp).

Offspring: all Pp. Phenotype: all purple. (This is how Mendel produced his F1 generation.)

2. F1 self-cross (Pp times Pp).

Genotypes: 1 PP : 2 Pp : 1 pp. Phenotypes: 3 purple : 1 white. This is Mendel's famous 3:1 ratio.

3. Heterozygous times homozygous recessive (Pp times pp). This is the test cross.

Genotypes: 1 Pp : 1 pp. Phenotypes: 1 purple : 1 white (1:1).

4. Homozygous dominant times heterozygous (PP times Pp).

Genotypes: 1 PP : 1 Pp. Phenotypes: all purple.

The test cross

A test cross is the cross between an organism showing the dominant phenotype (unknown genotype: PP or Pp) and a homozygous recessive organism (pp).

Why use the homozygous recessive as the tester? Because pp produces only one kind of gamete (p), so the offspring phenotypes directly reveal the alleles in the unknown parent's gametes.

Interpreting results:

• If all offspring show the dominant phenotype: the unknown parent is most likely homozygous dominant (PP), because PP × pp gives all Pp (all dominant).
• If offspring show both phenotypes in a 1:1 ratio: the unknown parent is heterozygous (Pp), because Pp × pp gives 1 Pp : 1 pp (1 dominant : 1 recessive).
• A test cross can also detect linkage between two genes if you cross dihybrids (see linked-and-unlinked-genes).

Sample-size caveat. With small numbers of offspring, a heterozygous parent might by chance produce all-dominant offspring just from random gamete sampling. The more offspring observed, the more confident the conclusion.

Worked example

A pea plant with round seeds (R dominant, r recessive) is found in a wild population. The grower wants to know if it is RR or Rr. They cross it with a known wrinkled pp plant (rr).

• If RR times rr: all offspring Rr, all round. Conclusion: the parent is RR.
• If Rr times rr: 1 Rr : 1 rr offspring, half round and half wrinkled. Conclusion: the parent is Rr.

After producing 20 offspring, the grower sees 11 round and 9 wrinkled. The roughly 1:1 split indicates the parent is heterozygous Rr.

Why monohybrid crosses matter

The 3:1 (and 1:1) ratios are the empirical signature of:

• One gene with two alleles.
• Complete dominance (one allele fully masks the other in heterozygotes).
• Independent segregation of alleles into gametes (Mendel's First Law: the Law of Segregation).

The Law of Segregation says that the two alleles for each gene separate from each other during gamete formation (this is what meiosis does in anaphase I), so each gamete carries only one allele.

When you scale up to two genes at once, the predictable 3:1 becomes 9:3:3:1 (the dihybrid cross; see linked-and-unlinked-genes for when this breaks down).

Beyond Mendel

The same approach works with non-classical dominance:

• Codominance. Two heterozygotes IA IB × IA IB gives 1 IA IA : 2 IA IB : 1 IB IB. Phenotypes: 1 A : 2 AB : 1 B.
• Incomplete dominance. Rr × Rr gives 1 RR : 2 Rr : 1 rr. Phenotypes: 1 red : 2 pink : 1 white.
• Sex-linked. Use sex notation in the Punnett square (see models-of-inheritance worked example).

Common traps

Mixing up genotypes and phenotypes in the ratio. The Pp × Pp cross gives a genotype ratio of 1 PP : 2 Pp : 1 pp but a phenotype ratio of 3 purple : 1 white. Always state which you mean.

Forgetting that a test cross requires the recessive homozygote. Crossing your unknown with a heterozygote (Pp) does not work cleanly because the heterozygote produces both kinds of gametes; you cannot infer the unknown's genotype from the offspring pattern.

Treating 3:1 as exact. Real offspring counts vary by chance. A 3:1 cross with 100 offspring might give 78:22 or 71:29 and still be consistent with 3:1.

Saying the test cross "creates" a homozygote. The test cross reveals the genotype by producing different offspring patterns from the two possibilities.

Skipping the gametes step. Drawing the Punnett square without listing the gametes is the most common source of errors. Be explicit: PP produces only P gametes; Pp produces 50% P and 50% p; pp produces only p.

In one sentence

A monohybrid cross tracks one gene at a time and gives a 3:1 phenotype ratio for a heterozygous cross (Pp times Pp) and a 1:1 ratio for a test cross (Pp times pp), which is used to determine whether an organism showing the dominant phenotype is homozygous dominant (PP, all dominant offspring) or heterozygous (Pp, 1:1 split) by crossing it with a homozygous recessive partner.