Erma and Harvey were a compatible barnyard pair, but a curious sight. Harvey's tail was only 6 cm long, while Erma's was 30 cm. Their F₁ piglet offspring all grew tails that were 18 cm. When inbred, an F₂ generation resulted in many piglets (Erma and Harvey's grandpigs), whose tails ranged in 4-cm intervals from 6 to 30 cm (6, 10, 14, 18, 22, 26, and 30). Most had 18-cm tails, while 1/64 had 6-cm tails and 1/64 had 30-cm tails.
If one of the 18-cm-tail F₁ pigs is mated with one of the 6-cm-tail F₂ pigs, what phenotypic ratio will be predicted if many offspring resulted? Diagram the cross.

Verified step by step guidance

1. Step 1: Identify the inheritance pattern. The tail length varies in 4-cm intervals and the F1 offspring have an intermediate tail length (18 cm) between the parents (6 cm and 30 cm). This suggests incomplete dominance with multiple alleles or additive gene action, where tail length is determined by the sum of alleles from each parent.
2. Step 2: Assign genotypes to the parents. Let’s denote alleles corresponding to tail length increments. For example, assign 'A' alleles contributing 6 cm each. Harvey (6 cm) would be homozygous for the smallest allele (e.g., aa), Erma (30 cm) homozygous for the largest (e.g., AA), and the F1 (18 cm) heterozygous (e.g., Aa). The F2 generation shows a 1:6:15:20:15:6:1 distribution, consistent with a trinomial expansion of a three-allele system or multiple additive loci.
3. Step 3: Determine the genotype of the 6-cm-tail F2 pig. Since 6 cm is the smallest tail length, this pig is likely homozygous for the smallest allele (aa). The 18-cm F1 pig is heterozygous (Aa).
4. Step 4: Set up the Punnett square for the cross between the 18-cm F1 pig (Aa) and the 6-cm F2 pig (aa). The possible gametes from Aa are A and a; from aa, only a. The offspring genotypes will be Aa and aa.
5. Step 5: Predict the phenotypic ratio. Since Aa corresponds to 18 cm and aa to 6 cm, the offspring will be 50% 18-cm tails and 50% 6-cm tails. Diagram the cross showing the gametes and resulting genotypes to visualize this ratio.

Key Concepts

Incomplete Dominance and Quantitative Traits

Incomplete dominance occurs when heterozygotes display an intermediate phenotype between the two homozygotes, as seen in the F₁ piglets with 18 cm tails. Quantitative traits, like tail length here, are controlled by multiple alleles or gene copies, producing a range of phenotypes in the offspring rather than discrete categories.

Polygenic Inheritance and Additive Gene Effects

Polygenic inheritance involves multiple genes contributing additively to a trait, resulting in continuous variation such as the 4-cm interval tail lengths in the F₂ generation. Each gene adds a small effect, and the combination of alleles determines the phenotype, explaining the range and frequency distribution observed.

Punnett Square and Predicting Phenotypic Ratios

A Punnett square is a tool to diagram genetic crosses and predict offspring genotypes and phenotypes. By assigning alleles to represent tail length contributions, one can cross an 18-cm F₁ pig with a 6-cm F₂ pig to calculate expected phenotypic ratios based on allele combinations and additive effects.