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.
Explain how these tail lengths were inherited by describing the mode of inheritance, indicating how many gene pairs were at work, and designating the genotypes of Harvey, Erma, and their 18-cm-tail offspring.

Verified step by step guidance

1. Step 1: Identify the mode of inheritance by analyzing the tail length distribution in the F2 generation. The presence of multiple phenotypic classes with tail lengths in 4-cm intervals (6, 10, 14, 18, 22, 26, 30 cm) and the fact that the F1 offspring have an intermediate tail length (18 cm) suggests that tail length is controlled by polygenic inheritance, specifically additive gene action.
2. Step 2: Determine the number of gene pairs involved. Since the F2 generation shows 7 distinct phenotypic classes, and the number of phenotypic classes in additive polygenic traits is given by \$2n + 1\(, where \)n\( is the number of gene pairs, solve for \)n\( using \)7 = 2n + 1$. This will give the number of gene pairs contributing to tail length.
3. Step 3: Assign genotypes to the parents. Let each gene pair have two alleles: a '+' allele that adds 2 cm to tail length and a '-' allele that adds 0 cm. Harvey, with the shortest tail (6 cm), would be homozygous recessive at all gene pairs (all '-' alleles). Erma, with the longest tail (30 cm), would be homozygous dominant at all gene pairs (all '+' alleles).
4. Step 4: Determine the genotype of the F1 offspring. Since the F1 piglets have intermediate tail length (18 cm), they are heterozygous at all gene pairs, carrying one '+' and one '-' allele per gene pair. This heterozygosity results in an intermediate phenotype due to additive effects.
5. Step 5: Explain the F2 phenotypic ratios. When F1 individuals are inbred, the segregation of alleles at each gene pair produces the range of tail lengths observed in the F2 generation, with phenotypes spaced in 4-cm intervals. The extreme phenotypes (6 cm and 30 cm) occur at a frequency of \$1/64$, consistent with the probability of inheriting all recessive or all dominant alleles across the gene pairs.

Key Concepts

Polygenic Inheritance

Polygenic inheritance involves multiple genes contributing additively to a single trait, resulting in continuous variation. Traits like tail length showing a range of phenotypes in defined intervals suggest several gene pairs influence the trait, rather than a single gene with discrete alleles.

Quantitative Trait Distribution and Genotypic Ratios

The presence of offspring with phenotypes in regular intervals and specific ratios (e.g., 1/64) indicates segregation of multiple gene pairs with additive effects. The 1/64 frequency corresponds to homozygosity at all gene loci, helping to infer the number of gene pairs involved and predict genotype-phenotype relationships.

Genotype Designation in Polygenic Traits

In polygenic traits, each gene pair contributes incrementally to the phenotype. Assigning genotypes involves representing each gene pair with alleles (e.g., A/a, B/b, C/c), where dominant alleles add to tail length. Harvey and Erma’s genotypes reflect homozygosity for opposite alleles, while their F₁ offspring are heterozygous at all loci, producing intermediate tail length.