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. Identify the pattern of inheritance by analyzing the phenotypic ratios in the F₂ generation. Notice that the tail lengths form a continuous range, suggesting polygenic inheritance.
2. Recognize that the extreme phenotypes (6 cm and 30 cm tails) appear at a frequency of 1/64, which is indicative of a polygenic trait controlled by multiple gene pairs.
3. Determine the number of gene pairs involved by using the formula for polygenic inheritance: (1/4)^n = frequency of extreme phenotypes, where n is the number of gene pairs. Solve for n using the given frequency of 1/64.
4. Assign genotypes to Harvey, Erma, and their F₁ offspring. Since the F₁ generation shows an intermediate phenotype (18 cm tails), it suggests that Harvey and Erma were homozygous for different alleles at each gene pair, and the F₁ offspring are heterozygous.
5. Conclude that the mode of inheritance is polygenic, involving multiple gene pairs, with each contributing additively to the tail length. Harvey and Erma's genotypes are homozygous at each locus, while the F₁ offspring are heterozygous.

Key Concepts

Mode of Inheritance

The mode of inheritance refers to the way traits are passed from parents to offspring, which can be influenced by dominant and recessive alleles. In this case, the tail length appears to follow a quantitative trait inheritance pattern, where multiple genes contribute to the phenotype, resulting in a range of tail lengths in the offspring.

Polygenic Inheritance

Polygenic inheritance involves multiple gene pairs influencing a single trait, leading to continuous variation in phenotypes. The tail lengths of the piglets suggest that several genes are involved, as evidenced by the range of tail lengths observed in the F₂ generation, which indicates a complex interaction of alleles.

Genotype Designation

Genotype designation involves identifying the specific alleles present in an organism. For Harvey (6 cm tail) and Erma (30 cm tail), their genotypes can be inferred as homozygous recessive (hh) and homozygous dominant (HH), respectively. The F₁ offspring (18 cm tail) would be heterozygous (Hh), representing an intermediate phenotype due to the influence of both parental alleles.