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. insert step 1: Understand the genetic basis of the trait. The tail length in pigs is likely controlled by multiple genes, as indicated by the continuous range of phenotypes in the F₂ generation. This suggests a polygenic inheritance pattern.
2. insert step 2: Determine the genotypes of the parents. The F₁ generation, with 18-cm tails, suggests they are heterozygous for the genes controlling tail length. The 6-cm F₂ pig likely has a homozygous recessive genotype.
3. insert step 3: Set up the cross between the F₁ pig (heterozygous) and the 6-cm F₂ pig (homozygous recessive). Use a Punnett square to predict the genotypic and phenotypic outcomes of this cross.
4. insert step 4: Analyze the Punnett square results. Since the F₁ pig is heterozygous, each gene pair will segregate independently, and the offspring will have a range of genotypes.
5. insert step 5: Predict the phenotypic ratio. Given the polygenic nature, the phenotypes will likely show a range centered around the mid-parent value, with more offspring having intermediate tail lengths and fewer at the extremes.

Key Concepts

Phenotypic Ratio

The phenotypic ratio refers to the relative number of offspring displaying each phenotype in a genetic cross. In this scenario, it is essential to understand how traits are expressed in the offspring based on the genetic contributions from the parents. The phenotypic ratio can be predicted using a Punnett square, which visually represents the possible combinations of alleles from the parents.

Incomplete Dominance

Incomplete dominance occurs when the phenotype of heterozygous individuals is intermediate between the phenotypes of the two homozygous parents. In this case, the F₁ generation exhibits an intermediate tail length of 18 cm, suggesting that tail length may be influenced by multiple alleles or incomplete dominance. Understanding this concept is crucial for predicting the phenotypic outcomes in the F₂ generation.

Mendelian Inheritance

Mendelian inheritance describes the patterns of inheritance for traits controlled by single genes with dominant and recessive alleles. The F₂ generation's tail lengths, which vary in specific intervals, reflect the principles of segregation and independent assortment as outlined by Gregor Mendel. This concept helps explain the observed ratios and variations in the offspring's phenotypes when different parental combinations are crossed.