Question

Erma and Harvey were a compatible barnyard pair, but a curious sight. Harvey's tail was only \(6 \mathrm{cm}\) long, while Erma's was \(30 \mathrm{cm}\) Their \(F_{1}\) piglet offspring all grew tails that were \(18 \mathrm{cm} .\) When inbred, an \(\mathrm{F}_{2}\) generation resulted in many piglets (Erma and Harvey's grandpigs), whose tails ranged in 4 -cm intervals from 6 to \(30 \mathrm{cm}(6,10,14,18,22,26, \text { and } 30) .\) Most had 18 -cm tails, while \(1 / 64\) had 6 -cm tails and \(1 / 64\) had 30 -cm tails. (a) 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. (b) If one of the 18 -cm \(\mathrm{F}_{1}\) pigs is mated with one of the 6 -cm \(\mathrm{F}_{2}\) pigs, what phenotypic ratio would be predicted if many offspring resulted? Diagram the cross.

Short answer

Answer: The mode of inheritance is polygenic using additive alleles. The phenotypic ratio among the offspring when mating an 18-cm F1 pig (AaBbCc) with a 6-cm F2 pig (aabbcc) is 1:3:3:1 for tails of 6cm, 10cm, 14cm, and 18cm, respectively.

Step-by-step solution

Part (a): Mode of Inheritance, Gene Pairs, and Genotypes

1. Observe the given information: Harvey's tail is 6 cm, Erma's tail is 30 cm, their F1 offspring's tails are 18 cm, and F2 offspring's tails range from 6-30 cm in 4-cm intervals (6, 10, 14, 18, 22, 26, and 30). 2. Since the traits are quantitative and there are multiple F2 phenotypes, this suggests that the mode of inheritance is polygenic using additive alleles. 3. Notice that there are 7 phenotypic categories in F2, and the phenotypic difference between adjacent categories is 4 cm, suggesting that 3 gene pairs (A, B, and C) are involved. Each gene pair has two alleles: one additive allele (A, B, or C) that contributes 4 cm to the tail length, and the other non-additive allele (a, b, or c) that does not contribute. 4. Assign genotypes to Harvey, Erma, and their F1 offspring: - Harvey's tail length is 6cm, which is the minimum phenotypic value (6cm) that the offspring can inherit. Therefore, Harvey’s genotype must be aabbcc (three non-additive alleles with 0 contribution). - Erma's tail length is 30cm, which is the maximum phenotypic value (6cm + 3(4cm)) that the offspring can inherit. Therefore, Erma’s genotype must be AABBCC (three additive alleles contributing 12 cm in total). - The F1 offspring have 18-cm tails. They inherit one allele from each parent, resulting in a heterozygous genotype AaBbCc (each additive allele contributing 4 cm to tail length).

Part (b): Predicting Phenotypic Ratio and Diagramming the Cross

1. To predict the phenotypic ratio, we will cross an 18-cm F1 pig (AaBbCc) with a 6-cm F2 pig (aabbcc). 2. Set up a Punnett square to perform the cross: - The possible gametes of the F1 parent are ABC (contributing 12 cm), ABc (contributing 8 cm), AbC (contributing 8 cm), Abc (contributing 4 cm), aBC (contributing 8 cm), aBc (contributing 4 cm), abC (contributing 4 cm), and abc (contributing 0 cm). - The possible gametes of the F2 parent are all a, b, and c, which does not contribute to the tail length. 3. Perform the cross and calculate the phenotypic ratio among the offspring. Since all F2 parent's gametes do not contribute to the tail length, the phenotypic ratio can be obtained by simply observing the F1 parent's gametes contribution. - Offspring with 6cm tails - 1 combination (abc) - 1/64 probability - Offspring with 10cm tails - 3 combinations (AbC, aBC, ABc) - 3/64 probability - Offspring with 14cm tails - 3 combinations (Abc, aBc, abC) - 3/64 probability - Offspring with 18cm tails - 1 combination (ABC) - 1/64 probability 4. The predicted phenotypic ratio among the offspring when mating an 18-cm F1 pig (AaBbCc) with a 6-cm F2 pig (aabbcc) is 1:3:3:1 for tails of 6cm, 10cm, 14cm, and 18cm, respectively.

Key concepts

Quantitative Traits

Quantitative traits are characteristics that show a range of possible phenotypes, rather than distinct categories. These traits are influenced by multiple genes, and their expression can vary from one organism to another. In the context of the tail lengths of pigs, where we see variations from 6 cm to 30 cm, each incremental change such as 4 cm represents a different quantitative trait expression.

• These traits are usually influenced by environmental factors, as well as genetic factors.
• In our example, the piglets' tail lengths are distributed across several possible lengths, not just a singular trait like "long" or "short."

This wide range of possibilities is what characterizes the quantitative nature of this trait, reflecting its polygenic inheritance.

Additive Alleles

Additive alleles are a key concept in understanding quantitative traits. In the case of the piglets' tail lengths, each additive allele contributes a specific amount to the trait's expression—in this instance, 4 cm per additive allele.

• This means that each allele has an additive effect on the phenotype, enhancing the trait incrementally.
• For example, Erma’s genotype of AABBCC indicates six additive alleles, contributing a total of 24 cm (4 cm per allele) to her tail length, alongside the base 6 cm length already present in Harvey.

Understanding additive alleles helps in predicting the possible outcomes of different genetic crosses, as each gamete can pass on varying numbers of additive alleles, influencing the eventual phenotype of the offspring.

Genotype

The concept of genotype is foundational to understanding inheritance patterns. A genotype refers to the genetic makeup of an individual, specifically the alleles they possess. In the example of Harry, Erma, and their offspring, we assign the genotypes to interpret the observed tail lengths.

• Harvey’s genotype is aabbcc, as he exhibits the shortest tail possible with his alleles contributing nothing additive.
• Erma’s genotype AABBCC represents maximum additive alleles, reflecting her long tail.
• The F1 generation, represented by AaBbCc, shows a blend, inheriting one allele from each parent, resulting in an intermediate phenotype.

By analyzing genotypes, we can predict possible phenotypic expressions in successive generations, allowing us to understand how traits like tail length can be passed down and vary among offspring.