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 \(\mathrm{F}_{1}\) 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 \(4-\mathrm{cm}\) intervals from 6 to \(30 \mathrm{cm}(6,10,14,18,22,26, \text { and } 30) .\) Most had \(18-\mathrm{cm}\) tails, while \(1 / 64\) had \(6-\mathrm{cm}\) tails and \(1 / 64\) had \(30-\mathrm{cm}\) 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 \(18-\mathrm{cm} \mathrm{F}_{1}\) pigs is mated with one of the \(6-\mathrm{cm}\) \(\mathrm{F}_{2}\) pigs, what phenotypic ratio will be predicted if many offspring resulted? Diagram the cross.

Short answer

Answer: The phenotypic ratio of the offspring's tail lengths is 50% with 6-cm tails and 50% with 18-cm tails.

Step-by-step solution

Understanding the Problem and Terminology

To solve this exercise, it's important to understand several genetic concepts: - F1 generation: This refers to the first generation of offspring produced by crossing two parental individuals. - F2 generation: This refers to the generation produced by inbreeding the F1 generation. - Phenotype: The observable characteristics of an organism, such as tail length. - Genotype: The specific genetic makeup of an organism that determines its phenotype. - Mode of inheritance: The pattern in which a particular genetic trait is passed on from one generation to another.

Determine the Mode of Inheritance and Gene Pairs Involved

Given that F1 offspring had tail lengths intermediate between those of their parents (18 cm) and F2 piglets on inbreeding F1, show a range of tail lengths at regular intervals, this suggests that the inheritance falls under quantitative or polygenic inheritance. In quantitative inheritance, multiple gene pairs, also known as polygenes, act together to determine a trait with continuous variation. Each gene pair contributes a small additive amount to the trait. In this case, we are seeing variation in tail lengths in 4-cm intervals. There is a 24 cm difference between the shortest and the longest tails (30 cm - 6 cm), so 24 / 4 = 6 intervals. This suggests that 3 gene pairs (A, B, and C) are involved, as each can contribute two possible 4-cm intervals (A: 0 or 4 cm, B: 0 or 4 cm, and C: 0 or 4 cm).

Designate the Genotypes of Harvey, Erma and F1 Offspring

Now that we know three gene pairs are determining tail length, we can assign genotypes for Harvey, Erma and the F1 offspring. Harvey's tail length is 6 cm, which means he has the shortest tail possible (none of the gene pairs contribute to tail length). His genotype can be represented as AABBCC (where A, B, and C each represent 0 cm contribution to tail length). Erma has the longest tail length of 30 cm. All three gene pairs contribute 4 cm each to her tail length. Her genotype can be represented as aaBBcc (where a, b, and c each represent 4 cm contribution to tail length). Their F1 offspring have tails that are 18 cm long. Each parent contributes one allele of each gene pair to the offspring. So, the F1 offspring genotype would be AaBbCc (one allele from Harvey: ABC and one allele from Erma: abc).

Predict the Phenotypic Ratio for a Specific Cross

Now we have to find the phenotypic ratio when an F1 pig with an 18-cm tail (AaBbCc) mates with an F2 pig with a 6-cm tail (AABBCC). F1 pig (AaBbCc) x F2 pig (AABBCC) The possible gametes from the F1 pig would be ABC and abc. From the F2 pig, there is only one possible gamete, which is ABC (no variation since all the alleles are the same). So, the offspring genotypes would be AABBCC (50% of the offspring) and AaBbCc (50% of the offspring). This results in a phenotypic ratio of: - 50% 6-cm tails (AABBCC genotype) - 50% 18-cm tails (AaBbCc genotype)

Key concepts

F1 generation

In the study of genetics, the **F1 generation** is crucial as it represents the first filial generation produced by crossing two distinct parental organisms. In this scenario, Erma and Harvey are the parental pair, each with different tail lengths—Erma with a long 30 cm tail and Harvey with a short 6 cm one. When they are bred, their offspring, the F1 pigs, interestingly all exhibit a tail length of 18 cm. This intermediate tail length suggests that their offspring are heterozygous for the tail length trait.

In genetics, heterozygous indicates that the offspring carry two different alleles for a particular trait—one from each parent. Thus, each F1 pig's genotype contributes to this average tail length phenotype, combining the genetic input from both Erma and Harvey. Understanding such outcomes helps in predicting how traits may appear in subsequent generations.

F2 generation

The **F2 generation** arises from breeding the F1 offspring with each other. This generation showcases a more extensive variety of traits than seen in the F1. When the F1 pigs were inbred, the resulting F2 generation showed a wide range of tail lengths from 6 cm to 30 cm, appearing in 4 cm intervals. This outcome reflects on the inheritance patterns and diversity in genetic combinations.

The variation found in the F2 generation indicates that several combinations of the alleles are possible, resulting in different phenotypic outcomes. Each added genetic pair contributes to these variations, illustrating the complexity of genetic inheritance. In the context of the exercise, this variability exemplifies how genetic traits can manifest across a spectrum rather than in simple dominant-recessive patterns.

Polygenic inheritance

**Polygenic inheritance** is a mode of inheritance that is characterized by multiple genes (polygenes) affecting a single trait. In the context of Erma and Harvey's piglets, their tail length is an exemplary trait determined through polygenic inheritance. Unlike single-gene traits, polygenic traits display continuous variation, resulting from the additive effects of multiple genes.

The regular intervals in the F2 generation's tail lengths highlight this concept. With three gene pairs involved (as determined for the tail variation), each contributes to the trait's overall expression. Here, a gene pair can add varying amounts to tail length, allowing complex and diverse phenotypic combinations. Thus, polygenic inheritance is what allows for the frequent intermediate forms that arise naturally, as seen in these pigs' tails, and predicts the wide phenotypic distribution seen in large populations.