A geneticist from an alien planet that prohibits genetic research brought with him to Earth two pure-breeding lines of frogs. One line croaks by uttering 'rib-it rib-it' and has purple eyes. The other line croaks more softly by muttering 'knee-deep knee-deep' and has green eyes. With a newfound freedom of inquiry, the geneticist mated the two types of frogs, producing F₁ frogs that were all utterers and had blue eyes. A large F₂ generation then yielded the following ratios:
27/64 blue-eyed, 'rib-it' utterer
12/64 green-eyed, 'rib-it' utterer
9/64 blue-eyed, 'knee-deep' mutterer
9/64 purple-eyed, 'rib-it' utterer
4/64 green-eyed, 'knee-deep' mutterer
3/64 purple-eyed, 'knee-deep' mutterer
In another experiment, the geneticist crossed two purple-eyed, 'rib-it' utterers together with the results shown here:
9/16 purple-eyed, 'rib-it' utterer
3/16 purple-eyed, 'knee-deep' mutterer
3/16 green-eyed, 'rib-it' utterer
1/16 green-eyed, 'knee-deep' mutterer
What were the genotypes of the two parents?

Verified step by step guidance

1. Step 1: Analyze the phenotypes and ratios in the F₁ and F₂ generations. The F₁ generation is uniform, suggesting that the traits are controlled by dominant and recessive alleles. The F₂ generation shows a variety of phenotypes with specific ratios, indicating independent assortment of multiple genes.
2. Step 2: Identify the traits and their inheritance patterns. The traits are eye color (purple, green, blue) and croaking style ('rib-it' utterer vs. 'knee-deep' mutterer). The ratios suggest that eye color is controlled by two genes (epistasis may be involved), and croaking style is controlled by a separate gene.
3. Step 3: Deduce the genotypes of the F₁ generation. Since all F₁ frogs are blue-eyed 'rib-it' utterers, they must be heterozygous for both traits. For eye color, the F₁ frogs likely have a genotype that combines alleles for purple and green eyes, resulting in blue eyes due to epistasis. For croaking style, the F₁ frogs are heterozygous for the 'rib-it' utterer trait.
4. Step 4: Examine the F₂ generation ratios to determine the parental genotypes. The 9:3:3:1 ratio in the second experiment suggests a dihybrid cross. The parents in this experiment are purple-eyed 'rib-it' utterers, which means they are heterozygous for both traits. Their genotypes are likely AaBb, where 'A' and 'B' represent the dominant alleles for eye color and croaking style, respectively.
5. Step 5: Conclude the genotypes of the original pure-breeding lines. The pure-breeding 'rib-it' utterer with purple eyes must be homozygous dominant for both traits (AABB), while the pure-breeding 'knee-deep' mutterer with green eyes must be homozygous recessive (aabb). These genotypes explain the F₁ generation and subsequent ratios observed in the F₂ generation.

Key Concepts

Mendelian Genetics

Mendelian genetics is the study of how traits are inherited through generations based on the principles established by Gregor Mendel. It involves understanding dominant and recessive alleles, genotype versus phenotype, and the segregation and independent assortment of genes during gamete formation. This framework is essential for predicting the outcomes of genetic crosses, such as those described in the frog experiment.

Punnett Squares

Punnett squares are a graphical method used to predict the genotypic and phenotypic ratios of offspring from a genetic cross. By organizing the possible gametes from each parent, a Punnett square allows for a visual representation of how alleles combine, making it easier to analyze inheritance patterns. This tool is particularly useful in determining the genotypes of the parent frogs based on the observed ratios in the F₂ generation.

Phenotypic Ratios

Phenotypic ratios represent the relative frequencies of different phenotypes in the offspring resulting from a genetic cross. In the context of the frog experiment, the ratios observed in the F₂ generation provide critical insights into the underlying genotypes of the parent frogs. Analyzing these ratios helps in deducing the dominance relationships between traits and the potential combinations of alleles present in the parents.