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
After years of experiments, the geneticist isolated pure-breeding strains of all six F₂ phenotypes. Indicate the F₁ and F₂ phenotypic ratios of the following cross using these pure-breeding strains: blue-eyed, 'knee-deep' mutterer x purpled-eyed, 'rib-it' utterer.

Verified step by step guidance

1. Step 1: Begin by analyzing the F₁ generation. The F₁ frogs are all 'rib-it' utterers and have blue eyes. This suggests that the traits for 'rib-it' utterance and blue eyes are dominant over 'knee-deep' muttering and other eye colors (green and purple). Determine the genotypes of the F₁ frogs based on this dominance pattern.
2. Step 2: Examine the F₂ generation phenotypic ratios. The ratios (27/64, 12/64, etc.) suggest a dihybrid cross involving two genes, each with two alleles. Use the phenotypic ratios to deduce the inheritance pattern of the traits (e.g., whether they follow Mendelian inheritance and whether there is any epistasis or interaction between the genes).
3. Step 3: Identify the genotypes of the pure-breeding strains isolated by the geneticist. Pure-breeding strains are homozygous for their respective traits. For example, a pure-breeding blue-eyed, 'knee-deep' mutterer would be homozygous recessive for the 'knee-deep' trait and homozygous for the blue-eye trait. Write out the genotypes for all six phenotypes.
4. Step 4: Set up the cross between the pure-breeding blue-eyed, 'knee-deep' mutterer and the pure-breeding 'rib-it' utterer. Determine the genotypes of the parents and predict the genotypes and phenotypes of the F₁ generation using a Punnett square. Consider the dominance relationships established earlier.
5. Step 5: Use the F₁ generation genotypes to predict the F₂ generation phenotypic ratios. Perform a dihybrid cross (if applicable) and calculate the expected phenotypic ratios based on Mendelian inheritance. Ensure that the ratios align with the observed F₂ generation data provided in the problem.

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 and phenotype distinctions, and the laws of segregation and independent assortment. These principles help predict the outcomes of genetic crosses, such as the ratios of phenotypes in offspring.

Phenotypic Ratios

Phenotypic ratios represent the relative frequencies of different observable traits (phenotypes) in the offspring resulting from a genetic cross. In the context of the question, the F₂ generation's phenotypic ratios provide insight into the inheritance patterns of traits like eye color and croaking sounds. Analyzing these ratios is crucial for understanding the genetic makeup of the offspring.

Pure-Breeding Strains

Pure-breeding strains are genetically uniform lines that consistently produce offspring with the same phenotype when self-crossed. These strains are essential for genetic studies as they provide a stable genetic background for experiments. In the context of the question, isolating pure-breeding strains of the F₂ phenotypes allows the geneticist to perform controlled crosses and predict the phenotypic ratios of the resulting offspring.