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
Assign gene symbols for all phenotypes and indicate the genotypes of the P₁ and F₁ frogs.

Verified step by step guidance

1. Step 1: Identify the traits and their phenotypes. We have two traits: the croaking sound ("rib-it rib-it" vs. "knee-deep knee-deep") and eye color (purple vs. green). The F₁ frogs all have blue eyes and utter "rib-it," indicating these are likely heterozygous or a new phenotype resulting from the cross.
2. Step 2: Assign gene symbols for each trait. For croaking sound, assign a gene with two alleles, for example, \( R \) for "rib-it" (dominant) and \( r \) for "knee-deep" (recessive). For eye color, assign another gene with alleles, for example, \( P \) for purple eyes and \( G \) for green eyes. Since F₁ has blue eyes, which is a new phenotype, this suggests incomplete dominance or codominance at the eye color locus.
3. Step 3: Determine the genotypes of the P₁ (parental) lines. Since the parental lines are pure-breeding, their genotypes are homozygous. The "rib-it" and purple-eyed line would be \( RRPP \), and the "knee-deep" and green-eyed line would be \( rrGG \).
4. Step 4: Determine the genotype of the F₁ generation. Since F₁ frogs all utter "rib-it" and have blue eyes, their genotype is heterozygous for both traits: \( RrPG \). The blue eye color is likely due to the heterozygous combination \( PG \) showing incomplete dominance or codominance.
5. Step 5: Analyze the F₂ phenotypic ratios to confirm the inheritance pattern. The ratios given (27/64, 12/64, etc.) suggest a dihybrid cross with two genes assorting independently, possibly with incomplete dominance for eye color. Use the Punnett square for \( Rr \times Rr \) and \( P G \times P G \) to predict the F₂ genotypes and phenotypes, matching them to the observed ratios.

Key Concepts

Dihybrid Cross and Mendelian Ratios

A dihybrid cross involves two genes, each with two alleles, and their independent assortment during gamete formation. Mendelian ratios, such as 9:3:3:1 in F2 progeny, help predict phenotypic outcomes when genes assort independently. Deviations or specific fraction patterns can indicate gene linkage or epistasis.

Gene Symbol Assignment and Allelic Notation

Gene symbols represent different alleles of a gene, typically using uppercase for dominant and lowercase for recessive traits. Assigning symbols requires identifying traits and their dominance relationships from phenotypes. This notation clarifies genotypes and helps track inheritance patterns across generations.

Phenotypic Ratios and Genotype Inference

Analyzing phenotypic ratios in F2 offspring allows inference of underlying genotypes and dominance relationships. By comparing observed ratios to expected Mendelian ratios, one can deduce which alleles are dominant, recessive, or linked, and assign genotypes to parental (P1) and first filial (F1) generations.