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
Indicate the genotypes of the six F₂ phenotypes.

Verified step by step guidance

1. Step 1: Identify the traits and their inheritance patterns. The problem involves two traits: croaking sound ('rib-it' vs. 'knee-deep') and eye color (purple, blue, green). Since the F₁ generation all show 'rib-it' and blue eyes, this suggests incomplete dominance or multiple alleles for both traits.
2. Step 2: Assign symbols to the alleles for each trait. For croaking sound, let’s use R for 'rib-it' and r for 'knee-deep'. For eye color, since there are three phenotypes (purple, blue, green), this suggests two loci or multiple alleles with incomplete dominance. We can assign alleles P and G for purple and green, respectively, with blue as the heterozygote (P G).
3. Step 3: Determine the genotypes of the parental pure-breeding lines. The 'rib-it' purple-eyed frogs are likely homozygous for R and P alleles (R R P P), and the 'knee-deep' green-eyed frogs are homozygous for r and G alleles (r r G G).
4. Step 4: Predict the F₁ genotype and phenotype. Crossing R R P P with r r G G produces F₁ heterozygotes R r P G, which show 'rib-it' (dominant or incomplete dominance of R) and blue eyes (heterozygous P G).
5. Step 5: Analyze the F₂ phenotypic ratios and assign genotypes. Use a dihybrid Punnett square for R/r and P/G alleles to find all possible genotype combinations. Match each F₂ phenotype ratio to the corresponding genotype based on the combination of alleles for croaking and eye color.

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 predict the distribution of phenotypes in the F2 generation, often following a 9:3:3:1 or modified ratio depending on dominance and linkage. Understanding these ratios helps interpret the observed phenotypic frequencies in offspring.

Dominance and Incomplete Dominance

Dominance describes how one allele can mask the expression of another in heterozygotes. Incomplete dominance occurs when heterozygotes show an intermediate phenotype, such as blue eyes resulting from crossing purple and green eyes. Recognizing dominance patterns is essential to deduce genotypes from phenotypes.

Genotype-Phenotype Relationship and Allelic Combinations

Each phenotype corresponds to specific allele combinations (genotypes) at the loci involved. By analyzing phenotypic ratios and traits, one can assign genotypes to each phenotype, considering homozygous and heterozygous states. This relationship is key to solving genetic problems involving multiple traits.