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
How many total gene pairs are involved in the inheritance of both traits? Support your answer.

Verified step by step guidance

1. Step 1: Identify the phenotypes and their ratios in the F₂ generation and recognize that the traits are likely controlled by multiple gene pairs. The traits are eye color (purple, blue, green) and croaking sound ('rib-it' vs. 'knee-deep'). The F₁ generation is uniform with blue eyes and 'rib-it' croaking, indicating dominance patterns.
2. Step 2: Analyze the F₂ phenotypic ratios given: 27/64, 12/64, 9/64, 9/64, 4/64, and 3/64. Notice that the denominators are all 64, which is a clue that the total number of gene pairs involved is related to the number of possible genotype combinations, since \$2^n = 64\( implies \)n=6$ gene pairs if each gene is independently assorting with two alleles.
3. Step 3: Consider that each gene pair segregates independently and contributes to the phenotypic ratios. The total number of genotypic combinations for \(n\) gene pairs is \$2^{2n}\(, but since each gene pair has two alleles, the number of phenotypic classes in a dihybrid cross is \)4^n\(. Here, the denominator 64 suggests \)4^n = 64\(, so solve for \)n\( by setting \)4^n = 64$.
4. Step 4: Calculate \(n\) by taking logarithms: \(n = \log_4 64\). Since \$4^3 = 64\(, this means \)n=3$. Therefore, three gene pairs are involved in the inheritance of both traits combined.
5. Step 5: Support this conclusion by explaining that the observed phenotypic ratios correspond to a trihybrid cross (three gene pairs), where each gene pair contributes to the traits of eye color and croaking sound, and the F₂ ratios reflect the independent assortment and combination of these gene pairs.

Key Concepts

Dihybrid and Multihybrid Crosses

Dihybrid and multihybrid crosses involve tracking inheritance of two or more gene pairs simultaneously. The phenotypic ratios in offspring reflect the number of gene pairs and their independent assortment. For example, a typical dihybrid cross yields a 9:3:3:1 ratio, while more gene pairs produce more complex ratios based on 4^n total phenotypic classes.

Mendelian Ratios and Probability

Mendelian genetics predicts offspring ratios based on dominant and recessive alleles segregating independently. The total number of phenotypic classes is 4^n for n gene pairs with two alleles each. Observed ratios can be compared to expected ratios to deduce the number of gene pairs controlling traits.

Phenotypic Classification and Gene Interaction

Phenotypes result from combinations of alleles at different loci. Each gene pair can influence distinct traits, and their combinations produce unique phenotypes. Understanding how to classify phenotypes by traits and their ratios helps infer the number of gene pairs involved in inheritance.