Question

A geneticist from an alien planet that prohibits genetic research brought with him two true-breeding lines of frogs. One frog line croaks by uttering "rib-it rib-it" and has purple eyes. The other frog line croaks by muttering "knee- deep knee-deep" and has green eyes. He mated the two frog lines, producing \(\mathrm{P}_{1}\) frogs that were all utterers with blue eyes. A large \(\mathrm{F}_{2}\) generation then yielded the following ratios: \(27 / 64\) blue, utterer \(12 / 64\) green, utterer \(9 / 64\) blue, mutterer \(9 / 64\) purple, utterer \(4 / 64\) green, mutterer \(3 / 64\) purple, mutterer (a) How many total gene pairs are involved in the inheritance of both eye color and croaking? (b) Of these, how many control eye color, and how many control croaking? (c) Assign gene symbols for all phenotypes, and indicate the genotypes of the \(P_{1}, F_{1},\) and \(F_{2}\) frogs. (d) After many years, the frog geneticist isolated true-breeding lines of all six \(\mathrm{F}_{2}\) phenotypes. Indicate the \(\mathrm{F}_{1}\) and \(\mathrm{P}_{2}\) phenotypic ratios of a cross between a blue, mutterer and a purple, utterer.

Short answer

Based on the analysis of the generation ratios, a cross between a blue-eyed mutterer and a purple-eyed utterer frog produces offspring with a phenotypic ratio of 1:1:1:1 for blue-eyed utterers, blue-eyed mutterers, purple-eyed utterers, and purple-eyed mutterers.

Step-by-step solution

STEP 1: Identify the gene pairs and inheritance pattern

First, let's analyze the data given for different ratios in F2 generation: - \(27 / 64\) blue, utterer - \(12 / 64\) green, utterer - \(9 / 64\) blue, mutterer - \(9 / 64\) purple, utterer - \(4 / 64\) green, mutterer - \(3 / 64\) purple, mutterer The ratios are consistent with Mendelian inheritance, specifically with a dihybrid cross with two gene pairs for each trait. This results in a 9:3:3:1 phenotypic ratio. 9 (Utterer, Blue Eyes) : 3 (Utterer, Green/Purple Eyes) : 3 (Mutterer, Blue Eyes) : 1 (Mutterer, Green/Purple Eyes)

STEP 2: Determine the number of gene pairs

(a) Since there is a 9:3:3:1 ratio, we can conclude that two total gene pairs are involved in inheritance of both eye color and croaking. One gene pair for croaking and one for eye color. (b) As previously mentioned, one gene pair controls eye color, and one gene pair controls croaking.

STEP 3: Assign gene symbols and identify genotypes

(c) Let's assign gene symbols as follows: - E for eye color: EE (blue eyes), Ee (green eyes), ee (purple eyes) - C for croaking: CC (utterer), Cc (mutterer) Now, we can determine the genotypes for each generation: - P1 (rib-it rib-it, purple eyes): eeCC - P1 (knee-deep knee-deep, green eyes): EECc - F1 (all utterers with blue eyes): EeCC - F2 (based on ratios given): - \(27 / 64\) blue, utterer: EeCC - \(12 / 64\) green, utterer: EECC - \(9 / 64\) blue, mutterer: EeCc - \(9 / 64\) purple, utterer: eeCC - \(4 / 64\) green, mutterer: EECc - \(3 / 64\) purple, mutterer: eeCc

STEP 4: Determine F1 and F2 phenotypic ratios for specific cross

(d) We want to know the phenotypic ratios for a cross between a blue-eyed mutterer (EeCc) and a purple-eyed utterer (eeCC). When these two frogs are crossed, the possible combinations for eye color genes are Ee and ee, and for croaking genes are Cc and CC. From these combinations in progeny, we can identify the following phenotypes: - \(\frac{1}{4}\) blue-eyed utterers (EeCC) - \(\frac{1}{4}\) blue-eyed mutterers (EeCc) - \(\frac{1}{4}\) purple-eyed utterers (eeCC) - \(\frac{1}{4}\) purple-eyed mutterers (eeCc) Summarizing the results: (a) Two gene pairs are involved. (b) One gene pair for eye color and one gene pair for croaking. (c) The genotypes for the P1, F1, and F2 generations are given above. (d) The phenotypic ratios for a cross between a blue-eyed mutterer (EeCc) and a purple-eyed utterer (eeCC) are 1:1:1:1.

Key concepts

Mendelian Inheritance

Mendelian inheritance is a type of biological inheritance that follows the laws originally proposed by Gregor Mendel in 1865. These laws were derived from his work on pea plants and they represent the cornerstone of classical genetics. Mendel concluded that organisms inherit traits by way of discrete units of inheritance, today known as genes.

Fundamental to Mendelian inheritance are the concepts of dominant and recessive alleles. A dominant allele is one that will express its effect even when paired with a different allele, while a recessive allele requires two copies to express its effect. Mendel's work demonstrated that the inheritance of each trait follows a specific pattern, which can be predicted through the use of Punnett squares and the understanding of genotype and phenotype.

The recent alien frog example follows a classic Mendelian dihybrid cross, revealing that the frogs have two distinct traits inherited independently – croaking sound and eye color. This can be explained by Mendel's law of independent assortment, which states that different genes are passed on independently of one another.

Dihybrid Cross

A dihybrid cross is a breeding experiment between P generation (parental generation) organisms that differ in two traits. Mendel's dihybrid crosses on peas led to his second law, the Law of Independent Assortment, which states that the alleles for a pair of traits segregate independently of each other during the formation of gametes.

In the exercise, the cross of two true-breeding lines of frogs with distinct croaking and eye color traits results in an F1 generation with a uniform phenotype. However, crossing these F1 individuals among themselves, thus performing a dihybrid cross, produced an F2 generation with diverse phenotypes distributed in a specific ratio. It's important for a student to grasp that this dihybrid cross unveils the independent inheritance of these traits and can be mapped using a 16-cell Punnett square to predict offspring.

Genotypic Ratios

The genotypic ratio refers to the ratio of different genetic combinations that can exist among offspring. This ratio is created by considering all possible allele combinations in the offspring's genotypes for a given set of parental alleles.

In the case of the frogs' inheritance patterns, assigning gene symbols allows us to differentiate between homozygous (same alleles) and heterozygous (different alleles) pairings. For instance, EE or ee for eye color, and CC or cc for croaking are homozygous, while Ee or Cc are heterozygous. The genotypic ratio is crucial for predicting the probability of an offspring inheriting a particular genotype.

It's insightful to note that the Mendelian ratio for a dihybrid cross is typically 9:3:3:1 for phenotypes, however, a deep dive into genotypes reveals a more detailed combination of allele pairings. With regard to the frog example provided, a variety of genotypes amongst the F2 generation can be calculated to mirror the 9:3:3:1 phenotypic ratio.

Phenotypic Ratios

The phenotypic ratio refers to the observable traits of the offspring in a particular cross, typically noted as a simple ratio or fraction. Unlike the genotypic ratio, which focuses on the underlying alleles, the phenotypic ratio looks at the expressed characteristics that are physical or biochemical.

In a dihybrid cross, if we consider two dichotomous traits, each with a dominant and recessive variant, and follow Mendelian inheritance patterns, we get the classic 9:3:3:1 phenotypic ratio. This ratio helps predict the likelihood of each phenotype occurring in the offspring. To put this into context, out of the 64 frog offspring in our example, we observed ratios like 27 blue-eyed utterers. These numbers are in line with the expected phenotypic ratios from a dihybrid cross with independent assortment of alleles.

Understanding phenotypic ratios is essential for genetics and can often help with identifying the types of alleles involved in trait inheritance, dominant or recessive, and can be a real-world application help for agricultural, medical, or conservation genetics.