Question

In a study of black guinea pigs and white guinea pigs, 100 black animals were crossed with 100 white animals, and each cross was carried to an \(\mathrm{F}_{2}\) generation. In 94 of the crosses, all the \(\mathrm{F}_{1}\) offspring were black and an \(\mathrm{F}_{2}\) ratio of 3 black: 1 white was obtained. In the other 6 cases, half of the \(\mathrm{F}_{1}\) animals were black and the other half were white. Why? Predict the results of crossing the black and white \(\mathrm{F}_{1}\) guinea pigs from the 6 exceptional cases.

Short answer

Answer: The predicted result for crossing the black and white F₁ guinea pigs from these 6 exceptional cases is a 1:1 black-to-white ratio in the offspring.

Step-by-step solution

Understand the typical Mendelian inheritance pattern

In the 94 typical cases, all of the \(\mathrm{F}_{1}\) offspring were black, and the \(\mathrm{F}_{2}\) generation showed a 3:1 black-to-white ratio. This indicates that the black guinea pig color is dominant, which we can represent with the letter B, and the white color is recessive, represented with the letter b. Hence, all 94 typical crosses can be represented as BB x bb, resulting in all Bb (black) offspring in the \(\mathrm{F}_{1}\) generation.

Analyze the 6 exceptional cases

In the 6 exceptional cases, half of the \(F_{1}\) offspring were black and the other half were white. We can deduce that one parent must have been heterozygous (Bb) and the other homozygous recessive (bb). We can represent the cross as Bb x bb for these exceptional cases. Since we have to study the same black and white guinea pigs, we cross black \(\mathrm{F}_{1}\) guinea pigs with white \(\mathrm{F}_{1}\) guinea pigs from the exceptional cases, which is equivalent to Bb x bb.

Predict the results of the exceptional cross

Now, let's use a Punnett square to determine the offspring genotype and phenotype ratios for the exceptional cross of Bb x bb: | | B | b | |---|---|---| | b | Bb | bb | | b | Bb | bb | As we can see, 50% of the offspring are expected to have the Bb genotype (black color) and 50% are expected to have the bb genotype(white color). Therefore, the predicted result of crossing the black and white \(\mathrm{F}_{1}\) guinea pigs from the 6 exceptional cases is 1:1 black-to-white ratio in the offspring.

Key concepts

Punnett Square

A Punnett square is a simple graphical way of predicting all possible genotypes of an offspring from two parents. It's a handy tool used in genetics to visualize and calculate the probability of an offspring inheriting specific traits. Here's how to use it:

Using the letters B and b to represent dominant and recessive alleles respectively, we can create a square divided into four parts. Each part will represent a possible genotype for the offspring. For a cross of homozygous dominant (BB) and homozygous recessive (bb) parents, you place the alleles of one parent across the top and the alleles of the other along the side.

Creating the Punnett Square for the Typical Cases

For the 94 typical cases of black and white guinea pigs, the square would look like this:| | B | B ||---|---|---|| b | Bb | Bb || b | Bb | Bb |Each box now represents the genotype of one potential offspring. Since B (black) is dominant over b (white), all the offspring are black, having the genotype Bb.

Using this method allows students and geneticists alike to predict the likelihood of traits in offspring, making it a fundamental tool in understanding Mendelian inheritance.

Genotype and Phenotype Ratios

In genetics, the terms 'genotype' and 'phenotype' describe different aspects of the genetic makeup and physical characteristics of an organism. The genotype refers to the genetic constellations (alleles) present in the organism, while the phenotype is the observable traits expressed.

Understanding Genotype and Phenotype through Ratios

A ratio is a way to express the proportion of different genotypes or phenotypes in a given population. In our guinea pig example, the typical Mendelian inheritance pattern was observed with a phenotype ratio in the \(F_2\) generation of 3 black:1 white, which means that for every four offspring, three are expected to show the dominant trait (black color), and one the recessive trait (white color).The genotype ratio, often closely examined in an \(F_2\) generation, represents the frequency of the genotypes among the offspring. A 1:2:1 genotype ratio—1 homozygous dominant (BB), 2 heterozygous (Bb), and 1 homozygous recessive (bb)—is characteristic of a Mendelian monohybrid cross of two heterozygous parents.Understanding these ratios is crucial as it helps predict the expected genotypes and phenotypes in offspring which, in turn, can be applied to more complex inheritance patterns.

Dominant and Recessive Traits

Dominant and recessive traits are fundamental in understanding the patterns of inheritance described by Gregor Mendel, the father of genetics. Dominant traits are those that are expressed or seen when a heterozygous genotype is present. Recessive traits, on the other hand, are only expressed when two recessive alleles are present (homozygous recessive).

Identifying Dominant and Recessive in Guinea Pigs

Using our guinea pigs scenario, the black coat color is a dominant trait, represented by B. White coat color is a recessive trait, represented by b. This means that a guinea pig only needs one allele for black coat color (B) to appear black. For a guinea pig to be white, it must have two white alleles (bb), as white is masked by black if both alleles are present (Bb).In those 6 exceptional cases where the \(F_1\) generation showed a 1:1 ratio of black to white, it revealed that not all dominant traits are homozygous dominant. Instead, one of the parents was carrying both a dominant and a recessive allele (Bb), making some patterns of inheritance less straightforward and demonstrating the complexity within even the most classic genetic principles.