Question

An abnormal behavior pattern called waltzing is seen in some mice. Waltzers twirl aimlessly and irregularly until they collapse exhausted. When waltzers and wild-type mice are crossed, the \(\mathrm{F}\), generation exhibits normal behavior but the \(F_{2}\) generation produces normal and waltzer mice in a \(3: 1\) ratio. Explain.

Short answer

The waltzing behavior in mice is controlled by a single gene with two alleles: the dominant allele W, responsible for normal behavior, and the recessive allele w, responsible for the waltzing behavior. The F1 generation has a normal phenotype because they are all heterozygous (Ww). After crossing two F1 mice with each other, the F2 generation follows a Mendelian 3:1 ratio (normal:waltzer), with 75% normal mice and 25% waltzer mice resulting from their genotypes (WW, Ww, and ww).

Step-by-step solution

Hypothesize the mode of inheritance

From the information given, hypothesize that the waltzing behavior is governed by a single gene, with two alleles: one dominant (W) which results in normal behavior, and one recessive (w) which causes the waltzing behavior.

Determine the genotypes of parents (P)

Since the waltzer mice exhibit the abnormal behavior, we can deduce that their genotype must be homozygous recessive (ww). On the other hand, wild-type mice have normal behavior, which means they can either be homozygous dominant (WW) or heterozygous (Ww).

Set up the Punnett square for the F1 generation

Cross a waltzer (ww) mouse with a wild-type (Ww) mouse. The Punnett square would look like this: | | W | w | |---|-----|-----| | w | Ww | ww | | w | Ww | ww | Note that we don't use WW wild-type mice for the cross because the F1 generation exhibits normal behavior. A WW x ww cross would result in Ww offspring, but it is more likely that this cross involves two heterozygous Ww parents.

Examine the genotypes of the F1 generation

From the Punnett square, we see that all of the F1 offspring have the genotype Ww. Since the dominant allele (W) is responsible for normal behavior, all F1 mice will exhibit normal behavior.

Set up the Punnett square for the F2 generation

Now, cross two F1 mice (both Ww). Their Punnett square would look like this: | | W | w | |---|-----|-----| | W | WW | Ww | | w | Ww | ww |

Analyze the genotypes and phenotypes of the F2 generation

From the F2 generation Punnett square, we can see the following genotypes: - WW: 1/4 - Ww: 1/2 - ww: 1/4 Since the W allele is dominant and responsible for normal behavior, mice with WW or Ww genotypes will exhibit normal behavior. Mice with ww genotype will exhibit the waltzing behavior. Calculating the ratios, we have 1/4 + 1/2 = 3/4 (75%) normal mice and 1/4 (25%) waltzer mice, which follow the given 3:1 ratio in the problem statement.

Conclusion

The waltzing behavior in mice is controlled by a single gene with two alleles: the dominant allele W, responsible for normal behavior, and the recessive allele w, responsible for the waltzing behavior. The F1 generation has a normal phenotype because there are two heterozygous (Ww) individuals. After crossing with each other, the F2 generation follows a Mendelian 3:1 ratio (normal:waltzer).

Key concepts

Punnett Square

The Punnett square is a simple graphical way to predict the results of a genetic cross. It's a grid that allows us to determine which alleles from the parents can combine when they reproduce. Here’s how it works:

Start with the genotype of each parent, which consists of two alleles, one from each of their own parents. Place one parent’s possible alleles along the top row and the other parent’s along the side column. For the waltzer mice example, we’d put the wild-type mouse (Ww) along the top and the waltzer mouse (ww) along the side. Then, fill in the boxes by combining the alleles from the top row and side column.

Each box represents a possible genotype for their offspring. The resulting Punnett square for the F1 generation shows all offspring will be Ww - heterozygous for the trait, exhibiting normal behavior due to the dominant ‘W’ allele.

Genotype

A genotype is the genetic makeup of an organism, referring to the specific combination of alleles that it carries for a particular gene. Alleles are different forms or variations of the same gene. In our example, we have two alleles: W for the normal behavior and w for the waltzing behavior. Organisms can be homozygous, meaning they have two identical alleles (like WW or ww), or heterozygous, with two different alleles (like Ww). The genotype is like the recipe for the trait, whereas the resulting physical expression will be the finished dish, known as the phenotype. In the waltzer mice case, mice with Ww and WW genotypes display the same phenotype because the W allele masks the expression of the w allele.

Phenotype

The phenotype is the observable physical or physiological trait of an organism, which arises from the interaction of its genotype with the environment. Unlike genotypes, phenotypes are what you can see or measure directly. For instance, in the mouse example, the phenotype can be categorized as either ‘normal behavior’ or ‘waltzing behavior.’ Although F1 generation mice have the Ww genotype, their phenotype will be normal due to the presence of the dominant allele W. The observed 3:1 ratio of normal to waltzing mice in the F2 generation is a clear manifestation of phenotypes directly influenced by their genotypes.

Dominant and Recessive Alleles

Genes have different versions called alleles, and these can be either dominant or recessive. Dominant alleles, like ‘W’ for normal behavior in mice, are expressed in the phenotype even if there is only one copy present in the genotype. In contrast, recessive alleles, like ‘w’ for waltzing behavior, are masked by dominant alleles and are only expressed when two copies are present (as in genotype ww).

An organism with a dominant allele will exhibit the dominant trait, while the recessive trait will only be seen if the organism is homozygous recessive. This is precisely what we observe in the F2 generation of the waltzer mice exercise: 75% show the dominant phenotype (normal behavior) because they have at least one W allele, and the remaining 25% are homozygous recessive (ww) displaying the recessive phenotype (waltzing behavior).