Question

In mice, a short-tailed mutant was discovered. When it was crossed to a normal long-tailed mouse, 4 offspring were short-tailed and 3 were long-tailed. Two short-tailed mice from the \(\mathrm{F}_{1}\) generation were selected and crossed. They produced 6 short-tailed and 3 long-tailed mice. These genetic experiments were repeated three times with approximately the same results. What genetic ratios are illustrated? Hypothesize the mode of inheritance and diagram the crosses.

Short answer

Answer: The hypothesized mode of inheritance for the short-tailed phenotype is simple Mendelian dominance. The genetic ratios observed in the offspring are 4:3 for the initial cross and 2:1 for the \(\mathrm{F}_{1}\) cross.

Step-by-step solution

Analyze the Initial Cross

In the initial cross between a short-tailed mouse and a long-tailed mouse, 4 offspring were short-tailed and 3 were long-tailed. Let's express the short-tailed phenotype as "S" and the long-tailed phenotype as "L." We will use the given information to determine the probability of offspring having either phenotype. Probability of short-tailed offspring (S) = \(\frac{4}{7}\) Probability of long-tailed offspring (L) = \(\frac{3}{7}\)

Analyze the \(\mathrm{F}_{1}\) Cross

In the cross between two short-tailed \(\mathrm{F}_{1}\) mice, 6 offspring were short-tailed and 3 were long-tailed. We will calculate the probability of offspring having either phenotype. Probability of short-tailed offspring (S) = \(\frac{6}{9} = \frac{2}{3}\) Probability of long-tailed offspring (L) = \(\frac{3}{9} = \frac{1}{3}\)

Determine the Genetic Ratios

The genetic ratios can be derived from the probability of each phenotype in the offspring. For the initial cross: S : L = 4 : 3 For the \(\mathrm{F}_{1}\) cross: S : L = 2 : 1

Hypothesize the Mode of Inheritance

Given the data, we can hypothesize that short-tailed phenotype is dominant and follows a simple Mendelian inheritance pattern. This assumption is based on the ratio of phenotypes observed in the offspring and the fact that crossing two short-tailed mice still produced long-tailed offspring.

Diagram the Crosses

Initial cross (P generation): Short-tailed (SS) x Long-tailed (LL) = \(\mathrm{F}_{1}\) generation Offspring: Short-tailed (SL), Short-tailed (SL), Short-tailed (SL), Short-tailed (SL), Long-tailed (LL), Long-tailed (LL), Long-tailed (LL) (in a 4:3 ratio) \(\mathrm{F}_{1}\) cross: Short-tailed (SL) x Short-tailed (SL) = \(\mathrm{F}_{2}\) generation Offspring: Short-tailed (SS), Short-tailed (SL), Short-tailed (SL), Short-tailed (SL), Short-tailed (SL), Short-tailed (SL), Long-tailed (LL), Long-tailed (LL), Long-tailed (LL) (in a 6:3 or 2:1 ratio)

Key concepts

Genetic inheritance patterns

Understanding genetic inheritance patterns is fundamental in genetics. These patterns explain how traits are passed on from parents to offspring and can predict the likelihood of an offspring having a particular trait. In the classic mouse tail length example, the patterns observed in the offspring suggest that the trait is inherited in a straightforward manner.

Essentially, there are several inheritance patterns, with Mendelian inheritance being one of the most fundamental. Others include incomplete dominance, co-dominance, X-linked inheritance, and polygenic inheritance. The short-tailed and long-tailed traits in mice follow a pattern consistent with Mendel's principles, which provides a clear example of a single gene with two alleles influencing a single trait.

Phenotypic ratios

The term phenotypic ratios refers to the relative numbers of offspring exhibiting each different phenotype. It's a clear way to express the result of a genetic cross. In our mouse example, the first cross resulted in a 4:3 phenotypic ratio, and the second cross in a 2:1 ratio. These ratios provide insight into the dominance and recessiveness of the alleles involved.

Such ratios aid scientists and students alike in deciphering the genetic makeup of the parents. When teaching these concepts, explaining that these ratios stem from the principles of probability and segregation of alleles during gamete formation can be invaluable for understanding.

Mendelian inheritance

Named after Gregor Mendel, who laid the foundation for modern genetics, Mendelian inheritance encompasses the basic laws of inheritance. Mendel observed that traits are passed from parents to offspring in predictable patterns.

There are two key principles: the law of segregation, which states that allele pairs separate during gamete formation, and the law of independent assortment, indicating different genes independently separate from one another when reproductive cells develop. The mouse tail length cross demonstrates the law of segregation, as the alleles for tail length separated into the gametes, producing the phenotypic ratios observed.

Genotype and phenotype

Genotype refers to the genetic makeup of an individual, including all their genes, while phenotype is the observable physical or biochemical characteristics of an organism, as determined by both genotype and environmental influences.

In the mouse example, genotypes represented by 'SS' or 'SL' correspond to the short-tailed phenotype, whereas 'LL' corresponds to long-tailed mice. The distinction between genotype and phenotype is critical in understanding how certain traits appear in an organism and predicting how those traits may be passed on to future generations.

Dominant and recessive traits

The concepts of dominant and recessive traits are pivotal to Mendelian genetics. A dominant trait is expressed or visible when at least one dominant allele for a characteristic is inherited. A recessive trait, on the other hand, requires that the organism inherits two copies of the recessive allele for the characteristic to be expressed.

For instance, in our mouse exercise, the short-tailed trait appears to be dominant, as it is expressed in mice that have either one or two 'S' alleles. On the flip side, the long-tailed trait is recessive, only appearing in mice with two 'L' alleles. When teaching this concept, using pedigrees or Punnett squares can greatly help students visualize and understand how dominant and recessive traits are inherited through generations.