Question

The trait represented in the pedigree below is inherited through a single dominant gene. Calculate the probability of the trait appearing in the offspring if the following cousins should marry. (a) \(\mathrm{F}_{2,2} \times \mathrm{F}_{2,4}\); (b) \(\mathrm{F}_{2,1} \times \mathrm{F}_{2,3}\)

Short answer

(a) The probability of the trait appearing in the offspring for the cousin pair \(\mathrm{F}_{2,2} \times \mathrm{F}_{2,4}\) is 75%. (b) The probability of the trait appearing in the offspring for the cousin pair \(\mathrm{F}_{2,1} \times \mathrm{F}_{2,3}\) is also 75%.

Step-by-step solution

Analyze the Pedigree

In the pedigree, we can identify individuals with the trait and without the trait. If an individual has the trait, their genotype must be either heterozygous or homozygous dominant (with at least one dominant allele). If an individual does not have the trait, their genotype must be homozygous recessive (with two recessive alleles). Let's denote the dominant allele as "D" and the recessive allele as "d." Using this information, we can infer the genotypes of the family members as follows: - F₁,₁: D? - F₁,₂: recessive (dd) since they do not have the trait - F₂,₁: Dd (one dominant allele from F₁,₁ and one recessive allele from F₁,₂) - F₂,₂: Dd (one dominant allele from F₁,₁ and one recessive allele from F₁,₂) - F₂,₃: Dd (one dominant allele from F₁,₁ and one recessive allele from F₁,₂) - F₂,₄: Dd (one dominant allele from F₁,₁ and one recessive allele from F₁,₂)

Calculate Probabilities for Cousin Pairings

Now that we know the genotypes, we can calculate the probability of the trait appearing in the offspring for each cousin pair using the Punnett square method. (a) \(\mathrm{F}_{2,2} \times \mathrm{F}_{2,4}\): | | D | d | |---|---|---| | D | DD | Dd | | d | Dd | dd | The result is a: - 25% chance of DD (homozygous dominant) - 50% chance of Dd (heterozygous) - 25% chance of dd (homozygous recessive) Since the trait is dominant, both DD and Dd will have the trait. Therefore, the probability of the trait appearing in the offspring is 75%. (b) \(\mathrm{F}_{2,1} \times \mathrm{F}_{2,3}\): | | D | d | |---|---|---| | D | DD | Dd | | d | Dd | dd | The result is the same as the previous situation: - 25% chance of DD (homozygous dominant) - 50% chance of Dd (heterozygous) - 25% chance of dd (homozygous recessive) Again, since the trait is dominant, both DD and Dd will have the trait. Therefore, the probability of the trait appearing in the offspring is 75%.

Key concepts

Dominant Inheritance

When we talk about dominant inheritance, we're referring to the way certain traits are passed down through generations. In genetics, if a trait is dominant, it means that only one copy of the gene is necessary for the trait to be expressed. This is opposed to recessive traits, which require two copies of the gene (one from each parent) to be visible in an individual.

In our exercise, the trait in question is inherited in a dominant fashion, meaning if an individual carries even one allele (the form of a gene) for the trait, they will show it. This can lead to a variety of genetic combinations in offspring, subsequently affecting the likelihood—a referred to as probability—that the offspring will show the trait in question.

Punnett Square

A key tool used in the study of genetics is the Punnett square. It's a diagram that lets us predict the genotypic and phenotypic outcomes of a genetic cross. It's named after Reginald Punnett, a British geneticist who devised the method. The square allows us to plot possible combinations of maternal and paternal alleles and thus assess the probability of their offspring displaying certain genetic traits.

In the problem we're discussing, we use a simple 2x2 Punnett square to visually represent the genetic crossing of two individuals (the cousins), where the alleles 'D' (dominant) and 'd' (recessive) are combined. The Punnett square helps us understand the possible genotypes of their offspring and, since 'D' is dominant, how likely it is that the offspring will display the trait.

Genotypic Ratio

The term genotypic ratio refers to the ratio of different genotypes that come from a particular genetic cross, like the breeding of our two cousins in the exercise. This ratio is expressed as a proportion of the total possibilities of genotypes. For example, in a simple dominant-recessive cross like our hypothetical cousins, you might end up with a genotypic ratio that can be 1:2:1.

This ratio corresponds to one part homozygous dominant (DD), two parts heterozygous (Dd), and one part homozygous recessive (dd). Therefore, our exercise solution indicates a genotypic ratio of 1 DD : 2 Dd : 1 dd for the offspring of each cousin pair, when simplifying it to the probabilities of each genotype manifesting.

Probability of Genetic Traits

The probability of genetic traits can be affected by how genes are inherited (dominance and recessiveness) and the specific genotypes of the parents. Probability, in genetics, is a way to quantify the likelihood of a particular trait being expressed in the next generation.

By performing a cross like the one between our hypothetical cousin pair and using a Punnett square, we calculate that there is a 75% chance of the dominant trait appearing in the offspring. This is because there is a 25% chance for homozygous dominant (DD), a 50% chance for heterozygous (Dd), and a 25% chance for homozygous recessive (dd) genotypes to occur. In this instance, since we're considering a dominant trait, the combined probability of showing the trait (either DD or Dd) is the sum of their individual probabilities, resulting in 75%.