Question

A man and a woman are heterozygous for tongue rolling, and have three sons. The three sons marry women who are not tongue rollers. Assuming that each of the three sons has a different genotype, show by diagram what proportion of their children might have the ability to roll their tongues.

Short answer

On average, 50% of the children from the three sons' marriages might have the ability to roll their tongues. This is calculated based on each son's genotype (RR, Rr, rr) and their wives' genotypes (rr, rr, rr), using Punnett squares to analyze each marriage's offspring.

Step-by-step solution

Understand the genetics of tongue rolling

The ability to roll one's tongue is a dominant trait (represented by R), while the inability to roll the tongue is a recessive trait (represented by r). Since both the man and the woman are heterozygous tongue rollers (Rr), they can pass either the dominant or the recessive gene to their children. The three sons must have different genotypes: RR, Rr, and rr.

Analyze the first son's marriage (RR)

The first son has a genotype of RR, which means he can pass on either the dominant gene R or the same dominant gene R, giving a 100% probability of passing on the dominant gene for tongue rolling. His wife, however, has a genotype of rr (not tongue rollers) and can only pass on the recessive gene, r. Using a Punnett square to analyze their offspring, we get: | | R | R | |:-:|----|----| | r | Rr | Rr | | r | Rr | Rr | All their children (100%) will have the genotype Rr, and thus, the ability to roll their tongues.

Analyze the second son's marriage (Rr)

The second son has a genotype of Rr, which means he can pass on either the dominant gene R or the recessive gene r. His wife, like the first son's wife, has a genotype of rr (not tongue rollers) and can only pass on the recessive gene, r. Using a Punnett square to analyze their offspring, we get: | | R | r | |:-:|----|----| | r | Rr | rr | | r | Rr | rr | Half of their children (50%) will have the genotype Rr (tongue rollers), and the other half will have the genotype rr (not tongue rollers).

Analyze the third son's marriage (rr)

The third son has a genotype of rr, which means he can only pass on the recessive gene r. His wife, like the other sons' wives, has a genotype of rr (not tongue rollers) and can also only pass on the recessive gene, r. Using a Punnett square to analyze their offspring, we get: | | r | r | |:-:|----|----| | r | rr | rr | | r | rr | rr | All their children (100%) will have the genotype rr, and thus, no ability to roll their tongues.

Calculate the overall proportion of children with tongue rolling ability

Now, we need to combine the proportions from the marriages to find the overall proportion of children with the ability to roll their tongues in the next generation: - First son's marriage: 100% of children are tongue rollers - Second son's marriage: 50% of children are tongue rollers - Third son's marriage: 0% of children are tongue rollers If we assume each son has the same number of children, the overall proportion of tongue rolling children in the next generation will be: \((100\% + 50\% + 0\%)/3 = 50\%\) So, on average, 50% of the children from these marriages might have the ability to roll their tongues.

Key concepts

Genotype and Phenotype

When we talk about genetics, the terms 'genotype' and 'phenotype' are fundamental to understanding heredity.
The genotype refers to the genetic makeup of an individual – that is, the set of genes that they carry. For example, regarding tongue rolling, 'RR', 'Rr', or 'rr' are all possible genotypes one could have. These combinations determine the potential traits that can be passed on to offspring.

On the other hand, the phenotype is the physical expression or characteristics of that genotype. This means it's what you can actually observe. So, for tongue rolling, the phenotype is whether the individual can or cannot perform the act of rolling their tongue.

In the given problem, the phenotype of both the man and the woman is that they can roll their tongues, but their genotype is 'Rr', meaning they carry one dominant and one recessive allele for the trait.

Punnett Square

To predict the outcomes of genetic crosses, biologists use a tool called a Punnett square. It's like a simple grid that allows us to visualize how alleles from each parent can combine in their offspring.
A Punnett square maps out all possible combinations of parental alleles based on their genotypes. For example, if a parent is heterozygous for tongue rolling ('Rr'), they can contribute either an 'R' (dominant) or an 'r' (recessive) allele.

When solving genetic problems like the one involving tongue rolling ability, we create a Punnett square for each parental pairing to see the chances of their children inheriting certain traits. As illustrated in the solution, this powerful tool simplifies the calculation of probabilities, helping us predict the genotype and phenotype frequencies in offspring.

Dominant and Recessive Traits

In genetics, traits are determined by alleles, with each characteristic typically having a dominant and a recessive version. Dominant alleles are expressed even if only one copy is present (hence the 'R' for rolling tongues), whereas recessive alleles are masked by dominant ones and only show up when both alleles are recessive.

In the context of tongue rolling, the ability to roll the tongue is a dominant trait, represented by 'R'. Conversely, the inability to do so is a recessive trait, represented by 'r'. This means that a person needs just one copy of the 'R' allele to be able to roll their tongue.

The exercise shows the inheritance pattern of these traits clearly. The first son has two dominant alleles ('RR'), the second has one of each ('Rr'), and the third has two recessive alleles ('rr'), leading to varying proportions of offspring with the tongue-rolling phenotype. This is a classic example of how dominant and recessive traits are passed on and expressed in a simple Mendelian inheritance pattern.