Question

From 146 students tested for PTC tasting ability, 105 were tasters and 41 were non-tasters. Calculate the frequencies of tasters and non-tasters.

Short answer

The frequencies for tasters and non-tasters are approximately 0.719 and 0.281, respectively. This means that about 71.9% of the students are tasters, and 28.1% are non-tasters.

Step-by-step solution

Find the total number of students

To find the total number of students, we can simply add the numbers of tasters and non-tasters: \(146 = 105 + 41\).

Calculate the frequency of tasters

To find the frequency of tasters, divide the number of tasters by the total number of students: \[\text{Tasters frequency} = \frac{\text{Number of tasters}}{\text{Total number of students}}\] \[= \frac{105}{146} \approx 0.719\]

Calculate the frequency of non-tasters

Similarly, to find the frequency of non-tasters, divide the number of non-tasters by the total number of students: \[\text{Non-tasters frequency} = \frac{\text{Number of non-tasters}}{\text{Total number of students}}\] \[= \frac{41}{146} \approx 0.281\]

Present the results

Finally, the frequencies for tasters and non-tasters are approximately 0.719 and 0.281, respectively. This means that about 71.9% of the students are tasters, and 28.1% are non-tasters.

Key concepts

Genetics Frequency Calculations

Understanding the frequency of specific traits within a population is a fundamental exercise in genetics. Frequency, in this context, refers to how common a particular trait is among a given group of individuals.

For example, to calculate the frequency of a trait like PTC tasting ability, which is an inherited ability to taste the chemical compound phenylthiocarbamide, the number of individuals who can taste PTC ('tasters') is divided by the total number of individuals tested. It is essential to know that this ratio, expressed as a decimal, gives us a direct understanding of the trait's prevalence within a group.

Mathematically, it can be represented as:
\[\begin{equation}\text{Frequency} = \frac{\text{Number of individuals with trait}}{\text{Total number of individuals tested}}\end{equation}\]
In the exercise provided, the calculation was performed by dividing the number of tasters and non-tasters each by the total number of students to find their respective frequencies.

PTC Tasting Ability

PTC (phenylthiocarbamide) tasting ability is a heritable trait that varies among individuals. People can be broadly classified into 'tasters' or 'non-tasters' based on their sensitivity to the compound. This genetic variation is due to a difference in a single gene known as TAS2R38. The ability to taste PTC has been used in genetic and anthropological research as a classic example of a simple Mendelian trait with dominant and recessive alleles.

Those with a 'tasting' version of the gene (usually the dominant allele) will experience PTC as bitter, while those with a 'non-tasting' version (recessive allele) may not taste anything at all. The ability to taste PTC is not particularly advantageous or disadvantageous, but it serves as an easily studied marker of genetic variation.

Population Genetics

Population genetics is the study of the distribution and change in frequency of alleles within populations. This branch of genetics considers the genetic makeup of a population and how it evolves over time. Factors like natural selection, genetic drift, mutation, and gene flow influence these genetic variations.

Frequencies calculated like those for PTC tasting provide valuable data for population geneticists, as they can indicate the genetic structure of a population. By examining these frequencies and their changes over time or across different groups, scientists can infer patterns of inheritance, adaptation, and even historical migrations. In educational exercises, these calculations not only give students a first-hand experience with data analysis in genetics but also insights into the dynamics of evolution and the genetic links that connect populations.