A Bitter Gene to Swallow\text{A Bitter Gene to Swallow}

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A gif showing broccoli, chocolate, spinach, and coffee.

DNA is kind of a big deal despite being so small. In honor of DNA Day, let’s explore how our genetic information is inherited.

Hidden inside of DNA are segments of code called genes, which contain specific kinds of genetic information called alleles. An organism with at least one form of a dominant allele will display that form of the trait. As a toy model, let’s look at how we inherit the recessive allele for PTC non-tasting.

Coffee, spinach, and dark chocolate all contain a sizeable amount of the chemical compound PTC. People who can taste PTC find it to being incredibly bitter and will often avoid eating the foods that contain it. Some people, however, can’t taste the PTC and are aptly called “non-tasters”. They do not experience the bitter flavor of broccoli and kale. Lucky them.

The ability to taste the chemical compound PTC is controlled by a single gene called TAS2R38. Coincidentally, this is the top baby name of 2018. TAS2R38 has two common alleles: the dominant PTC-tasting and the recessive PTC non-tasting. In order to inherit the non-tasting trait, you need two copies of that recessive allele.

Let’s let T be the tasting allele and N be the non-tasting allele. Suppose a population has the genotypes (gene combinations) TT, TN, and NN. Each combination respectively makes up 0.49, 0.42, and 0.09 of the population. Assume that all pairings occur randomly and that the population is large.

How long will it take the recessive PTC non-tasting trait to disappear from the gene pool? In other words, how long until the population contains no NN genotypes?

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