Punnett Squares

Dominant and recessive phenotypes

A natural question that arises is how can we translate genotypes to phenotypes; given a specific genotype, what phenotype will be displayed? This question is simplified in the case of homozygotes because both alleles correspond to the same phenotype. For example, let's say that the B allele encodes the brown eye phenotype and the b allele encodes the blue eye phenotype. Then, it follows that a BB homozygote will certainly have brown eyes and a bb homozygous individual will definitely have blue eyes. However, what happens in the case of a heterozygous Bb individual?

In the case of eye color, a heterozygous Bb individual will have brown eyes. This brown eye phenotype (and therefore the B allele) is said to be dominant, whereas the blue eye phenotype (and the b allele) is recessive. In fact, in genotype notation, uppercase letters denote dominant alleles whereas lowercase letters denote recessive alleles.

As an example, let's talk earlobes. Humans can have either attached or detached earlobes:

This earlobe phenotype is determined by a genotype. Through many studies, it has been determined that attached earlobes is a dominant phenotype and detached earlobes is a recessive phenotype.*

Phenotype ratios

We can visualize the inheritance of genotypes from parents to offspring using Punnett squares. Punnett squares show the genotype of each parent along two sides of a square and all of the potential genotypes of the offspring inside the square. Recall that Mendel often observed a 3 : 1 ratio of dominant to recessive phenotypes (phenotypes included pea color, plant height, flower color, etc.) when he crossed two heterozygous peas. Using a Punnett square, we can understand why a Aa x Aa cross (heterozygous cross) yields this ratio: essentially, this cross had four possible offspring with equal probability:

• 1 AA genotype, dominant phenotype

• 2 Aa genotype, dominant phenotype

• 1 aa genotype, recessive phenotype

Let’s say we want to write a piece of code to determine if a given sample shows a 3:1 phenotype ratio. We can store each of the observed numbers of pea phenotypes in a variable, and then divide these values to calculate the phenotype ratio.

To determine if this ratio is equal to 3, we can deploy an if statement.

If you flipped a coin 100 times and observed 57 heads and 43 tails, would you assume that the coin was rigged? Probably not. In the same way, phenotypic ratios can vary slightly around the ‘true’ or expected value due to random chance. In a real scientific experiment, we do not expect to observe an exact 3 : 1 phenotype ratio due to random noise in the system. For example, if you flip a fair coin twice, you will most often observe one head and one tail, but that is not necessarily true. If you continue to flip your coin hundreds of times, you are increasingly likely to observe approximately 50% heads and 50% tails. In real life, we would need to modify the above code to accommodate an approximate 3 : 1 ratio, rather than an exact 3 : 1 ratio. Let's say that we will allow ratios as low as 2.7 and as high as 3.3 (plus or minus 10% of 3) to be called a 3 : 1 ratio. Then, our if statement would look look like the following:

Now it's your turn!

1. Write code to determine if Mendel observed a 3 : 1 phenotype ratio in his pea texture data (he observed 1005 smooth peas and 350 wrinkled peas) and his pea plant heights (he observed 6 tall plants and 1 short plant).

A note about coding...

Although writing this code right now may not feel more efficient than doing the calculation by hand, imagine if you had hundreds of experiments -- the reusability of the code would allow you perform this analysis much more quickly and accurately. As you'll learn in subsequent lessons, we can use a single block of code to quickly analyze many different samples.

What if we asked you to predict phenotypes from genotypes? You know now that in a Mendelian trait, homozygous dominant (AA) and heterozygous (Aa) genotype carriers will display the dominant phenotype, while homozygous recessive genotype carriers will display the recessive phenotype.

What do peas have to do with human health?

So far, we've talked about Mendelian inheritance in terms of traits like pea color and eye color. However, Mendelian inheritance also governs the transmission of many less desirable qualities, such as diseases. We refer to these diseases, appropriately, as "Mendelian diseases." Mendelian diseases can be recessive (examples include Tay-Sachs disease and cystic fibrosis) or dominant (examples include Huntington's disease and Marfan syndrome).

Although there are many Mendelian traits, most traits are not actually controlled by a single gene. Instead, many different genes contribute to the final phenotype. We refer to these traits as "polygenic" (i.e. "multiple genes"). For example, height, skin tone, weight, and susceptibility to heart disease are polygenic. In the next section, we will discuss principles applicable to the study of these kinds of traits, which necessitate more advanced computational skills and tools.

*Note: recent work has shown that attached and detached earlobes are likely the result of a more complicated genetic model than dominant/recessive, but we have kept the text here to illustrate the general principle (for more information, see this story).