Monday, January 10, 2022

Mendelian Genetics And Probability

Biology Index

Where are we going with this? The information on this page should increase understanding related to this standard:  Identify patterns of inheritance to predict genotype/phenotype and solve punnett square problems.

Article includes ideas, images, and content from Troy Smigielski (2022-01)

Mendelian Genetics And Probability
(Why does this make me think of Star Wars?)

To get started, let's reprise some of the content from the overview page

Gregor Mendel is a famous scientist who studied the genetics of pea plants. 

He coined the terms “dominant” and “recessive” to describe alleles.


Over the course of seven years, Mendel conducted several experiments that led him to this conclusion.

Check out the overview page for more information on what he found out!

What does this tell us?

Mendel concluded that alleles must separate independently from each other in meiosis so that each gamete (reproductive cell) only carries one allele.

He called this the Law of Segregation.

This is essentially confirming how meiosis works.

Punnett Squares

These days, we can do Mendel's experiment using a Punnett square. Check this out!

Punnett square is a diagram used to predict the genotype and phenotype of offspring.

To do a Punnett Square, put the genotype of one parent at the top and the other parent down the side. Then, make the matches of the alleles. 

In the square to the left of the image, there is a capital P in each box, so all of the flowers expressed the purple trait. 

In the Punnett Square to the right, mixing two Pp flowers allowed for one box to have the pp genotype resulting in a phenotype of being white.

Okay… now, on to using this to make predictions…

Probability and Ratios

Suppose you cross the flowers like Mendel did… What is the probability that you will get a white flower? Obviously, you'd need to know the genotype of the parent flowers, but you also need to know how to go from some "this out of that" number thing, to percentages.

Probability is the odds of a certain event happening. It can be expressed as a "this out of that" chance or as a percentage.
  • What is the probability of a coin flip landing on heads?
  • What is the probability of a coin flip landing on heads four times in a row?
  • What is the probability of a coin flip landing on heads if the previous 6 flips landed on tails?
These are questions that understanding probability will allow you to answer.

Say you flip a coin 6 times. How many would you expect to land on heads? On tails? Since there are only two sides to a coin, it has to come up heads or tails. And it makes sense that either one could come up.

So you'd expect to get 3 heads and 3 tails.

A ratio is a way of expressing the number of one thing compared to the number of another thing. For instance, in water, there is a fixed ratio of hydrogen and oxygen atoms: 2:1. Bicycles have a ratio of 2 tires for every 1 handlebars. Skateboards have a ratio 4 wheels per 1 deck. Birds have 2 wings per 1 beak. Birds also have a ratio of 2 wings per 2 feet.

Usually, you want to reduce your numbers to "lowest terms" so you'd say birds have a 1 to 1 ratio of beaks to wings.

So, when you flip a coin, you can expect to get the same number of heads and tails. Thus, the expected ratio is what you should get in a theoretical situation.

But, what actually happens does not always follow what is expected. It is possible to flip a coin 6 times and get heads 5 times. The actual ratio is a report of what really happened in an actual trial situation.

While some things are bound to fixed ratios (like bicycles having a 2 to 1 wheel to handlebar ratio), other things are free to vary. 

Some things are constrained to a fixed ratio by design (bicycles) or laws of nature (water). 

Other things tend to follow a fixed ratio, but are free to vary. Like flipping a coin.

Where things only tend to follow a fixed ratio, it is possible to get surprising results. It is certainly possible to flip a coin and get "heads" 10 times in a row. However, it is unlikely. Or another way to say that is this:

"The probability is very low."

The more times you flip a coin, the less effect "luck" will have on the out come. You might get "lucky" and flip "heads" three times. Maybe four. But, you are equally lucky to get "unlucky" and flip "tails" the same number of times.

In the long run, the more times you flip the coin, the closer to a 1 to 1 ratio you'll get.

Here, it's worth pausing to add that ratios can be written with a colon. So, 1 to 1 would be written as 1:1.

We will be working with probabilities and ratios when we do Punnett squares, and the same concept applies.

When crossing parents with different genotypes, the more children you have, the closer to the expected ratio you will get.

The diagram used by geneticists to predict gene combinations and probabilities is called a Punnett square. These are commonly used to test for the presence of genetic disorders.

Stem Cells and Research into Genetic Disorders

  • Cystic fibrosis is a disorder that causes the body to produce thick, sticky mucus that can clog up the lungs.
  • Huntington’s disease is a brain disorder that causes uncontrollable movements and loss of thought, and it generally appears around age 30-40.
  • Hemochromatosis is a disorder where too much iron is absorbed in your body.

Scientists are beginning to investigate the use of stem cells to treat some of these disorders and other neurological (CNS or PNS) disorders such as Alzheimer’s disease. 

Stem cells that can develop into any kind of bodily cell are called pluripotent cells. 

The cells that have found their place and function in an organism are referred to as differentiated cells.

Stem cells divide to create division of labor (to divide the workload of the body). A stem cell can differentiate into specific types of cells.

Example of differentiated cells: Neuron

A neuron is a cell of the nervous system. 

The elongated, branched structures of these cells enable them to receive and transmit electrical messages quickly.

Example of differentiated cells: Muscle

Muscle cells are responsible for producing force and motion. 

These cells have filaments that move past each other to change the size of the cell, allowing it to contract and relax.

Example of differentiated cells: Blood

Red blood cells transport oxygen. 

They are disc-shaped, thinner in the center than at the edges. This shape maximizes the surface area available to transport oxygen and allows the cells to pass through the narrowest blood vessels.

Okay… back to Punnett Squares!

As we were saying…

The diagram used by geneticists to predict gene combinations and probabilities is called a Punnett square. These are commonly used to test for the presence of genetic disorders.

If a child has the genotype “ee”, he/she will suffer from sickle-cell anemia.

If both parents are heterozygous for the sickle-cell anemia trait, what are the chances that their child will have the disease? Will not have the disease?

If a child has the genotype “ee”, he/she will suffer from sickle-cell anemia. That is to say that the expressed trait, the phenotype would be the presence of sickle-cell anemia.

So, that will look like this:

So, the phenotype of the offspring would occur in an expected Dominant:recessive ratio of 3:1.

From the Punnett square, you can also find a genotype ratio. Since there are three possible combinations in the above, you can find a ratio of EE:Ee:ee (Think of the colons as "to" so EE to Ee to ee)

The genotype ratio of EE:Ee:ee is 1:2:1.

Now… keep this in mind!

There is a difference between genotype and genotype ratio. Genotype is the genetic makeup of an organism (ex: Ee). Genotype ratio shows the probability of an organism being “EE”, “Ee”, or “ee.” 

The same holds true for phenotype and phenotype ratio.

Two parents are heterozygous for dwarfism (Tt). Since dwarfism is a dominant trait, both parents are dwarfs. Do a Punnett square and determine the probabilities for their children.

Take a moment and figure out the genotype and phenotype ratios. 

Genotype ratio = TT:Tt:tt

Phenotype ratio = Dominant:Recessive

Spoiler alert!
A heterozygous cross will always have a genotype ratio of 1:2:1 and a phenotype ratio of 3:1.

A botanist is crossing a homozygous tall plant (TT) with a heterozygous tall plant (Tt) for fun. A Punnett square can determine the probabilities for the plant children.

Tall stem is dominant, T and short stem is recessive, t…

Looking at the genotype possibilities, you can count:

TT = 2
Tt = 2
tt = 0

Out of 4 plants, then, 50% were TT and 50% were Tt

There are only 2 possible phenotypes (tall or not tall). 

Let's do that ratio thing again!

Genotype ratio = TT:Tt:tt

Phenotype ratio = Dominant:Recessive

The genotype ratio of TT : Tt : tt is 2:2:0.

The phenotype ratio of Tall : not tall is 4:0.

For any cross of  homozygous dominant and heterozygous, the above ratios will be present.

Another one!

One parent is homozygous dominant (RR) for a widow’s peak while the other is homozygous recessive (rr). Since widow’s peaks are a dominant trait, one parent has one while the other does not. Do a Punnett square and determine the ratios for their children.

And that looks like…

The genotype ratio of RR : Rr : rr is 0:4:0

The phenotype ratio of Widow's Peak : No Widow's Peak is 4:0.

Additional Thoughts on Punnett Squares

There are only three possible genotypes. Using A to represent dominant and a to represent recessive, the ONLY combinations you can have are:


Since any Punnett square is made up of two of those three traits, there (because, math) only six possible Punnett squares:

Thus, there are only six different possible genotype and phenotype ratios:

AA x AA:           4:0:0 and 4:0
AA x Aa:            2:2:0 and 4:0
Aa x Aa:             1:2:1 and 3:1
Aa x aa:              0:2:2 and 2:2
AA x aa:             0:4:0 and 4:0
aa x aa:               0:0:4 and 0:4 

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