Why do we need to learn about Punnett squares?
You learned in the last lesson's material how to figure out a genotype from a phenotype. So if a pea plant has white flowers, you know that it's genotype is: pp (homozygous recessive for flower color). If a pea plant has purple flowers, its genotype is either PP or Pp (homozygous dominant or heterozygous for flower color). You even learned that if an individual with a homozygous dominant genotype is crossed with any other individual, its offspring will have to have at least one dominant allele.
However, you haven't learned how to best predict the chances of the different phenotypes or genotypes showing up in the offspring regardless of the parents in the cross. You might not care what the chances are of getting white flowers from the next generation when a purple flowering plant crosses with a white flowering plant. But if you were a gardener breeding roses and the question had to do with rose flower color (when one flower color is more valuable than another), you might care. You might also care about chances in inheritance if you thought that a certain disease ran in your family-- I carry the Tay Sachs disease gene, for example. Should I be worried about having a child with Tay Sachs disease? (if you don't know about this disease, follow the link to see how devastating it is).
Punnett squares enable one to understand the probabilities involved in passing alleles to the next generation. They are rather straightforward when done for monohybrid crosses. In principles of biology II, you will continue with genetics and need to apply Punnett squares to dihybrid crosses, too. But that is not necessary right now.
What is a Punnett Square and how do we use it?
A Punnett Square is simply a tool to help you understand how alleles are passed to the next generation. It enables you to follow each parental allele as it could get passed to the next generation.
Use your book, the book CD, and the following figure to help you along here with a monohybrid cross. All you have to do is know the genotypes of the parents-- that tells you which alleles each parent could offer to the next generation. The alleles they could give are what you write along the side and top of the square; once you figure out what letters to write along the side and the top of your square, it is easy to fill in. Here's a description for how to do a parental generation monohybrid cross between individuals that are purebred.
The punnett square has four boxes in it. These boxes get filled out by writing the alleles from the side along their row and by writing the alleles from the top along their column. To see this done step-by-step, follow this link. Once filled out, those four boxes represent all the possible genotypes that can exist in the next generation. These genotypes are random combinations of the parent alleles.
Each of the four possible genotypes in the Punnett square have an equal chance of occurring. Of course, in the above cross, all four are the same. So let's figure out the ratio of possible phenotypes and/or genotypes in the next generation: Yy x Yy.
Note that when these two heterozygotes cross, their are 2 possible phenotypes in the next generation, and three possible genotypes.
2 Phenotypes: yellow peas and green peas
3 Genotypes: homozygous dominant, heterozygous, and homozygous recessive.
And, each of the F2 offspring represented by each box has an equal chance of occurring. So, one is just as likely to get a YY individual out of this cross as they are to get a yy individual.
Because of these equal probabilities, we can figure out what the likelihood is for getting a green pea producing plant in the next generation. Out of four possibly progeny, only one could have green peas. So our chance is 1/4, which is 25%. Another way to describe this is to say that 1 could have green peas while 3 would not, so the ratio of green peas to non-green peas is 1:3. The ratio of yellow peas to non-yellow peas is 3:1, and the likelihood of getting a plant with yellow peas is 75%.
Keep in mind that 3:1 is not 66.7%. With ratios, one has to say that for every three plants there is one other that is different, so that 3 out of 4, or 3/4 (75%), is how you get the percentage. Ratios are hard. I'll give you one more example.
What percentage of the above cross end up as heterozygotes? Click here to check your answer! What percentage are homozygous dominant? Click here to check your answer! What percentage are homozygous recessive? Click here to check your answer! I'll bet that you figured out these genotype percentages. Now let's do the genotype ratios. What is the ratio of homozygous dominant to heterozygous to homozygous recessive offspring? I'll give you a hint-- just count them up (like we did with the phenotype ratios). Have you figured it out? If you think so, click here to check your answer!
Consider something more important... at least to me. I told you above that I am a carrier for Tay Sachs disease. That means that I am heterozygous for the gene affected-- such that I have one normal allele and one Tay Sachs allele. The Tay Sachs allele is recessive. Knowing all this, what are the chances that I could have a child with Tay Sachs if I have a child with:
I could not have a child with someone who is homozygous recessive, because that person would have had Tay Sachs and would have died by the time they were 5 years old. Meanwhile, since it is totally random as to which alleles combine, even if there is only a small chance to have a child with the disease, it is possible that every child I have with another heterozygote would have it.
You see, probability is like flipping a coin. There might be a 50% chance that when you flip a coin it will end up heads, but it is also possible to flip it 5 times in a row and get heads each time. There was only a 25% chance that my parents could have a child with an eye color other than brown, they only had two children, and one of us (half) have brown eyes (me) while the other one (my sister) has green eyes. Mendel did thousands of crosses-- and with thousands, the numbers end up approximating the predictions. But with only a few offspring, like people tend to do, the numbers within a family do not always match the probabilities.
The fact that a parent randomly gives one allele out of its two to the next generation is something that Mendel figured out. We now call that Mendel's law of segregation. This is described on page 65, and it is the very last section of chapter 3 that you need to read. However, one thing precedes that-- the discussion about sickle cell anemia. That is next.
Sickle cell anemia
Your book describes sickle cell anemia. An "anemia" is any problem that causes you to have too little oxygen in your blood. With sickle cell anemia, the problem is with the molecule inside of red blood cells that carries oxygen through your blood-- the molecule is hemoglobin. Sickle cell hemoglobin is less able to carry oxygen through the blood than regular hemoglobin. Hemoglobin is often represented with the letters Hb. With sickle cell anemia, the way that the hemoglobin is messed up causes the entire red blood cell to collapse on itself into a sickle shape and to be less flexible. This causes additional problems for the person with this type of red blood cell.
The way sickle cell anemia is inherited is the same as any other trait that has dominant and recessive forms. The diseased form is recessive, and the normal one is dominant. You would think that this would be represented by something like N and n or HbN and Hbn, but it is not. The lettering to abbreviate this disease is a little more complicated-- but the inheritance is not. Keep that in mind.
The normal hemoglobin gene is represented by HbA and the sickle cell hemoglobin gene is represented by HbS. A person who has two normal alleles is then represented by HbA/HbA, where the "/" is used to help you see the two alleles clearly from one another. There are some different crosses that could be made between people with the disease and those without, or between carriers for the disease. Some crosses are:
Your book also describes the word carrier a little bit. Basically, if anyone is heterozygous for something bad, where the bad thing is recessive, they can pass that bad allele on-- so they are a carrier. We don't really talk about carriers for blue eyes, but we do talk about carriers for sickle cell anemia, Tay Sachs disease, and muscular dystrophy.
The only thing left in our genetics topic is the test cross... go on to read about that!
© 2006 STCC Foundation Press, content by Dawn A. Tamarkin, Ph.D.
Last changed: January 21, 2007