Understanding Punnett Squares in Genetics

Hi. It's Mr. Andersen and today I'm going to give you a beginner's guide to Punnett squares. There are a few mistakes that students always make when they're doing Punnett squares. So I hope to kind of clear those up. First of all we should talk about the namesake. This is Reginald Punnett. He didn't really work with Punnett squares. However he did work with genetics quite a bit. He did work with mimicry in the butterflies. And so his name is probably associated with with genetics just as much as Mendel. And it's through the use of the Punnett square. Now the Punnett square is often overused as just a quick way to solve genetics problems without really understanding what's going on with the genetics. And so I want to kind of get to that root. And if you could remember one thing from this whole video podcast, it's this right here. The two sides of a Punnett square represent the alternatives after meiosis. In other words, You have a bunch of genes and you give half of those genes to a sperm or an egg. And that happens through meiosis. And so the organization of those gametes, in this case it's just a monohybrid cross, are going to be on either side of this. Just like a flip of the coin. This would be for one parent and then this would be the other parent on the other side. And so what do the boxes on a Punnett square stand for? They simply stand for all the alternatives that could occur. If we had mating between each of these different gametes. And so let's get to some examples and hopefully that will help. So we're going to start with a monohybrid cross. A monohybrid cross is simply a cross that is looking at one trait. And so let's do one that's really, really simple. And so let's say we're crossing purple flowers that are homozygous, purple, with those that are homozygous, white flowers. In other words this is the dominant trait. This is the recessive trait. And so if you look at the parents what you want to do first of all is figure out what are the possible gametes that could be produced in meiosis. In other words this one could either give a big P or it could give a big P. What does that mean? It can only give one thing. It can only give a big P or that dominant allele. And so if you're doing a problem like this you don't even need a big Punnett square. One parent can only contribute big P. So let's look at the other parent. The other parent can either give a little p, and I try to make them really small, or a little p because p's look the same. And so the other parent can only give a little p. And so we can put that on the other side. And so what are the opportunities that we could have as far as fertilization goes? Well this one is automatically going to give it big P. The other one is going to give a little p. And so this is the only possible outcome we could get between a cross of a homozygous dominant and a homozygous recessive. And so don't really need a big Punnett square. Now you could do that. You could fill it in. Big P over here, little p over here. But if you do that you're going to get the same thing in all of the boxes. And so it's still a one to one ratio. In other words 100% of the time you're going to have that. Okay. So let's get to one that's a little more complicated. Let's say we have a heterozygous cross. And so this is for purple flowers as well. Well if you look at this one now the problem has changed a little bit. This one could give a big P. p. But it also could give a little p. And so we have to show both of those possible gametes of meiosis. And so this would be the big P. And then this would be the little p over here. So half of the time it's going to give the big P. Half of the time it's going to give the little p. If we look at the other parent, same thing. It's going to give the big P half of the time. And it's going to give the little p half of the time as well. So we're going to put that here. Now we simply fill in the boxes. And so this would be a big P with a big P because I'm taking this here and that there. And then we're going This is going to go over to here to give us a big P and a little p. By convention we usually write the dominant allele first. So that would be one alternative here. Here would be a big p, little p as well. So we get the big P here and the little p here. And then finally we're going to get little p over here and little p over here. Since they're each contributing a little p. And so what do we get from this cross? Well we get a 1 to 2, since these are exactly the same, to 1 genotypic ratio. So we get 1 to 2, since these are exactly the ratio. Because the genotype is the letter. So there's one that's like this. There's two that look like this. And there's one that looks like that. So that's going to be our one to two to one genotypic ratio. What about phenotypic? Well this one is going to be a purple flower. And so are these other two. And so if we're looking at the phenotypic ratio, the phenotypic ratio now is going to be a three to one ratio. We're going to have three purple to every one white that we have. Okay. Let's try another one. Let's say we're looking at incomplete dominance. So incomplete dominance, a snapdragon would be an example of that. that. A snapdragon has two genes. If it has a red gene and a white gene then it is going to be pink. And so this one actually has two alleles that it can contribute and the same on the other side. And so we just write those out. So this would be the parent. This would be a 50% chance of giving the red, 50% chance of the white. And then the same thing on this side over here. So now if we fill in our Punnett square. Like that. What do we get for all the different choices? Well now we have a 1 to 2 to 1 genotypic ratio. But we also have a 1 to 2 to 1 phenotypic ratio. So if you're doing a question where it's incomplete dominance you use a Punnett square the same way. Codominance would be the same way. The difference is in incomplete dominance the... heterozygous or the hybrids are going to be somewhere between the two. If it's co-dominant they'll actually, they're going to express both of those genes, both of those proteins. Now let's try one that's a sex linked chromosome or an X linked chromosome. And so in this one we've got a parent. So this is a mom because she's XX chromosome. And she's a carrier of let's say color blindness of the gene. And this is a dad that's normal. And so I'm going to put dad up here, XY. Because half of the time he's going to give the X and half of the time he's going to give the Y. If we put mom over here, I'm going to put that carrier up there, she is not colorblind because she has one deficient gene, colorblind gene, but she has another gene that works well on her other X chromosome. So if I fill in this one here it's going to be XCX. So this would be a female because two X chromosomes. But they're going to be a carrier of that gene. If we look down here this would just be a normal female. So we're going to put If we look down here I'm grabbing the x from here and the y from up there. So that would be xy. So that would be a normal male. And then if we look at this one right here, this would be a male who is color blind. The reason he is color blind is that he doesn't have an x chromosome or another gene as a backup copy to that. So those are monohybrid crosses. And usually students do fairly well on those. Next are dihybrid crosses. And this is where the mistakes really start. And so if we look at this parent, this is a typical dihybrid cross. Let me tell you what the letters stand for. The R stands for round pea seeds and the Y stands for yellow seeds. If it's the recessive that stands for wrinkled. And if it's a little Y that stands for green. And so we're looking at a dihybrid. So that means two traits. We're looking at seed shape, round or wrinkled and seed color, yellow or green. So now we have to do a dihybrid cross. And so the tendency, if we look at this parent, the tendency is is to see that there are four letters over here. There's four boxes over here. And then you just simply write them out. Big R, little r. Big Y, little y. And you get a weird answer and you don't know what to do with it. Okay? That's wrong. That's a mistake. Okay? Whenever you're figuring out the gametes, remember that you have to give one of each letter. In other words, each of the gametes is going to have one of each of the alleles. And so let me clear this mess out of the way. So what do we do? Let's say this parent right here. And I'm going to write it up here so it makes a little more sense. Big R, little r, big Y, little y. What possibilities could they produce? They're giving one of each letter, remember. Well they could give the big R and the big Y. So big R, big Y. That would be one possibility. They could also give the big R and the little Y. So they could give the big R, little y. They could also give the little r, big Y or the little r. y. Since they're giving one of each color, there's only four, one of each letter, excuse me, there's only four possibilities that they can give. So it's getting to be kind of a mess. But those are the four right here. And so those four are going to go across the top. So we've got big R, big Y, big R, little y, little r, big Y, little r, little y. So those are the four gametes that you could produce. In other words with this parent you can only get four combinations of each of the two letters. Same thing down this side. So it's going to be the same thing written down this side because this other parent is going to be exactly the same. Okay. So it would take me a long time to write all of those out. So let me throw those in here. So these would be the parents. All the possible gametes you could get. And if I fill those in, these first nine, if you look at them, let me get a color. It's different. Let me grab a yellow color. And so this one right here is going to be round and it's going to be yellow. So it's going to be round and yellow. And this one you can see is going to be round and yellow and then yellow and round and yellow and round and yellow and round and yellow and round and yellow and round and yellow. In other words nine of them are going to be round and yellow in shape. And the only reason why is that the R is dominant. And so you could have one like this where they're hybrid for both and they're still going to be round and yellow. And so let me try to add the next ones. So what about these next ones? Well the next ones are going to be round and green. So let me get a different color. So these ones are going to be round and green. because the round is dominant but they don't have the dominant for the yellow. So they're not going to be. Let me get rid of that. Let's add the next ones. So these ones are going to be wrinkled and yellow. So again I got to get a different pen. So these ones are going to be wrinkled and yellow. And then if we look at the last one. It's going to get all of the recessive alleles. And so that one is going to be green. It's going to be green and wrinkled. Okay. And so when we say there's a 9 to 3 to 3 to 1 ratio, that's just a typical dihybrid cross. We're going to have 9 of the phenotypes that are round and yellow. 3 of the phenotypes that are round and green. three of the phenotypes that are yellow and wrinkled and then only one that's not. And that's only going to work if you are able to set up your gametes correctly on the side. Now it's super hard for you to answer a question like this on a test. You're rarely going to have to draw a dihybrid cross. But it's important that you understand the concept of it because most of the genes inside your body are not caused by one gene. They're caused by multiple genes. So how tall you are is caused by probably a dozen different genes inside your body. So you can imagine how big the Punnett square is going to be for that. An example that I'll leave you with would be this one. So let's say we have a parent here. And the parent is big R, little r, big y, little y. Little r, little r, little y, little y. The question I'm asking you is how big would your Punnett square have to be? And so you're going to have to figure out what are all the possible gametes that you could get from both of those. And then then draw it out. Figure out all the possibilities you can get. If you're thinking it's going to be a 4x4 you're doing way too much work. And so those are ponnet squares and I hope that's helpful.

This is Reginald Punnett. He didn't really work with Punnett squares. However he did work with genetics quite a bit.

He did work with mimicry in the butterflies. And so his name is probably associated with with genetics just as much as Mendel. And it's through the use of the Punnett square. Now the Punnett square is often overused as just a quick way to solve genetics problems without really understanding what's going on with the genetics.

And so I want to kind of get to that root. And if you could remember one thing from this whole video podcast, it's this right here. The two sides of a Punnett square represent the alternatives after meiosis. In other words, You have a bunch of genes and you give half of those genes to a sperm or an egg.

And that happens through meiosis. And so the organization of those gametes, in this case it's just a monohybrid cross, are going to be on either side of this. Just like a flip of the coin. This would be for one parent and then this would be the other parent on the other side.

And so what do the boxes on a Punnett square stand for? They simply stand for all the alternatives that could occur. If we had mating between each of these different gametes.

And so let's get to some examples and hopefully that will help. So we're going to start with a monohybrid cross. A monohybrid cross is simply a cross that is looking at one trait. And so let's do one that's really, really simple. And so let's say we're crossing purple flowers that are homozygous, purple, with those that are homozygous, white flowers.

In other words this is the dominant trait. This is the recessive trait. And so if you look at the parents what you want to do first of all is figure out what are the possible gametes that could be produced in meiosis. In other words this one could either give a big P or it could give a big P.

What does that mean? It can only give one thing. It can only give a big P or that dominant allele. And so if you're doing a problem like this you don't even need a big Punnett square.

One parent can only contribute big P. So let's look at the other parent. The other parent can either give a little p, and I try to make them really small, or a little p because p's look the same. And so the other parent can only give a little p. And so we can put that on the other side.

And so what are the opportunities that we could have as far as fertilization goes? Well this one is automatically going to give it big P. The other one is going to give a little p.

And so this is the only possible outcome we could get between a cross of a homozygous dominant and a homozygous recessive. And so don't really need a big Punnett square. Now you could do that. You could fill it in.

Big P over here, little p over here. But if you do that you're going to get the same thing in all of the boxes. And so it's still a one to one ratio. In other words 100% of the time you're going to have that.

Okay. So let's get to one that's a little more complicated. Let's say we have a heterozygous cross. And so this is for purple flowers as well. Well if you look at this one now the problem has changed a little bit.

This one could give a big P. p. But it also could give a little p. And so we have to show both of those possible gametes of meiosis.

And so this would be the big P. And then this would be the little p over here. So half of the time it's going to give the big P.

Half of the time it's going to give the little p. If we look at the other parent, same thing. It's going to give the big P half of the time.

And it's going to give the little p half of the time as well. So we're going to put that here. Now we simply fill in the boxes.

And so this would be a big P with a big P because I'm taking this here and that there. And then we're going This is going to go over to here to give us a big P and a little p. By convention we usually write the dominant allele first.

So that would be one alternative here. Here would be a big p, little p as well. So we get the big P here and the little p here. And then finally we're going to get little p over here and little p over here. Since they're each contributing a little p.

And so what do we get from this cross? Well we get a 1 to 2, since these are exactly the same, to 1 genotypic ratio. So we get 1 to 2, since these are exactly the ratio. Because the genotype is the letter.

So there's one that's like this. There's two that look like this. And there's one that looks like that.

So that's going to be our one to two to one genotypic ratio. What about phenotypic? Well this one is going to be a purple flower.

And so are these other two. And so if we're looking at the phenotypic ratio, the phenotypic ratio now is going to be a three to one ratio. We're going to have three purple to every one white that we have.

Okay. Let's try another one. Let's say we're looking at incomplete dominance. So incomplete dominance, a snapdragon would be an example of that. that.

A snapdragon has two genes. If it has a red gene and a white gene then it is going to be pink. And so this one actually has two alleles that it can contribute and the same on the other side. And so we just write those out. So this would be the parent.

This would be a 50% chance of giving the red, 50% chance of the white. And then the same thing on this side over here. So now if we fill in our Punnett square. Like that.

What do we get for all the different choices? Well now we have a 1 to 2 to 1 genotypic ratio. But we also have a 1 to 2 to 1 phenotypic ratio. So if you're doing a question where it's incomplete dominance you use a Punnett square the same way.

Codominance would be the same way. The difference is in incomplete dominance the... heterozygous or the hybrids are going to be somewhere between the two.

If it's co-dominant they'll actually, they're going to express both of those genes, both of those proteins. Now let's try one that's a sex linked chromosome or an X linked chromosome. And so in this one we've got a parent. So this is a mom because she's XX chromosome.

And she's a carrier of let's say color blindness of the gene. And this is a dad that's normal. And so I'm going to put dad up here, XY.

Because half of the time he's going to give the X and half of the time he's going to give the Y. If we put mom over here, I'm going to put that carrier up there, she is not colorblind because she has one deficient gene, colorblind gene, but she has another gene that works well on her other X chromosome. So if I fill in this one here it's going to be XCX. So this would be a female because two X chromosomes.

But they're going to be a carrier of that gene. If we look down here this would just be a normal female. So we're going to put If we look down here I'm grabbing the x from here and the y from up there. So that would be xy. So that would be a normal male.

And then if we look at this one right here, this would be a male who is color blind. The reason he is color blind is that he doesn't have an x chromosome or another gene as a backup copy to that. So those are monohybrid crosses.

And usually students do fairly well on those. Next are dihybrid crosses. And this is where the mistakes really start.

And so if we look at this parent, this is a typical dihybrid cross. Let me tell you what the letters stand for. The R stands for round pea seeds and the Y stands for yellow seeds.

If it's the recessive that stands for wrinkled. And if it's a little Y that stands for green. And so we're looking at a dihybrid.

So that means two traits. We're looking at seed shape, round or wrinkled and seed color, yellow or green. So now we have to do a dihybrid cross. And so the tendency, if we look at this parent, the tendency is is to see that there are four letters over here. There's four boxes over here.

And then you just simply write them out. Big R, little r. Big Y, little y. And you get a weird answer and you don't know what to do with it.

Okay? That's wrong. That's a mistake.

Okay? Whenever you're figuring out the gametes, remember that you have to give one of each letter. In other words, each of the gametes is going to have one of each of the alleles.

And so let me clear this mess out of the way. So what do we do? Let's say this parent right here. And I'm going to write it up here so it makes a little more sense.

Big R, little r, big Y, little y. What possibilities could they produce? They're giving one of each letter, remember. Well they could give the big R and the big Y. So big R, big Y.

That would be one possibility. They could also give the big R and the little Y. So they could give the big R, little y.

They could also give the little r, big Y or the little r. y. Since they're giving one of each color, there's only four, one of each letter, excuse me, there's only four possibilities that they can give. So it's getting to be kind of a mess.

But those are the four right here. And so those four are going to go across the top. So we've got big R, big Y, big R, little y, little r, big Y, little r, little y.

So those are the four gametes that you could produce. In other words with this parent you can only get four combinations of each of the two letters. Same thing down this side.

So it's going to be the same thing written down this side because this other parent is going to be exactly the same. Okay. So it would take me a long time to write all of those out.

So let me throw those in here. So these would be the parents. All the possible gametes you could get. And if I fill those in, these first nine, if you look at them, let me get a color.

It's different. Let me grab a yellow color. And so this one right here is going to be round and it's going to be yellow. So it's going to be round and yellow.

And this one you can see is going to be round and yellow and then yellow and round and yellow and round and yellow and round and yellow and round and yellow and round and yellow. In other words nine of them are going to be round and yellow in shape. And the only reason why is that the R is dominant. And so you could have one like this where they're hybrid for both and they're still going to be round and yellow.

And so let me try to add the next ones. So what about these next ones? Well the next ones are going to be round and green.

So let me get a different color. So these ones are going to be round and green. because the round is dominant but they don't have the dominant for the yellow.

So they're not going to be. Let me get rid of that. Let's add the next ones. So these ones are going to be wrinkled and yellow.

So again I got to get a different pen. So these ones are going to be wrinkled and yellow. And then if we look at the last one.

It's going to get all of the recessive alleles. And so that one is going to be green. It's going to be green and wrinkled.

Okay. And so when we say there's a 9 to 3 to 3 to 1 ratio, that's just a typical dihybrid cross. We're going to have 9 of the phenotypes that are round and yellow.

3 of the phenotypes that are round and green. three of the phenotypes that are yellow and wrinkled and then only one that's not. And that's only going to work if you are able to set up your gametes correctly on the side.

Now it's super hard for you to answer a question like this on a test. You're rarely going to have to draw a dihybrid cross. But it's important that you understand the concept of it because most of the genes inside your body are not caused by one gene. They're caused by multiple genes.

So how tall you are is caused by probably a dozen different genes inside your body. So you can imagine how big the Punnett square is going to be for that. An example that I'll leave you with would be this one. So let's say we have a parent here.

And the parent is big R, little r, big y, little y. Little r, little r, little y, little y. The question I'm asking you is how big would your Punnett square have to be?

And so you're going to have to figure out what are all the possible gametes that you could get from both of those. And then then draw it out. Figure out all the possibilities you can get. If you're thinking it's going to be a 4x4 you're doing way too much work. And so those are ponnet squares and I hope that's helpful.

Transcript for:Understanding Punnett Squares in Genetics

Transcript for:
Understanding Punnett Squares in Genetics