Learn how to use Punnett squares to calculate probabilities of different phenotypes. Includes worked examples of dihybrid crosses. independent assortment, incomplete dominance, codominance, and multiple alleles. Created by Sal Khan.
In the last video, I drew this grid in order to understand better the different combinations of alleles I could get from my mom or my dad. And this grid that I drew is called a Punnett square. And I looked up what Punnett means, and it turns out, and this might be the biggest takeaway from this video, that when you go to the farmers' market or you go to the produce and you see those little baskets, you see those little baskets that often you'll see maybe strawberries or blueberries sitting in, they have this little grid here, right there. Sometimes grapes are in them, and you have a bunch of strawberries in them like that. That green basket is a punnett. That's a punnett. Apparently, in some countries, they call it a punnett. I think England's one of them, and you UK viewers can correct me if I'm wrong. And so I guess that's where the inspiration comes for calling these Punnett squares, that these are kind of these little green baskets that you can throw different combinations of genotypes in. And these Punnett squares aren't just useful. If you're talking about crossing two hybrids, this is called a monohybrid cross because you are crossing two hybrids for only one trait. It could be useful for a whole set of different types of crosses between two reproducing organisms. It doesn't even have to be a situation where one thing is dominating another. Let's do a bunch of these, just to make you familiar with the idea. So let's say you have a mom. So instead of doing two hybrids, let's say the mom-- I'll keep using the blue-eyed, brown-eyed analogy just because we're already reasonably useful to it. Let's say that she's homozygous dominant. And let's say that the dad is a heterozygote, so he's got a brown and he's got a blue. And we want to know the different combinations of genotypes that one of their children might have. So what we do is we draw a Punnett square again. Let me draw a grid here and draw a grid right there. And up here, we'll write the different genes that mom can contribute, and here, we'll write the different genes that dad can contribute, or the different alleles. I didn't want to write gene. I wanted to write dad. So the mom in either case is either going to contribute this big B brown allele from one of the homologous chromosomes, or on the other homologous, well, they have the same allele so she's going to contribute that one to her child. The dad could contribute this one, that big brown-eyed-- the capital B allele for brown eyes or the lowercase b for blue eyes, either one. So the different combinations that might happen, an offspring could get both of these brown alleles from one copy from both parents. This could also happen where you get this brown allele from the dad and then the other brown allele from the mom, or you could get a brown allele from the mom and a blue-eyed allele from the dad, or you could get the other brown-eyed allele from the mom, right? When the mom has this, she has two chromosomes, homologous chromosomes. Each of them have the same brown allele on them. They both have that same brown allele, so I could get the other one from my mom and still get this blue-eyed allele from my dad. So if you said what's the probability of having a blue-eyed child, assuming that blue eyes are recessive? And remember, this is a phenotype. These particular combinations are genotypes. Well, in order to have blue eyes, you have to be homozygous recessive. You have to have two lowercase b's. So what's the probability of having this? Well, there are no combinations that result in that, so there's a 0% probability of having two blue-eyed children. What's the probability of having a homozygous dominant child? Let me write that. A homozygous dominant. And now we're looking at the genotype. We care about the specific alleles that that child inherits. Well, which of these are homozygous dominant? Well, you have this one right here and you have that one right there, and so two of the four equally likely combinations are homozygous dominant, so you have a 50% shot. And we can do these Punnett squares. They don't even have to be for situations where one trait is necessarily dominant on the other. For example, you could have the situation-- it's called incomplete dominance. Let's say you have two traits for color in a flower. You could have red flowers or you could have white flowers. And let's say I were to cross a parent flower that has the genotype capital R-- I'll just make it in a capital W. So that could be the mom or the dad, although the analogy breaks down a little bit with parents, although there is a male and female, although sometimes on the same plant. And let's say the other plant is also a red and white. The other plant has a red allele and also has a white allele. So what are the different possibilities? Well, we just draw our Punnett square again. Let me draw our little grid. So the child could inherit both of these red alleles. He could inherit this white allele and then this red allele, so this red one and then this white one, right? That's that right there and that red one is that right there. Or it could inherit this red one from-- let's say this is the mom plant and then the white allele from the dad plant, so that's that one right there. Or you could inherit both white alleles. What I said when I went into this, and I wrote it at the top right here, is we're studying a situation dealing with incomplete dominance. So what does that mean? Well, that means you might actually have mixing or blending of the traits when you actually look at them. So if this was complete dominance, if red was dominant to white, then you'd say, OK, all of these guys are going to be red and only this guy right here is going to be white, so you have a one in four probability to being white. But let's say that a heterozygous genotype-- so let me write that down. Let's say when you have one R allele and one white allele, that this doesn't result in red. This results in pink. So this is what blending is. It's kind of a mixture of the two. So if I said if these these two plants were to reproduce, and the traits for red and white petals, I guess we could say, are incomplete dominant, or incompletely dominant, or they blend, and if I were to say what's the probability of having a pink plant? And now when I'm talking about pink, this, of course, is a phenotype. So the probability of pink, well, let's look at the different combinations. How many of these are pink? This one is pink and this is pink. So two are pink of a total of four equally likely combinations, so it's a 50% chance that we're pink. And we could keep doing this over multiple generations, and say, oh, what happens in the second and third and the fourth generation? Actually, we could even have a situation where we have multiple different alleles, and I'll use almost a kind of a more realistic example. I'll use blood types as an example. So there's three potential alleles for blood type. You can have a blood type A, you could have a blood type B, or you could have a blood type O. What happens is you have a combination here between codominance and recessive genes. And I'm going to show you what I talk about when we do the Punnett squares. Maybe I'll stick to one color here because I think you're getting the idea. So let's say I have a parent who is AB. So that means that they have on one of their homologous chromosomes, they have the A allele, and on the other one, they have the B allele. That's what AB means. So the phenotype is the genotype. They're codominant. They both express themselves. They don't necessarily blend. They both express. That's an AB blood type. Let me write this right here. This is AB blood type. And then the other parent is-- let's say that they are fully an A blood type. Let's say they're an A blood type. Let's say their phenotype is an A blood type-- I hope I'm not confusing you-- but their genotype is that they have one allele that's an A and their other allele that's an O. So this is what's interesting about blood types. It's a mixture. O is recessive. O is recessive, while these guys are codominant. So if you have either of these guys with an O, these guys dominate. If you have them together, then your blood type is AB. So what are all the different combinations for these for this couple here? Well, you could get this A and that A, so you get an A from your mom and you get an A from your dad right there. And clearly in this case, your phenotype, you will have an A blood type in this situation. You could get the A from your dad and you could get the B from your mom, in which case you have an AB blood type. You could get the A from your mom and the O from your dad, in which case you have an A blood type because this dominates that. Or you could get the B from your-- I dont want to introduce arbitrary colors. You could get the B from your mom, that's this one, or the O from your dad. No, once again, I introduced a different color. And this is a B blood type. So if I said what's the probability of having an AA blood type? And once again, we're talking about a phenotype here. So which of these are an A blood type? This one definitely is, because it's AA. If you have two A alleles, you'll definitely have an A blood type, but you also have an A blood type phenotype if you have an A and then an O. O is recessive. So this is also going to be an A blood type. So these are both A blood, so there's a 50% chance, because two of the four combinations show us an A blood type. And you could do all of the different combinations. You say, well, how do you have an O blood type? Well, both of your parents will have to carry at least one O. So, for example, to have a-- that would've been possible if maybe instead of an AB, this right here was an O, then this combination would've been two O's right there. So hopefully, that gives you an idea of how a Punnett square can be useful, and it can even be useful when we're talking about more than one trait. So let's go to our situation that I talked about before where I said you have little b is equal to blue eyes, and we're assuming that that's recessive, and you have big B is equal to brown eyes, and we're assuming that this is dominant. And let's say we have another trait. I introduced that tooth trait before. So let's say little t is equal to small teeth. I don't know what type of bizarre organism I'm talking about, although I think I would fall into the big tooth camp. Let's say big T is equal to big teeth. So an individual can have-- for example, I might be heterozygous brown eyes, so my genotype might be heterozygous for brown eyes and then homozygous dominant for teeth. So this might be my genotype. And the phenotype for this one would be a big-toothed, brown-eyed person, right? Let me make that clear. This is big tooth phenotype. And this is the phenotype. What you see is brown eyes. A big-toothed, brown-eyed person. Now if we assume that the genes that code for teeth or eye color are on different chromosomes, and this is a key assumption, we can say that they assort independently. Let me write that down: independent assortment. So this is a case where if I were look at my chromosomes, let's say this is one homologous pair, maybe we call that homologous pair 1, and let's say I have another homologous pair, and obviously we have 23 of these, but let's say this is homologous pair 2 right here, if the eye color gene is here and here, remember both homologous chromosomes code for the same genes. They might have different versions. Those are alleles. And if teeth are over here, they will assort independently. So after meiosis occurs to produce the gametes, the offspring might get this chromosome or a copy of that chromosome for eye color and might get a copy of this chromosome for teeth size or tooth size. Or it could go the other way. Maybe another offspring gets this one, this chromosome for eye color, and then this chromosome for teeth color and gets the other version of the allele. So because they're on different chromosomes, there's no linkage between if you inherit this one, whether you inherit big teeth, whether you're going to inherit small brown eyes or blue eyes. Now, if they were on the same chromosomee-- let's say the situation where they are on the same chromosome. So let me pick another trait: hair color. Let's say the gene for hair color is on chromosome 1, so let's say hair color, the gene is there and there. These might be different versions of hair color, different alleles, but the genes are on that same chromosome. In this situation, if someone gets-- let's say if this is blue eyes here and this is blond hair, then these are going always travel together. You're not going to have these assort independently. And these are called linked traits. Let me highlight that. So these right there, those are linked traits. But for a second, and we'll talk more about linked traits, and especially sex-linked traits in probably the next video or a few videos from now, but let's assume that we're talking about traits that assort independently, and we cross two hybrids. So this is called a dihybrid cross. Very fancy word, but it just gives you an idea of the power of the Punnett square. So let's say both parents are-- so they're both hybrids, which means that they both have the dominant brown-eye allele and they have the recessive blue-eye allele, and they both have the dominant big-tooth gene and they both have the recessive little tooth gene. So this is the genotype for both parents. Both parents are dihybrid. They're hybrids for both genes, both parents. What are all the different combinations for their children? And I could have done this without dihybrids. I could have made one of them homozygous for one of the traits and a hybrid for the other, and I could have done every different combination, but I'll do the dihybrid, because it leads to a lot of our variety, and you'll often see this in classes. So if I'm talking about the mom, what are the different combinations of genes that the mom can contribute? Well, the mom could contribute the brown-- so for each of these traits, she can only contribute one of the alleles. So she could contribute this brown right here and then the big yellow T, so this is one combination, or she could contribute the big brown and then the little yellow t, or she can contribute the blue-eyed allele and the big T. So these are all the different combinations that she could contribute. And then the final combination is this allele and that allele, so the blue eyes and the small teeth. So that's from mom. And, of course, dad could contribute the same different combinations because dad has the same genotype. Let me write that down. Let me just write it like this so I don't have to keep switching colors. Actually, I want to make them a little closer together because I'm going to run out of space otherwise. Nope. Let me do it like that. OK, brown eyes, so the dad could contribute the big teeth or the little teeth, z along with the brown-eyed gene, or he could contribute the blue-eyed gene, the blue-eyed allele in combination with the big teeth or the yellow teeth. Not the yellow teeth, the little teeth. That would be a different gene for yellow teeth or maybe that's an environmental factor. So these are all the different combinations that can occur for their offspring. So let's draw-- call this maybe a super Punnett square, because we're now dealing with, instead of four combinations, we have 16 combinations. It looks like I ran out of ink right there. It's strange why-- 16 combinations. Let me write that out. Something's wrong with my tablet. Maybe there's something weird. OK, so there's 16 different combinations, and let's write them all out, and I'll just stay in one maybe neutral color so I don't have to keep switching. I could get this combination, so this brown eyes from my mom, brown eyes from my dad allele, so its brown-brown, and then big teeth from both. I could have this combination, so I have capital B and a capital B. And then I have a capital T and a lowercase t. And then let's just keep moving forward. So I could get a capital B and a lowercase B with a capital T and a capital T, a big B, lowercase B, capital T lowercase t. And I'm just going to go through these super-fast because it's going to take forever, so capital B from here, capital B from there; capital T, lowercase t from here; capital B from each and then lowercase t from each. You have a capital B and then a lowercase b from that one, and then a capital T from the mom, lowercase t from the dad. Hopefully, you're not getting too tired here. And so then you have the capital B from your dad and then lowercase b from your mom. Two lowercase t's-- actually let me just pause and fill these in because I don't want to waste your time. There I have saved you some time and I've filled in every combination similar to what happens on many cooking shows. But now that I've filled in all the different combinations, we can talk a little bit about the different phenotypes that might be expressed from this dihybrid cross. For example, how many of these are going to exhibit brown eyes and big teeth? So big teeth, brown-eyed kids. Let me write this down here. So if I want big teeth and brown eyes. All of a sudden, my pen doesn't-- brown eyes. So how many are there? Big teeth and brown eyes. So they're both dominant, so if you have either a capital B or a capital T in any of them, you're going to have big teeth and brown eyes, so this is big teeth and brown eyes. Big teeth right here, brown eyes there. Or maybe I should just say brown eyes and big teeth because that's the order that I wrote it right here. Brown eyes and big teeth, brown eyes and big teeth. Even though I have a recessive trait here, the brown eyes dominate. I had a small teeth here, but the big teeth dominate. This is brown eyes and big teeth. This is brown eyes and big teeth. Let's see, this is brown eyes and big teeth, brown eyes and big teeth, and let me see, is that all of them? Well, no. This is brown eyes and little teeth. This is brown eyes and big teeth right there, and this is also brown eyes and big teeth. They're heterozygous for each trait, but both brown eyes and big teeth are dominant, so these are all phenotypes of brown eyes and big teeth. So how many of those do we have? We have one, two, three, four, five, six, seven, eight, nine of those. So we have nine. Nine brown eyes and big teeth. Now, how many do we have of big teeth? Let me write in a different color, so let me write brown eyes and little teeth. Something on my pen tablet doesn't work quite right over there. So brown eyes and little teeth. So let's see, this is brown eyes and little teeth right there. This is brown eyes and little teeth right there. This is brown eyes and little teeth right there. So there's three combinations of brown eyes and little teeth. And if I were to say blue eyes, blue and big teeth, what are the combinations there? Well, this is blue eyes and big teeth, blue eyes and big teeth, blue eyes and big teeth, so there's three combinations there. And if I want to be recessive on both traits, so if I want-- let me do this. I want blue eyes, blue and little teeth. There's only one. Out of the 16, there's only one situation where I inherit the recessive trait from both parents for both traits. So if you look at this, and you say, hey, what's the probability-- there's only one of that-- what's the probability of having a big teeth, brown-eyed child? And these are all the phenotypes. There were 16 different possibilities here, right? There are 16 squares here, and 9 of them describe the phenotype of big teeth and brown eyes, so there's a 9/16 chance. So it's 9 out of 16 chance of having a big teeth, brown-eyed child. What's the probability of a blue-eyed child with little teeth? 1 in 16. So hopefully, in this video, you've appreciated the power of the Punnett square, that it's a useful way to explore every different combination of all the genes, and it doesn't have to be only one trait. It can be in this case where you're doing two traits that show dominance, but they assort independently because they're on different chromosomes. You could use it-- where'd I do it over here? You could use it to explore incomplete dominance when there's blending, where red and white made pink genes, or you can even use it when there's codominance and when you have multiple alleles, where it's not just two different versions of the genes, there's actually three different versions. So hopefully, you've enjoyed that.