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 bySal 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 A 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 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