Dihybrid Cross: Videos & Practice Problems

A dihybrid cross examines the inheritance of two traits, using two letters to represent each trait. The Punnett Square and branching diagram are methods to predict offspring genotypes and phenotypes, adhering to Mendel's law of independent assortment. The typical phenotypic ratio for a dihybrid cross is 9:3:3:1. Understanding the starting genotypes is crucial, especially when transitioning from parental to F₁ and F₂ generations. Mastery of these concepts is essential for success in genetics.

Punnet Square

Let's break it down. A dihybrid cross, where "di" usually means 2, involves examining the mating between organisms looking at 2 different traits. Examples of these traits might be color and shape. In a monohybrid cross, you might use one letter to indicate a trait, whereas a dihybrid typically uses two separate letters, one for each trait. Both organisms in this example are heterozygous for both traits.

There are two methods to determine the outcome of a dihybrid cross, and the first one is the Punnett Square, which we will discuss first. The second method is the Branch Diagram, covered in the next section. These methods are applied to genes that assort independently, which follows one of Mendel’s laws. This law indicates that two genes will assort independently, meaning each gamete randomly receives one allele from each trait, and these traits do not influence each other’s inheritance.

Starting with the Punnett Square, it looks similar to a monohybrid square but contains more cells because it deals with more combinations. I will give you the starting genotypes, which are heterozygous yy and heterozygous rr, representing the phenotypes yellow and round, respectively. To determine the gametes, handle one trait at a time. For the yy trait, the gametes combine as yy. For the rr trait, the gametes combine as rr. Each combination presents as YY, Yy, yy, RR, Rr, rr. The setup is mirrored between maternal and paternal gametes.

After deducing all gamete combinations, the next step is to cross these in the Punnett Square. During this process, it's helpful to understand and track which alleles come from which parent. This continues until all possible combinations are laid out in the Punnett Square.

Once complete, the next step is identifying specific offspring phenotypes such as yellow round. For example, the probability of yellow round offspring is determined by counting squares with dominant Y and R alleles, expressed either as a fraction or a ratio of the total possible offspring. Here, color coding identifies different phenotypes directly within the Punnett Square, simplifying the tracking process.

This dihybrid cross generates a well-known 9:3:3:1 ratio under Mendelian inheritance for two heterozygous traits. The understanding and fluency in this method are crucial for test scenarios. If your professor varies the parental generation conditions, it may affect the setup and outcomes of your Punnett Square, requiring you to consider these variations in your approach to solving dihybrid cross problems.

But now, let's move on to the next section where we will learn about the Branch Diagram method.

Branch Diagram

Okay. So now let's talk about the use of the branching diagram as the second way to look at a dihybrid cross. Branching diagrams are great because they keep you from having to do the Punnett squares and getting confused with all these different traits, but they're also really great if you need to do math to calculate the probability of something. I don't really know why there's a question mark here, but you can just exit that out. Just like before in the Punnett square, I'm starting you out with heterozygous. Uppercase and lowercase 'Y' with uppercase and lowercase 'R', and these represent the uppercase Y for yellow, which is dominant. Uppercase R is for round, which is dominant. The lowercase 'y' is going to be green, and the lowercase 'r' is going to be wrinkled. And I'm giving you this. They would give it to you likely in your normal question. So I'm giving you the starting phenotypes and the genotypes. Now, I want you to use the branching diagram. The first thing you do is take each trait independently. So, first we're going to deal with the Yy. This is the mother and this is the father, and we know that we put one allele of each in the box. Now, if we do just a normal cross, what we're going to get is this 3 to 1 phenotypic ratio and a 1 to 2 to 1 genotypic ratio. And now, I have these questions over here. You have to figure out independently. What's the probability of the offspring being yellow? Anything with an uppercase 'Y' is going to be yellow, so that's 3/4ths and green, that's going to be 1/4th. Now, if we were to erase this, which I'm going to, and repeat this for the Rr. And if we do this just like we know how to do, just a normal monohybrid cross, you're going to get the same ratio. So the probability of being round, 3/4ths. The probability of being wrinkled is 1/4th. These are ratios that if you're not 100%, just like can get them off the top of your head, you should be figuring out how to do that soon because a monohybrid cross, you just cross it, it's 3 to 1, that's the ratio, and you know that. So a branch diagram looks like this, it takes each trait and breaks it up, here's trait 1 which is color, here's trait 2, which is shape, and then at the end, it will give you the nice ratio that you want. The first one is what's the probability of it being yellow? Well, if you remember we wrote that here. So, this is 3/4ths and the probability of being green, 1/4th. Then you do the same thing for round and wrinkled. 3/4ths, 1/4th, 3/4ths, 1/4th. And remember, we got all of these numbers up here from doing just a monohybrid cross. And this is asking for phenotypes. Remember that not genotypes, phenotypes, which is how we get the 3/4ths and one fourth. Then because of the product law, which is a math law that we're going to talk about if you haven't seen the video for it yet. But essentially the product law states that you could just multiply these. So 3/4ths times 3/4ths is going to be 9/16ths. 3/4ths times 1/4th is going to be 3/16ths. 1/4th times 3/4ths, again, 3/16ths, and 1/4th times 1/4th is going to be 1/16th. What is this ratio? This is the 9 to 3 to 3 to 1 ratio that we saw with the Punnett square, but we had to take a lot more time to figure that out, because we had to write all the alleles and do all the crosses and that huge Punnett square. But this is much easier because you just take 2 monohybrid crosses, one for each trait, one for color and one for shape, and then you do math figure it out. Now some of you don't like math and that's okay and feel free either way is fine. You can do this either way. Like I said, we both got to this 9 to 3 to 3 to 1 ratio. So, you can use the Punnett square or the branching method. Either way is fine. They both get you to the same result, so I would just choose which one you're most comfortable with. But remember, like I said before, it's super important to know what your starting genotypes are, because sometimes, they will give you the parental, which would be this, then expect you to figure out that the F1 is this, which is where I started. I started here, but sometimes they start one step above, and then ask you about the F2 generation, which would be 9 to 3 to 3 to 1. Like I said, be careful, are they giving you this, or are they giving you this? Because people get very confused, because if you do the branching diagram on the parental generation, you're going to get a 1 to 1 to 1 to 1 ratio, which is not usually the answer they're looking for. Their answers are looking for this. So don't do the 1 to 1 to 1 to 1. Make sure you know what you're talking about and you don't get confused and you really figure out, you know, what are you starting with and what are they asking for. So that's the branching diagram. So, with that, let's now move on.

Assume you have mated a homozygous dominant purple, square plant with a homozygous recessive pink, spherical plant. What is the proportion of purple and spherical plants that would be produced in the F₂ generation? 

Okay. So in this question, we're going to be doing a Dihybrid cross with both the Punnett Square and the Branch Method. So you can walk through whichever one you prefer or walk through both. I suggest you walk through both. So, this question says, you made a homozygous dominant purple square. So homozygous dominant for both with a homozygous recessive pink spherical plant. What's the proportion of the purple spherical plants that would be produced in the F2 generation? So, first, the first thing you have to know when you figure this out, what were you given and what are you asked for? In this case, they said that you have a homozygous dominant purple, so we'll say PP, and a homozygous dominant square, so we'll do SS. And you mated that with a homozygous recessive pink, lowercase p's, spherical, lowercase s's. So, this is your parental cross. Let me back out of the way already. So this is what you started with. Now, if you cross this, you're going to get an F1 generation and that's fantastic, but what they're asking for is the F2. And they're asking you, what's the proportion of purple spherical plants? So they're asking for phenotypes, Purple Spherical. Okay. So the first thing we have to do is figure out the F1. Now the F1 can be figured out. They're going to be heterozygous for all the traits. Now, how did I do that? How did I know that it was going to be Pp? It's going to be these 2. Because if you take each one, let me get a different color. And cross it and you do that for each one. You're going to get uppercase P with lowercase p, uppercase P with lowercase p, uppercase S with lowercase s, uppercase S with lowercase s, and you're going to get that for every single thing that you do. Just 100%. It's what you're going to get. So, this is going to be your F1 generation. Now, you are welcome to do a Diverse Hybrid Cross to figure it out. But I suggest you just memorize the short term. That any time you cross a homozygous dominant with a homozygous recessive, you're going to get all heterozygous. So just you just memorize that. But if you forget or you're in a test and you're freaking out, feel free to do a Punnett Square to figure it out. So now we have our F1 and our F1 is going to be what we put into the Punnett Square. So remember how we do this? We take each trait individually. So we'll say this is the mother and this is the father. Let me scroll down. We're going to take each trait individually. So we start with the P, we have an uppercase P and a lowercase p, an uppercase P and a lowercase p. And we're going to do that for the father as well. So that's what we start out with. Then we have our S's. So we're going to start out with, uppercase S, lowercase s. But because this is the second trait, we do the opposite. Right? And that's just taking each combination that exists. So now that we have that, we can begin writing our traits. So, I suggest you practice this a lot because you are going to get questions on it and you're going to have to be able to do this in a test setting. Usually, you have limited time. So if you're not moving as fast as me right now, or you're not even close, you probably should put in some practice and make sure that you can actually do it this quickly. Because in a test setting, you may be given a lot of these, and you're going to have to be able to do them quickly. Okay, so here's our offspring. Here's our Dihybrid cross. How I did this is I took one from here, I took one from here, one from here, one from here. And I did that for every single box. Now, this is our offspring. So the question asks, what the proportion would be of purple spherical plants? So purple, so anything with a P in it. So that could be PP or uppercase lowercase p is going to be purple. Spherical though is only going to be recessive. That's a recessive trait, which they gave us up here. Homozygous recessive, pink, spherical. So we know that the genotypes we're looking for are this in order to give us the phenotype that it asked for. So let's go through and figure out where those are. So there's lots of uppercase P's and S's. But the first one that I see, off the top of my head, is here. So let's keep going. Do you see any others? Yeah. There's one here with an uppercase p, lowercase s's. And is there any more? Yeah. Here's 1. And so that is, 3 out of 16. So 3 out of 16. And that is your answer for this question. So that is the way to do it via Punnett Square. Now, let's try the branching method. So remember, we started off with our Homozygous Dominant and Recessive parents. There we go. We know because of this little cheat that I told you that the F1 generation is this. And it's asking us for the F2. We're looking for either this or this? How many? So the first thing you do is you take each trait individually. So if you take each trait individually, what you get Oh, see, I just got confused. Start with the parents. But we're starting with the F1 because it's asking about the F2. So if you tray each tray individually and do a monohybrid cross, get 2 uppercase, 1 uppercase, 1 lowercase, uppercase lower, and 2 lower. So then, you have your purple. And, what color was it? White? Is it white? Recessive pink. Pink. So, out of this cross, 3 of the 4 are purple and one is pink. That's our first. Now, we have the next trait. And that's going to be, round and or what was it? I don't remember the traits. It was square and spherical. Let me go back and redo this. So square, cool. Square, spherical. Okay. So now we have our second trait. So now you can do your second cross, or if you can just know it, which over time you'll just eventually get to know it. Essentially, we're working with uppercase and lowercase s's, because we're dealing with the F1 generation. So if I do this cross, what I get is the same proportion as I did with the color trait. So we have 3 that are square and one that is spherical. And so you input those numbers here. So then, to get your traits here, you have purple square, which we don't care about, purple spherical, which we do care about. So this is the one we're going to calculate. And how you do it is you do 3 fourths, which was here, times 1 fourth, which is here, equals 3 sixteenths. So your answer to this question would be 3/16. That is how you do the branching diagram. Now, you would be given that question, and you could do it however you want. So I suggest you practice both methods and figure out, you know, do I like the Punnett Square method? Do I like the Branch method? I personally prefer the Branch method, but I like math. If you're not good at math or the product law doesn't really make sense to you, then go ahead do the Punnett square. If you get confused or get a number you don't think is right, the Punnett square is, you know, you can visualize it and see it. So that will always help. So, I realize these questions take forever. They're going to take forever on your test. So really practice them. Get your speed up with these Punnett squares, so that you know what you're doing and can calculate these things quickly in, like, a test pressure situation. So with that, let's now move on.

Write out all of the following gametes that can be produced from individuals with the following genotypes. 
a. AaBB 
b. AaBb 
c. AaBbCc 
d. AaBbcc

Okay. So, in this question, we are going to practice writing out the gametes. Whoops. Let's get my pen. Of the following gametes that can be produced from individuals with the following genotypes. And I feel like a lot of people get mixed up on this, especially when creating Punnett squares, because they end up with gametes that have 2 of the same allele, and they end up messing up, like, drastically messing up their Punnett square. And so, if you are doing a Punnett square, especially a dihybrid one, and you're finding you're getting all sorts of weird numbers, or you didn't fill out the entire thing, go back and look at your gametes. Because I assure you that's probably where you messed up. So the thing about gametes is that when you produce a gamete, certain rules have to be met. One, is that you only need one letter. Let me rephrase that. You need one of each letter. So in a, every single gamete will have 1a, and 1b. If you get a gamete, if you're doing your Punnett Square and you have something that looks like this, that's wrong. You messed up somewhere because each of the gametes should only have one of each letter. So you need 1 a, and 1 b. So that's really where most people mess up. So let's go through and practice the first one. So this one is homo or heterozygous for a and homozygous for b. So how you do this is you take the first of each letter, so in this case, it's this dominant a, and you pair it with each of the other corresponding letters. So what I mean by that is if we take our first a, we pair it with our first b and that's your first gamete. Then, because we have a second b, right, you have to take your first a and you pair it with your second b. Then, now you made every combination with that first a you can make, so then you go with the second a and the first b, the second a and the second b. Now, you may say, well, do I need to do that because these are copies? Right? These are 2 copies of each other. If you feel comfortable not doing it, don't. It's not necessary. But if you're still iffy on how to make these gametes, write it, write them all out. It's not going to hurt you. It's not going to do anything, so just write them all out. So if we're practicing the second one, what we do is we take our first a, pair it with our first b. We take our first A, pair it with our second B. Right, now these 2 are different gametes, it's different than what we saw above. Then, because we finished our first a, we can take our second a, pair it with our first b and our second a and pair it with our second b. Now c is going to be a little bit more difficult because there's an extra trait here. We have this the letter c now. So what you have to do is you take your first a, you pair it with your first b, and you pair it with your first c. You take your first a, you pair it with your first b, and you pair it with your second c. Then you take your first a, you pair it with your second b, and your first c. You take your first a, you pair it with your second b, and your second c. So those are your first four gametes. These are the gametes you can make from using that first a. Then, if we do our second gamete, what you do is you take your second a, your first b, and your first c. You take your second a, your first b, and your second c. You take your second a, your second b, and your first c, and you take your second a, your second b, and your second c. Now, if you've been paying attention to these patterns, what you might notice is that the only thing that's different between these 4 and these 4 is that first a. And so, what do I mean by that? I mean that my first gamete that I made over here was all uppercase a, b, and c. The first gamete I made with my second was lowercase a but uppercase b, and c. And if you're going to follow that along, right, you can follow this along through all of them, and what you see is that the only difference between the first and the second that I made were the first and the second a. So if you want a shortcut, so if you have no idea what I'm talking about, that's okay. As long as you can write all 8 of these, that's all you're ever going to need to do. But if you're kind of holding on with me and you say, I want a faster way to do this, well the fastest way to do it is write out everything you can make from the first a, or the first trait, and then go back and redo it with the second. Just switch these. Rewrite them all and switch them. And that's the way you can do that. So, let's practice d here. We take our first a, take our first b, we take our first c. We take our first a, our first b, our second c. We take our first a, our second b, our first c. We take our first a, our second b, and our second c. So if you want to go ahead and rewrite out all the traits doing the same kind of pathway that I did before with the second a, the first b, and the first c, then go ahead. But, if you want that shortcut, all you got to do is you got to switch these out with a, b, c. Right? Switch this to lowercase and then copy these directly. Switch this to lowercase then copy these directly, and you end up with the same exact gametes that you would do the other way. It just saves you a little bit of time. So either way, make sure that you have this down. Make sure that you're not stumped or questioning anything about how to make gametes because the quickest way to mess up a dihybrid Punnett square, and especially one that, you know, gets 10 points or something on a test, is to mess up your gametes. So make sure that you can create gametes and get the same gametes that I'm creating from all these questions. So with that, let's move on.

Two organisms with the genotypes Aa bb Cc Dd Ee and Aa Bb Cc dd Ee were crossed. Use the branch method to determine the proportion of the following genotypes in the offspring. I. aa bb cc dd ee

• A. 1/256
• B. 1/64
• C. 1/16
• D. 1/4

Answer: (A)

Two organisms with the genotypes Aa bb Cc Dd Ee and Aa Bb Cc dd Ee were crossed. Use the branch method to determine the proportion of the following genotypes in the offspring. II. Aa bb Cc dd ee

• A. 1/256
• B. 1/64
• C. 1/16
• D. 1/4

Answer: (B)

Two organisms with the genotypes Aa bb Cc Dd Ee and Aa Bb Cc dd Ee were crossed. Use the branch method to determine the proportion of the following genotypes in the offspring. III. AA BB CC Dd ee

• A. 1/256
• B. 1/64
• C. 1/16
• D. 0

Answer: (D)

In melons, spots (S) are dominant to no spots (s) and bitterness (B) is dominant to sweet (b). Answer the following questions that arise from a crossing of a homozygous dominant plant with a homozygous recessive plant. Assume Mendelian inheritance. I. What is the F2 phenotypic ratio if the F1 generation is intercrossed?

• A. 12:3:1
• B. 4:3:2:1
• C. 9:3:3:1
• D. 3:1

Answer: (C)

Here’s what students ask on this topic:

What is a dihybrid cross and how does it differ from a monohybrid cross?

A dihybrid cross examines the inheritance of two different traits simultaneously, using two letters to represent each trait. For example, if we are looking at seed color (Y for yellow, y for green) and seed shape (R for round, r for wrinkled), a dihybrid cross would consider both traits together. In contrast, a monohybrid cross examines only one trait at a time. The Punnett Square for a dihybrid cross is larger (4x4) compared to a monohybrid cross (2x2), reflecting the combination of alleles for two traits. The typical phenotypic ratio for a dihybrid cross is 9:3:3:1, while for a monohybrid cross, it is 3:1.

How do you set up a Punnett Square for a dihybrid cross?

To set up a Punnett Square for a dihybrid cross, follow these steps: First, determine the genotypes of the parents. For example, if both parents are heterozygous for two traits (YyRr), list all possible gametes they can produce (YR, Yr, yR, yr). Next, create a 4x4 grid and place the gametes of one parent along the top and the other parent along the side. Fill in the squares by combining the alleles from the top and side gametes. This will give you the possible genotypes of the offspring. Finally, analyze the grid to determine the phenotypic ratios.

What is the phenotypic ratio of a dihybrid cross?

The phenotypic ratio of a dihybrid cross, when both parents are heterozygous for both traits (YyRr), is typically 9:3:3:1. This means that out of 16 possible offspring, 9 will exhibit both dominant traits, 3 will exhibit the first dominant and second recessive trait, 3 will exhibit the first recessive and second dominant trait, and 1 will exhibit both recessive traits. This ratio adheres to Mendel's law of independent assortment, which states that alleles for different traits segregate independently during gamete formation.

What is Mendel's law of independent assortment and how does it apply to dihybrid crosses?

Mendel's law of independent assortment states that alleles for different genes segregate independently of one another during the formation of gametes. In the context of a dihybrid cross, this means that the inheritance of one trait (e.g., seed color) does not affect the inheritance of another trait (e.g., seed shape). This principle is crucial for predicting the outcomes of dihybrid crosses, as it allows us to use methods like the Punnett Square or branching diagram to determine the possible combinations of alleles and their associated phenotypes in the offspring.

How do you use a branching diagram to solve a dihybrid cross problem?

To use a branching diagram for a dihybrid cross, follow these steps: First, separate the two traits and perform a monohybrid cross for each. For example, if the traits are Yy (yellow/green) and Rr (round/wrinkled), determine the phenotypic ratios for each trait independently (3:1 for both). Next, create a branching diagram where each branch represents the probability of each phenotype for one trait. Multiply the probabilities along the branches to find the combined probabilities for each phenotype combination. This method simplifies the process and avoids the complexity of a large Punnett Square.