Dihybrid cross and the Law of Independent Assortment | High school biology | Khan Academy

In this video, we're going to build on our understanding of Mendelian genetics and Punnett squares by starting to think about two different genes. So we're going back to the pea plant, and we're going to think about the gene for pea color and the gene for pea shape.

Let's say that in the parental generation you have one parent that is homozygous dominant for both of these genes. So their genotype is capital Y capital Y and capital R capital R, so their phenotype for sure is going to be yellow round. We also see the genotype; we see which alleles it has.

Now, let's say that that is crossed with a homozygous recessive parent. So in this case, it's going to be green colored peas. It's counterintuitive to write green with the lowercase y and the color yellow, but the lowercase y represents green. And also, these are wrinkled green peas, so I will write that with the lowercase r here. The phenotype here is going to be green and wrinkled for sure.

Now, what's going to happen when they cross? What does the F1 generation look like? Well, we know from Mendel's law of segregation that for each of these genes, when a gamete is created, it randomly gets one copy of each of these genes. So for this first one, it's going to randomly get one of these capital Y's, so it's going to get a capital Y for sure from this first parent.

And it's also going to randomly get one of these capital R's, so it's going to get a capital R for sure from that first parent. Then by the same logic, it's going to randomly get one of these two lowercase y's, so it's going to get a lowercase y for sure. It's going to randomly get one of these two lowercase r's, so it's going to get a lowercase r for sure.

So this is the genotype for all of the F1 generation. This is often known as a dihybrid; it is heterozygous in both genes. Now, what's the phenotype here? Well, we know yellow is dominant, and we know round is dominant. So if we looked at these plants right over here, their peas would still be yellow round, just like this homozygous parent over here.

Now, what's interesting is when you do what's known as a dihybrid cross. When you cross one of this F1 generation with itself or with each other, and to do that, I'm going to create a four by four Punnett square here. One parent here is going to be hybrid or heterozygous in the color gene and also heterozygous in the shape gene. That's going to be true of the other parent as well—heterozygous or hybrid in the color gene and also heterozygous in the shape gene.

That's why this is called a dihybrid cross—you're crossing things that are hybrid in two different genes. Now we've already talked about the law of segregation; a gamete is randomly going to get one copy of each gene. Mendel also has the law of independent assortment, which tells us the alleles of different genes segregate independently.

So for this first parent here, whether it contributes a capital Y or lowercase y is independent of whether it contributes a capital R or a lowercase r. Now, there is a little bit of an asterisk, a little caveat on there. We now know that genes sit on chromosomes—one chromosome will have many genes on it. This law of independent assortment only applies to genes that are actually sitting on different chromosomes. If they sit on the same chromosome, they generally are not going to assort independently. But let's just assume the law of independent assortment because this is true for most genes.

So this first parent can contribute a capital Y out of this first gene and a capital R out of the second gene, or they could contribute the lowercase copy of the first gene and the capital R copy of the second gene—the capital R, the round allele of the second gene. We could go through every combination here; it could also contribute the yellow allele and the wrinkled allele, or it could contribute the green allele and the wrinkled allele as well. The same would be true for this other dihybrid, this other parent right over here.

So let me just write that down. They could contribute capital Y in two of the scenarios; they could contribute a lowercase y or the green allele in two of the scenarios. They could contribute a capital R in two of the scenarios, a round allele, or lowercase r in two of the scenarios, a wrinkled allele.

So you have all of the different combinations that each of them can contribute, and you can once again—whether you get the yellow or the green is independent of whether you get the round or the wrinkled. So these are all equally probable right over here. When the two gametes from these two parents merge, we can then look at what the genotype of the offspring is going to be—the genotype of the F2 generation because we're crossing two members of the F1 generation.

I encourage you to pause this video and fill in this grid; see if you can figure out the different genotypes that will result. All right, now let's do this together. So this scenario right over here, you're getting a capital Y from both parents, and you're getting a capital R from both parents.

This scenario over here, you're getting a capital Y from this parent, lowercase y from that parent, and then you're getting a capital R from both. This scenario over here, capital Y from both parents, capital Y capital Y, and you're getting a capital R from this parent and a lowercase r from that parent.

Then this scenario over here, you're getting a capital Y allele from this parent and lowercase y from that parent, and you're getting a capital R from this parent and a lowercase r from that parent. Now I'm just going to speed up the video and just fill in the rest of these using the same logic.

All right, now that we've filled out this Punnett square, let's think about the different phenotypes. How many of these plants are going to produce yellow round peas? Pause the video and think about it. Well, it's yellow and round; it has to have at least one capital Y and one capital R.

So that one's going to be yellow and round. This is going to be yellow and round. This is going to be yellow and round; that's yellow and round as well. This is yellow and round; that's yellow and round. This is yellow and round, and that one is yellow and round.

Last but not least, I think this is the last one; that is both yellow and round. Actually, let me make a little color code here—yellow, yellow plus round. Here we're talking about the phenotype; you can see we have different genotypes here, but because both yellow and round are dominant, as long as you have at least one Y and one R, you're going to have a yellow plus round phenotype over here.

So you have one, two, three, four, five, six, seven, eight, nine, and I will say there's nine of these over here. Now, how many of these are going to be yellow plus wrinkled? Pause the video and think about that. For that phenotype, yellow and wrinkled, you're going to have to have a capital Y and two lowercase r's in order to be wrinkled.

So you have at least one capital Y and two lowercase r's. Let's see—at least one capital Y and two lowercase r's. It looks like you have exactly three of them that phenotype. What about the other way around? What if we are looking for—and I'll do it in this green color—green, green plus round?

How many of them exhibit that phenotype? Well, to be green and round, you have to have two lowercase y's and you have to have at least one capital R. So this would be green and round; this would be green and round. Then this would be green and round as well, so you have three of those.

How many of them are going to be both green and wrinkled? Well, I think you see that one scenario over here; that is both green and wrinkled having that homozygous recessive phenotype. If you were to do this many times, you'd expect the ratios between these various phenotypes to be nine to three to three to one.

When Mendel and many other people since Mendel have done these types of experiments, they have seen that statistically, this is what you see in that F2 generation. Now, you're unlikely to get exactly a nine to three to three to one ratio; it's all probabilistic. Every one of these 16 scenarios is equally likely, so you would expect this 9 to 3 to 3 to 1 ratio, but you're not always going to get that exact ratio. You'll probably get something close to it.