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2. Mendel's Laws of Inheritance

1

Punnet Square

15m

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Hi in this video, we're gonna be talking about a di hybrid cross. So let's break it down. A di hybrid cross die usually means two. So this is a cross that is looking at a mating between organisms examining two different traits. So color shape. Those are two separate traits. So typically what you see, whereas before with a mono hybrid, you would see it like this using one letter. Well, a di hybrid is typically going to use two separate letters. One that represents each of the traits. You can see here that both of these are hetero sickest. So there's two traits and both of them are hetero sickness. Now, a die hybrid cross using there's two ways to really figure it out and figure out what the offspring are gonna be, what the relative proportions of the offspring, genotype and phenotype and the first one is the opponent square. And that's what we're going to talk about first and then we'll go the next section. We'll talk more about the branch diagram, which is the second way. And both of these methods are done for genes that are independently assort if you remember what that means, That's one of Mendel's laws. And it says that these two genes are completely assorted independently, meaning that the gametes will take one random allele from one of the traits and one random a little from the other trait and that it's not that they are just, you know, always inherited together. It's just that these traits are completely independent of each other. So like I said, there's two methods, the punnett square and the branch diagram we're talking about the punnett square first. So when we go over this I'm gonna back out. So you can actually see, so the punnett square looks very similar to the mono hybrid. Um But you can see there's a lot more squares. And so um I am going to be extremely nice and give you the starting genotype. So here I've given you hetero Y. Y. And hetero sagas are are and these represent phenotype which are both yellow and around. So yellow is obviously going to be the white trait. Whereas the round phenotype is going to be the R. Train. Now when doing opponent square. The very first thing that you do is you figure out what are the gametes, what are leo's are in the gammas. And so I suggest that the way that you do this is you take it one at a time. So if you are to take this one at a time, what you get is you get um you start with A. Y. And we'll start with the mother. So we'll say this is the mother and this is the father's gimmes. So the egg and the sperm. Now if you're gonna start with the why, what you're gonna get is you're gonna get why why? And you're like okay well that only takes up two of the pills but you will realize very quickly that you actually need to double it. And the reason is because of the second trait. So the first trait, that's what you get then you start with the second trait and you go R. R. And that's fantastic. But then again there's only two gametes here. This time you need to reverse it. Are are now you may say how did I get this? Well one you just use each combination of why? Big case? Y. Little case. Why big case? Our little case are. So this is every combination. So you have to upper case is you have to lower cases. You have one where the Y. Is the upper case and you have one where the R. Is the upper case. And that's every combination of these two letters that you can make. Now let's see can you do the father? Can you figure out what the gametes are here? Take a second and figure out if you can do it right it in and then we'll check. So other than just if you wanted to cheat it's the exact same as the mother. But if you wanted to actually work through it you would take the Y. And the Y. And you'd repeat it. And then you could take the R. R. And that's every combination to uppercase to lowercase one where the Y. Is uppercase and one where the R. Is the upper case. So this is great. So actually let me take a second and I'm going to redo this in a different color so that we can very easily tell what we're talking about. Okay, so now when I write them, I'll write them with the appropriate color so that you can tell where they're coming from. So now you just cross them, do them exactly like you would normally with a normal punnett square. So I'm gonna move this up so I can actually see my colors. So I'm going to take why? Why are are and I'm gonna do it for each one. So I suggest that you work with me and see as if while I'm filling these in, you can fill them in as well. Hopefully the colors aren't confusing. Just trying to um make sure you understand which alil is coming from the mother and which Alil is coming from the father. So it's just gonna be second, I suggest you practice because you're going to be seeing these on test, you're gonna have to do them on test, you're gonna have to do them on quizzes. And the only way that you're going to be really successful is if you really understand how I'm getting these. So pretty much I just take one from the mother, one of the same allele from the father and then I do the same for the second level here. Did you do? So we are getting this done. It's a process. I know that's why the next, Some people really prefer doing this method, I know it's tedious but there's actually the second method that I'm going to talk to you about and it keeps you from having to like actually write all of these out. But some people really prefer this method because it's you can easily visualize it right? I mean I'm able to do this here with multiple different colors and really be able to uh show you which khalil is coming from, which parent? And finally the last row, here we go. I know this is super fun watching me. But hopefully you watch it enough times you're doing it at home and you can easily figure it out when it comes to his time And then finally the very last one. Okay, trust me, this is tedious choosing these colors too. Okay, so there we go. We have our di hybrid cross. So these are all our offspring and there's lots of them. And so now you're probably going to get asked lots of questions like these. Like what's the probability of having yellow round offspring? Remember? Yellow is the dominant, Y and round is the dominant are um so If you ask that question, what's the probability, well, the first thing is probability is going to be in terms of either a ratio or it can be terms of a fraction. So if we're doing it in terms of a fraction, we first need to figure out what our denominator is and the denominator is going to be total. So if you were to count these will be for a 1216. So our denominator is autumn 16. So we're looking for the number here, we're looking for the numerator and that is the number of yellow round. So when we're asking that question, what are we asking? Were asking for the number of dominant wise and dominant R. S. So if we go through here, I'm going to make this yellow anytime you see a yellow mark, you're gonna know that this is a yellow round offspring. So here we have a yellow round and that's because there are dominant uppercase wise and uppercase ours. Here we have another one, here's another one. Here's another one. So any time there's an uppercase Y. In an uppercase R. Now you'll notice I'm here right here and there's not an uppercase Y. Or uppercase R. So that's not going to be the case. We'll move on to the next one. Now I'm here there's an uppercase Y. Which means yellow but there's no uppercase R. So that's obviously not it. So we're going to keep skipping same in the next one. So any time there's an uppercase Y. And an uppercase R. I'm putting a yellow strike here and that is going to mean that this is a yellow round. So now I have all my yellow round chosen. So if I go and count them. Here's 123456789 99 out of 16 gonna be yellow round, then we have yellow wrinkled. Now I haven't told you anything about wrinkles yet. But obviously if round is dominant then wrinkled is going to be recessive. So we're going to choose a different color here. We'll choose green but we won't choose green. Let's choose something else, choose blue. So yellow wrinkled. So this is going to be upper case Y. And what lowercase R'S. So we'll start here with the first one that we haven't looked at and this has a lower case Y. So it's obviously not it the next one has uppercase Y. And lowercase R's. So that's it. And if we keep looking we're gonna see that that's another one that this is another one and that's it. So for this we have 123 it's gonna be three out of 16. Let's do the same thing. Now for the green round. And for this we will use green. So green haven't described it red at all. But if we know yellow is dominant then green has to be recessive. So now we're looking for the lower case wise and the upper case R. S. Or put a green spot their first one is not it? The second one is This one is and this one is so then we have 123 that's three out of 16. And then finally the very last one I'm gonna scroll down so you can see it that's green wrinkled. We'll use this pink color for it and there's obviously only one left which is here. And so this is going to be one out of 16. Now this is a really important ratio, this is 9331 and this is a really important di hybrid ratio. You're gonna see this all the time with hetero zig asse. But the hedgerows I guess mating, which is what we had because we had why why are are uppercase lowercase uppercase and lowercase. Both of these are hetero. I guess you will always get this ratio the state of medallion inheritance. Now I was really nice to you and I know it doesn't seem like it having gone over all of these different colors and where they come from. But the reason that I was nice to you is because I gave you a heterocyclic mating as what you start with. So I said this is what you're starting with your, starting with two mother and a father who hetero ziggy's and you're looking at the F. One, their offspring. But often times if your professor is really nice, that's what they'll give you, if they're not nice to you, what they're going to give you is something very different and I'm gonna box it here. What they're going to give you is they're going to say the parental is this and then they are going to ask you about the F two generation and that's gonna be how your question is designed and it's going to be in words, it's gonna be a paragraph or sentence format. But essentially they're gonna say you have a home as I guess dominant, yellow and round cross with a home as I guess recessive green and wrinkled. And what about the F. Two? Now, luckily I'm telling you because your F. One generation of this cross is going to be this. Now I you can go ahead and do your opponent square if you would like with these two. Um totally actually suggest that you do. But I guarantee you if you have a homeless I guess dominant the homos I guess recessive parental. And they ask you about the F. To your F. One generation will always be hetero cycles which is exactly what I just walked you through. It could be that cross. And so this here will be your F. Two generation and that's what you will sometimes see so don't get tripped up. So make sure whenever you're doing these questions that you actually look and you ask what the question is and what the mating is. Are they giving you the parental and asking for the F. Two, are they giving you a hetero side I guess and asking you to do it, what are they giving you because this ratio here? And what I just walked you through this is an example of two heterocyclic straights. So make sure that you don't get tripped up and that you understand, are they asked do they give me parental and asking for F. Two or did they give me hetero cigarettes and asking me just to do it from there? Obviously the second one is easier than having to go for the parental. But just make sure that you understand because it's so easy to get confused on this topic. And so you need to make sure that you read the question say is this parental or is this the F one? What am I actually looking for? But that's the punnett square. So that's a great way to do this. But let's now move on to the next page.

2

Branch Diagram

6m

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Okay so now let's talk about the use of the branching diagram as the second way to look at a di hybrid cross and 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 probability of something, I don't really know why there's a question mark here but you can just exit that out. So just like before in the punnett square I'm starting you out with heterocyclic. This um uppercase and lowercase wise uppercase and lowercase Rs. And these represent the upper case is yellow, it's dominant upper cases round dominant. The little Y. Is going to be green and the little R. Is gonna be wrinkled. And I'm giving you this they would give it to you likely in your you know normal question I'm giving you the starting genotype and the phenotype and I say okay I want you to use the branching diagram. So the first thing you do is you take each trait independently. So first we're going to deal with the Y. Y. So this is the mother and this is the father and we know that we just put one alil of each in the box. Now if we do just a normal cross, what we're gonna get is this 3 to 1 ratio that we're sorry backed up there. Hopefully you saw that that's why I came from here. This one from here and so and so forth. And we get this 321 tina tippet cross or 1 to 2 to one gina tippet cross. And so now I have these questions over here, you have to figure out independently what's the probability of the offspring being yellow? What did I say? Anything with an uppercase Y. It's gonna be yellow. So that's um that's 3/4 and green, that's gonna be 1/4. Now if we were to erase this which I'm going to and repeat this four, the green. We're going over the round, we're going to get the R. R. R. R. And if we do this just like we know how to do just a normal mono hybrid cross, you're gonna get the same ratio. So the probability of being around 123 is 3/4. The probability of being wrinkled is 1/4 and this is just a normal mono hybrid cross. 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 club soon because the mono hybrid 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. So this takes each trait and breaks it up. So here's trait one which is color, here's shape, a trait to which is shape. And then at the end it will give you the nice ratio that you want. So the first one is the what's the probability of it being yellow? Well, if you remember we wrote that here. So this is 3/4 and the probability of being green 1/4 then you do the same thing for round and wrinkled. 3/4 1 4th, 3/4 1 fourth. And remember we got all of these numbers up here from doing just a mono hybrid cross and this is asking for phenotype. Remember that? Not genotype phenotype, which is how we get the 3/4 and 1/4 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 can just multiply these. So 3/4 times 3/4 is gonna be 9/16 3 4th times 1/4 is going to be um 3/16 1, 4th times 3/4 again, 3/16 and 1/4 times 1/4 is gonna be 1 16. So 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 of more time to figure that out because we had to write all the wheels and do all the crosses and that huge punnett square. But this is much easier because you just take two mono hybrid cross, one for each trait, one for yellow, one for shape, one for color, 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 9-3 to 3-1 ratio. So you can use the Punnett Square, you can use the this is the branch method either way is fine, they both get you the same thing. 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 you're starting genotype sar because sometimes remember block this out sometimes they will give you the parental which would be this Then expect you to figure out that the F. one is this which is where I started I started here but sometimes they start one step above and then ask you about the F two 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. Your aunt's looking for this. So don't do the 1212121, 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.

3

Problem

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 F_{2} generation?

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4

Problem

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

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5

Problem

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

6

Problem

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

7

Problem

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

8

Problem

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

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