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Mendel's First Law
They tell me I’m supposed to start these things off with something to grab your attention. So I’m going to do so in about five seconds. Did you know our modern understanding of genetics is based on the work of a failed math teacher who'd walk around cutting up genitalia? It’s true.
Before you start developing a phobia of genetics, perhaps I should explain a little bit more. Gregor Mendel was a monk who back in the 1800s was clipping off the flower parts of pea-plants, so he could study how they passed on their traits from one generation to the next. And it’s his discovery, his statistical analysis of his results, that the two main laws of inheritance; Mendel’s first and second law are based on.
There is a lot of ground to cover in studying Mendel’s laws. Too much for me to cover at this moment. So what I’m going to do right now is I’m going to focus in on Mendel’s first law on the vocabulary of genetics. Then I’m going to address and go over to the major tools used in studying inheritance patterns, that are called Punnett squares and pedigrees. Once I’ve got that down, you should be able to have the main tools you need to study genetics.
But I do highly recommend that you go back to your textbook or watch my video on Mendel’s second law. One good reason to do that. is then I’ll also in that video I’ll address not only the Mendel’s second law, but I’ll look at how Mendel’s two laws are reflected in these either events of meiosis. And one of the reasons that I really recommend you do that, is because, that’s the kind of question that they love to ask in the essay portion in the AP biology exam.
So let’s get to it.
Let’s start off with Mendel’s first law and talk about some of the vocabulary that he came up with, to describe how genetics works. So Mendel's first law is often called the Law of Segregation. And this is the idea that, every inheritable trait is controlled by two or a pair of factors. And when you make your gametes, those factors segregate or separate more easily into making your separate gametes.
What does that mean? That means that you get two copies of every gene. You get them from one from mommy, one from daddy. When you go ahead you make your own sperma eggs, you are going to divide those up.
I just used the term called gene, what the heck is that? Let’s talk about that for a while, because this is an area that a lot of kids easily get confused about. That’s the difference between a gene and an allele. A gene is a section of your DNA that carries the instruction on controlling a particular trait, such as the shape of your earlobe, or your ability to roll your tongue.
Alleles are the different in versions of those genes. Some people have for example the detached earlobe that I have, others have an attached earlobe shape, as you can see in this here. So mine goes down and up, that’s detached, this is attached. What’s the difference between these kinds of things? It turns out that, some like this, if you can just get one copy of it, you will show it.
Well Mendel figured out that there are some versions, some alleles that you needed two copies in order to express. Express is what biologists call showing up. So let’s go and talk about the terms that he came up with. He said the dominant allele is the allele that will express its effects, even when combined with a different allele. Whereas recessive, is an allele that only expresses its effects, when it’s combined with an identical recessive allele. What’s the difference?
It turns out that we now know that dominant alleles are sections of your DNA, they are actually code for a functional protein. So if you make that protein you will see its effects.
Typically recessive alleles are ones that make either non functional or faulty proteins. There is something wrong with that protein. And so that’s why if you get one working copy, and one non working copy, or just new copy of your gene whatsoever, you still show the effects of protein because you got a copy from a working version.
But if you get two copies of a non working version then, it’s not showing up. For example, I can roll my tongue. Some of you out there can’t. Turns out that tongue rolling is a dominant allele. Which means that I know I have at least one copy of it because I can do this. And you guys out there who stick out your tongue go. You, I know have two copies of this non-functional recessive non-rolling allele.
Rather than me saying what you have and what I can see, scientists came up with some terms to describe this. Let’s take a look at those. The first of which is genotype. That’s easy because just think it’s your type of genes. It’s a combination of alleles that you have that make up your genetic background. It’s the interactions between your alleles. It's do you two dominants, do you have a recessive? Or do you have a dominant recessive that creates what people can actually see?
You can see my phenotype, my visible characteristic. You can’t see my DNA. So phenotype that’s the type of phenomenal or observable traits that somebody can see.
There’s these root words that we are going to be talking about a lot in biology. And there is a root we are called homo which means the same. Zyg is a root word that we use in words like zebra and means when things came together. So homozygous means two identical alleles or two similar alleles came together. So if you are homozygous for something, that means you have either two dominant or two recessive versions of it.
So what you do is you say homozygous dominant, or homozygous recessive. Hetero is a word that sounds you may have heard of it before, that means different. So heterozygous means you have a dominant and a recessive. You don’t need to say heterozygous dominant, because that’s kind of redundant.
Writing out homozygous dominant for the attached earlobe or the tongue rolling gene, that’s a lot of words. Biologists are people and people by definition are lazy. So they came up with a quick way to refer to all of this stuff.
So instead of saying homozygous dominant, they’ll are just use capital letters top represent the dominant allele. And for homozygous recessive, they’ll use lower case letters to represent the recessive allele. What you do is that, you pick the letter that’s usually associated with the dominant trait of that gene. So for example, for tongue rolling I’ll use big R for the dominant tongue rolling ability. And I’ll use little r for the recessive non-rolling allele.
And somebody who is heterozygous, they would have Rr. While somebody who is homozygous recessive will be rr. And somebody who is homozygous dominant will be RR. You notice, their phenotype is tongue rolling. So a homozygous dominant person, you can see them roll their tongue. Heterozygous person will have the exact same phenotype. The homozygous recessive people, they are the non-rollers. And when I start to show you how to solve these genetic problems, you are going to like the homozygous recessives. Because when you see their phenotype, that tells you their genotype.
How could you figure out if somebody is RR or Rr? What we are going to do is we are going to use Mendel’s first law. And we are going to use a technique called a Punnett square to solve this problem. Theoretically you could do this if you are a scientist and you did some DNA finger printing est of it. But that’s not going to happen on the AP exam. What they are going to do, is they are going to give you a bunch of genetic problems, and expect you to be able to use Punnett squares to do that.
Before we go to the Punnett squares, let’s think with Punnett squares you have two gametes. According to Mendel’s law, people make gametes when they separate their alleles. So let’s suppose we had somebody who is homozygous dominant. When their big R and big R separate from each other, they could make a sperm that is big R, or they can make a sperm that is big R.
Similarly if somebody is homozygous recessive when their little r separate, they make two identical gametes either sperma egg have the little r. What about somebody who is heterozygous who is big R or little r?
Think about it when they separate, you are going to end up with 50 percent of your sperma eggs as big Rs, or you are going to wind up with 30 percent of them with little rs. Let’s go ahead and take a look at how a Punnett square works.
Let’s suppose we have this person here. And what we are going to do is we are going to cross two people who are heterozygous. That means that they are Rr, and when we say cross, that’s a very polite way for saying we are going to do some breeding. If we used anything more explicit we are going to get into trouble. So we are going to stick with crossing.
So what you do with a Punnett square is you take one parent, let’s say this guy here. And we are going to put his gametes on the top. So I’ll put this big R here and his other allele is right there. And here I’ll add this, so you can see these other sperm. I’ll take this parent and I’ll use this parent’s allele in the various gametes, in this case egg, on this side. So this person can make a big R allele in their gamete, or they can out a little r in that gamete.
If these are gametes eggs and these are sperm then what are these? These are the babies. Scientists don’t like to say babies, they like to say offspring. Because when you are looking at a canal of corn, yes that’s a baby but people don’t like to think about 'I’m eating little corn babies'. Instead we say offspring because that way we feel nice about eating side of corn.
So this sperm swims to that egg and we make a big R big R. This sperm swims to that egg, and we make a big R little r. Following so far? This sperm swims to that and some of you might be tempted to put the little R first, but the general rule is you put the dominant one first.
So we write Rr, and then last we have this little r combined with that little r. And so what you can see here is genotypically, I have a ratio of one homozygous dominant to two heterozygotes to one homozygous recessive.
But when people look at a baby they don’t say, "Oh! Look at a homozygous dominant there, isn’t that cute." No they say, "Oh! This baby can roll his tongue oh! He can roll his tongue he can roll his tongue, or look at the little baby trying to roll his tongue." So we call that a phenotypic ratio. And so the standard hybrid cross between two heterozygotes, the ratio you are always going to see what’s called a 3:1 phenotypic ratio.
This shows me how a Punnett square works. This doesn’t answer my question again. How do we solve the problem if there is a person who is a RR? Are they one of those little stealth hereterozygotes? So what you do now is you do what’s called a test cross. A test cross is where you take a unknown person and we match them up with somebody who is homozygous recessive. Let me show you how that works, and see if you can figure out why this is called a test cross.
So here, let’s have the positive video while you fill out this Punnett square right there. So go out ahead and I guess I can fill for R. So I’ll go ahead and I’ll do it for you. So I’ll take this parentt and I’ll put their gametes up here on the top, like I did before. We’ll make this little sperm. And we’ll take this parent, and we’ll put her eggs right here. Again we’ll put this parent there, and then this parent there. Any problem so far? No, good.
So let’s combine them. So we have this egg and sperm come together here, and we get a Rr. Rr looking the same, big R little r and big R little r. Notice, if this unknown person because we are not quite sure, is the person big R big R or little r little r?
If they actually are homozygous dominant, look what happened? We have a100 percent or 1:0 phenotypic ratio of tongue rollers. Over here, let me do the match. Here is one baby can roll his tongue. Here is another baby can roll his tongue. So far, two out of our four offspring can roll their tongue. These ones here however, rr, rr we have our non-rollers. So when we mate an unknown person with a homozygous recessive, they're homozygous recessive because they can only make our little r gametes. If our unknown is heterozygous, we wind up with the 50:50 phenotypic ratio, with a homozygous dominant it’s a 100:0 phenotypic ratio.
So that seems pretty simple. But on the AP, what they really like to do is, they like to say let’s suppose we had a farmer. And he plants some seeds and it turns out when the seeds grow. Let's suppose there is a single gene in pea-plants that control their height. And it turns out that 79% of the offspring are tall, and 24% are short. How can we solve that?
First you are going to stop for a moment and take a look at the numbers. 79 to 24 roughly how many times does 24 go into 79? You do the math. It turns out this is roughly a 3:1 ratio phenotypically. So now that we know that, we can go onto our Punnett square to solve the next problem.
Just to remind you, you are not ever going to get a pure 75:25 ratio. I, a lot of times but I do as I try to drop off the last digit if it’s a 3 digit number. And that makes them math easier.
So let’s take a look at this. But instead of starting with the parents, because we doesn’t know what the parents were, because we just have a packet of seeds. What we do know are the offsprings. So let’s create them.
Remember it is a 3:1 ratio. So we start with the easy ones, those are the homozygous recessive ones. So I’m going to put that little baby here.
Since we are talking about tall versus short, I’m going to sue a lower case t for height. So little t are the three little short plants. This little t came from where? Had to have come from this parent. This little t came from where? Had to have come from this parent. With me so far? Good.
Now let’s take a look at the other three. We know those other three offspring were tall. So they had to have at least one big T. Where did this T come from? It did not come from that parent, it must have come from this parent. So now I can fill in. Oh! wait a second I got that it did it. Wait a second where did that big T come from? It must have come from this parent. There we go. We’ve got the parents. Practice this a bunch and you’ll get really good at it. And after you’ve practice a bunch, you’ll actually stop needing to use the Punnett squares. Because you see a 3:1 ratio, you know it's two heterozygous individuals. If you see a 1:0 ratio you know it’s the homozygous dominant where we don’t care. And if you see a 1:1 ratio you know it’s a heterozygote crossed with a homozygous recessive.
Let’s move on.
So what if you are trying to figure out if I was big R or big R little r. My wife for some reasons is not willing to let me have a whole bunch of children with some non-rolling women. Another way you can do this is by looking at my parents and maybe my grandparents. And what you do is we use a tool called a pedigree.
So let’s take a look at that.
A pedigree uses some simple symbols. We use a round circle to represent women, and a square to represent men. If we darken one of these in, you’ll see right here. That means person has some recessive traits. Then if I connect them with a line, that represents that they are hopefully married and they're crossing and having some children. So let’s show those. And then I’ll go ahead and fill in the rest of this.
When you look at a pedigree, to make it easy to refer to one generation after the next, we will talk about the first generation being referred to as I. The next generation as II and the third generation as III. For those who don’t speak Roman that’s one, two and three. Often, we AP biology people will sometimes call this the P1 generation which means parents number one. These will call the F1 generation that’s f for felio which is Latinish for children and then if this is f1, this will be f2.
But I’m going to stick with the I, II, III. Going from left to right, I’ll refer to this person as I1, this person is I2, this person is II1, II2, and so on and so forth. You will hopefully pick this up. Let’s suppose I’m person II2. How could you figure out what my genotype is using this?
What will do is we'll start with those people who are easily showing their genotype, and that’s the people with a recessive phenotype. So let’s take a look and we'll fill those people in. This person here, my sister rr for the non-rolling allele. My dad is also rr. He is homozygous recessive and therefore doesn’t show the tongue rolling ability instead my dad goes ah.
So let’s start figuring out something. If my dad is rr, that means everybody here has a little r including me. But, because we know that we have at least one big R, because we have the ability to roll our tongue, there we go. Where did that come from? Mommy. Now who else can you figure out besides me and my siblings? Take a look. Where did my sister come from? My sister known otherwise as II5, a lovely name I think. If she is recessive, that means my mom had to have carried at least one recessive trait.
Let’s take a look at my kids. Here is my daughter. She’s got at least one big R, here is my son he’s got another big R. And here is my second daughter, she has rr. What does that tell us about my wife? She’s got a big R and a little r. That little r being one of the ones in my third child here. What about these? We don’t know. And this is the situation that the AP biology people are trying to catch you up in. They’ll sit there and they’ll say is it a is it b or is it c which is both a and b. This person is either RR or Rr. And that’s how you do a pedigree.
So now you’ve got the tools that you need to solve basing genetic problems. You got the Punnett squares and the pedigrees, and that will give you the tools you need. Now despite the creepiness of this image of some guy walking through a corn field or a pea field locking up genitalia left and right, Mendel’s first laws of segregation is a really useful principle. You’ve also got the vocabulary now of gene versus allele, Dominant versus recessive, genotype and phenotype, so that you can solve many of the problems that are going to be on the AP biology and genetics.
If you want to take up the next step however, I’ll really recommend that you watch my video on Mendel’s second law. In that one, in the bonus materials, there is also a bunch of genetic problems that will help you go through the kinds of problems you expect to see on the AP biology exam.
If you check out your bonus materials, you’ll also find a link to the online virtual version of the official AP biology genetics lab. Again, some of the concepts in there go beyond Mendel’s first law, but once you are down with that stuff, this will actually become just a bunch of logic problems. So go ahead and play with it.