22. Evolution of Populations

Hardy-Weinberg Model

concept

## Hardy-Weinberg Model

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Hi. In this video, we're going to talk about the Harvey Weinberg principle, which is a way of modeling Lille and genotype frequencies in a particular population. But this model actually rests on some pretty stringent assumptions that are very hard to meet in real life in the wild. So what are these five assumptions? Well, the population you're looking at must have random mating, meaning that individuals choose mates randomly. Now we already know that sexual selection is very prevalent in nature, meaning this is a tough condition to meet. So you also cannot have any natural selection because all the individuals in the population have to be able to contribute to the gene pool equally for this model toe hold. Now again, it's very uncommon that there's no natural selection going on in the wild. So another condition that is difficult to meet you also cannot have any genetic drift. And this basically means that the illegals that get distributed to the offspring have to be distributed according to the probability rules that we talked about when we talked about men. DeLeon genetics. So this is much easier to meet in this is a much easier condition to meet in a large population where random errors tend to be smooth out. Ah, well, actually talk about genetic drift in a later video. But basically genetic drift is when a leal's are distributed toe offspring, and they don't follow those probability rules that we talked about before. It's kind of like a leal's air getting lucky and being distributed at higher probabilities than the mathematical models would have predicted. Again, it's an idea we'll revisit later. But the main point for Hardy Weinberg is that a leal's must be being distributed according to the probability rules we discussed Now. You also cannot have gene flow, meaning no new Leal's are added to the population and none are lost from it. So basically, the wheels are set and you don't get any new ones. You don't lose any. Just have the wheels you have, and you can't have mutation either. And that's because mutation would alter Leal's. So again, it's kind of following from that no gene flow idea. You can't have any changes in your Leal's. They have to stay static. So taking a look at this graph here, this graph visually displays the ideas in the Hardy Weinberg model, and this graph is looking at the genotype frequencies of a particular population. So Q squared that variable actually represents the Hamas, I guess. Recess, If individuals So ho Mose I guess. Homa zegas Recess Ivo two p. Q. Represents the hetero zygotes in the population, and P squared, as you may have guessed, represents the Hamas ICUs dominant individuals. So taking a look at this graph if we draw a line right down the center, meaning that we have a population where the frequencies of each individual Lille, that's what's displayed down here it the bottom, the frequencies of each individual wheel. So if the frequencies of our Tual eels are dead, even then, our genotype frequencies will be as such. Our hetero zygotes fall right about 50 percent mark or 0.5 So half of our population is going to be hetero. Zias are home. Is I got's. As you can see, they're both going to be at the same percentage because they actually those curves cross each other right there at the halfway mark that we selected. And that is going to be about 0.25 or a 25% frequency. So in this population. We had 50% hetero zygotes, 25% Hamas, I guess. Recessive and 25% Hamas, Agus dominant making, giving us 100% full population. Now let's actually take a look at how to work with these equations with some actual numbers. So before we jump into that, just want to point out that we will actually be using two equations that look at slightly different things. This first equation here that looks at Gina type frequencies, which is what we were talking about in that graph, looking at the percentage of the population that is Hamas, I guess. Recessive, hetero zegas or Hamas, I guess. Dominant. This second equation just looks at Lille frequencies. So what percentage of the population has the capital? A liel. What percentage has the lower case? A. A Leo. So how do we actually use thes equations? Well, let's say that in a given population we know that there is a particular condition that results from having two copies of a recess Civil Lille, something we should be familiar with by now. So that means that that percentage of the population let's call it 16% let's say, 16% of our population of pop has recess ivo condition. That means that Q squared equals 0.16 because Q squared, that's going to be the members of the population who are Hamas, I guess. Recessive, meaning the members of the population who are going to display this recess of condition. So if 16% of the population has that recessive condition, that means Q squared equals 160.16 Now, how do we figure out how many people in our population, our hetero zygotes, we know we can say with confidence that 84% is unaffected? But let's say we want to assess the risk for the future generations. So we want to know how many people are headers. I guess how many people are carriers for this particular trait? Well, how do we do that? We actually have to turn and use the second equation that equation for illegal frequencies. So if Q squared is 0.16 we can take the square root of 0. which is four. That means that in our population, 40% of people have the hey oh Leo. So by what that equation shows us, that means that 60% have the capital a Oh Leo, because the value for Q and the value for P must equal one. So if que is 0. than P must be 0.6 or 60% now, how do we determine how many people are hetero zygotes? Well, we know. Q. We know P, and we know that hetero zygotes are two p Q. So we do, too times the value for P just 0.6 or 0.6 times the value for Q, which is zero point four. And that means that there are 0.4 that equals 0.48 So that means that 48% of the population, our hetero zygotes and just to be complete, you could also figure out how many our home is. I go to take myself out of the image here, so I have a little more room to write. So if P equals than P, squared equals 0.36 and that means that 36% of our population is home. Ozai Ghous dominant, so these equations are not extremely complicated to use, however, they offer a powerful tool for us to determine the Gina types and illegal frequencies in a population at least one that meets those five conditions laid out by Hardy, Weinberg, Hardy and Weinberg. So that is how you use the Hardy Weinberg equations. That's what they represent, and that's all I have for this video, so I'll see you guys next time.

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