Hello and welcome back to Introductions to Genetics and Evolution. In the previous videos we've been trying to distinguish what fraction of phenotypic variance. How much of the variation you see in traits like height, skin color etc., come from genetics versus the environment. In this video I'll introduce you to what's refered to as the Breeder's Equation. But first, let me recap a couple of points. Now the trait variance that we are interested in, so this is any trait that you can be looking at, such as height, eye color, or anything that you can quantify in some way, has some genetic fraction and some environmental fraction. And we can simpilize this with a very simple formula. VP which is the phenotypic variance is equal to VG. That's the fraction of the phenotypic variance that is genetic, plus VE, which is the fraction of the phenotypic variance that comes from the environment. And again, we want to quantify how much is genetic versus environmental. The concept I introduced last time was that of heritability. That is the proportion of the total phenotypic variance, that is genetic. Now this is important, because this genetic component is the component that can respond to selection, whether that selection is natural or artificial. Now, again, this is a proportion, it ranges from 0, meaning that all the variation is environmental, to 1 meaning that all the variation you see is genetic in origin. Now we talked about means of identifying this before. But a new means I want us to start looking at here is in response to selection. Now this picture shows several students. The ones in white are girls. The ones in black are boys. The average height in this population, as you can see, is about 5 foot 7 inches. Now let's imagine that we take the circled individuals here, that guy and that girl, and let's say they had a bunch of kids. What would we expect? How tall would those kids be? Now one possibility is that they would be, on average, about 6' 0", just like their parents. That's a possibility. The other possibility is they might be 5' 7" on average, just like the overall population. Now, these are two very different outcomes. Now, if height was purely determined by the environment, then we might expect this latter one. We might expect that the offspring would look like the original population because it didn't really matter who the parents were. In contrast, if height was purely genetic, then we might expect the kids to look just like their parents because they inherit the genes from their parents. Well, we can calculate heritability by looking at this response to artificial selection. By looking at individuals who are not representative of the original population, breeding them and seeing what happens in terms of their offspring. So let's use corn, one of my favorite examples. Let's say you're looking at corn height. Now let's say corn height averages around 5 feet. Okay, so the population you're looking at, that's the average height of plants of corn. Let's say you select a group of 7 foot tall corn and you breed them. Now if the offspring of these 7 foot tall plants averaged 7 feet also. So you looked at a lot of individual offspring, on average they ended up having a distribution look something like this. Then that suggested the variance that we see here is purely genetic. The heritability is 1, because you see the offspring inherit the traits of their parents completely, okay? In contrast, if the height of the 7 foot plants were actually 5 feet instead. So, instead, the offspring would be more like this, then that suggests the variance in height is purely environmental or a heritability of 0. So this was a heritability of 0. I showed you previously the heritability of 1. What would happen if the height of the offspring of the 7 foot plants averaged 6? What might you expect heritability to be? Well it's a very simple answer. Well, 5 feet meant it was 0. 7 feet meant it was 1. So, 6 foot would unsurprisingly mean the heritability is 0.5, right? Or we can do the same thing and divide this up. That again if they averaged 5 feet, heritability was 0. If they averaged 6 feet it's 0.5. In between, if they're 5.5 feet it would be 0.25. Essentially what we're looking at is, we're looking at the point from where we started which was 5 feet. That was the starting population average. We're looking at the average of the selected group, which in this case was 7. And we're looking and seeing the offspring. How far did they get from the starting population average to the selected population average? A fraction of the way they make it is the heritability, and that is true. And that is actually how you can estimate the genetic component to whatever trait you're looking at. Now let me give you an analogy that might make this a little bit easier to see. This is a map of a subsection of the state of North Carolina where I live. So I live over here in Durham, North Carolina. That's where Duke University is. Now let's say I was trying to go from Durham, North Carolina along this interstate. This is I-85 I think, I can't remember. Let's say I was trying to go down to Charlotte, North Carolina. Now, if you start in Durham, you're trying to get to Charlotte, this is 150 miles away. That is similar to the selected group, so the starting thing was here. The place you're trying to get was over here, but let's say I only got to the city of Greensboro, I only got 50 miles from here. So what fraction of the way did I make it to my destination? Well, I was trying to go 150 miles, I only made it 50 miles. So, I made it a third of the way there. Well, that's the same concept when you look at artificial selection in estimating heritability from it. That, you're starting with a population average of 5, you're trying to get to this average, cuz this is the selected group. So these are the 7 foot tall corn. So, the distance I was trying to go here was from 5 to 7. So, I was trying to go 2. In fact, I only got 1. This is the new population's or the next generation's average which is 6. So I started with 5, was trying to get to 7, but I only made it as far as 6. So therefore, the heritability in this case would be 1 over 2. So 1, which is the response to selection, over 2 which is the selected group. So in this sense we can redefine heritability from one generation selection experiment, heritability can be defined as how far you got, or the response to selection after one generation. Relative to how far you were trying to get, or basically how intensely you were selecting. So heritability can be defined as R over S. The reason we can do this, is because R is dictated by the genetic variance. Whereas S is a combination of genetic, and environmental variance. Because that's what was in the original population there, right? Because again, as I mentioned earlier, the response to selection can only be through genetic variance. Now again, this measures the fraction of phenotypic variation that is genetic, because this is equivalent to Vg/(Vg + Ve). Or, as we said before, Vg/Vp. So let me give you a sample problem to try. Let's say you're selecting for plumper turkeys to have a nice dinner. Let's say you start with a population of turkeys, the average weight 25 pounds. And let's say you select turkeys with an average weight of 45 pounds from this overall population. Right, so in the population let's draw how this might look. Here's the distribution of weights of turkey. Here's your 25 pound turkey. There's a subset that are 45 pounds, so you select this group. Now let's say the offspring of these 45 pound turkeys weigh 40 pounds. So the offspring maybe like here. What is the heritability of weight in these turkeys? Try this problem. Welcome back, I hope that wasn't a very difficult problem. Again we're starting with 25 pound turkeys, we're selecting for 45 pound turkeys, and the offspring that we got were 40 pound turkeys. So what is first the intensity of selection here? Well, we're trying to go from 25 to 45. So in this case S = 20 because that is the difference between 45 and 25. The response, in this case we started at 25 and we only got to 40. In this case that is 15, which comes from 40- 25. So R / S would be equal to 15 / 20. In this case would be 0.75, so the heritability in this case is fairly high. That 75% of the variation that we see is genetic in origin. Now, I should remind you these are not perfect predictions. This is just giving you an estimate of heritability. And this comes back to the points that I raised at the very end of the last video. The amount of environmental variance is not necessarily constant. Some populations may have more or less genetic variance than other populations. This is what you saw for your turkeys and your farm. In another farm you may get a different outcome, and you have to remember what you're calculating. You're looking at the fraction of total phenotypic variance in the population you're studying that is genetic. So that is the Vg over Vg plus V. But again, this is very important and this is something that's not only utilized just in the context of artificial selection, but this is important for both artificial and natural selection. With artificial selection, and these are very, very similar concepts, the breeder is choosing desirable traits and has organisms with the most extreme desirable traits breed to do it. So let's say for example you're trying to select for friendlier collies. You take your two friendliest collies and you breed them. The same sort of thing happens with natural selection, that particular traits will facilitate survival or reproduction and organisms with the most extreme such traits end up having the most offspring. So the same principle applies. And again the response to either kind of selection, whether it's natural or artificial is always going to be in terms of the genetic variance. Well, thank you very much. I hope that was helpful.
