Welcome back this is third module in the third week. And in this module, I'm going to talk about how biometricians go about trying to estimate hereditability for phenotype. And recall from last time, the last module. What we did, is we introduced the notion that a variance of trait is a measure of the extent to which in individuals in the population differ on that trait. And what biometricians look in variance. Is they look at trying to decompose that variance, into components associated with genetic factors and components associated with environmental factors. Heritability is a statistic that will relate to the proportion of variance that is associated with genetic factors. So, the way we formulated this last time, the way that biometricians formulate it, is the variance in the phenotype is decomposed into genetic and environmental, portions. And, in turn, the genetic, variance component can be decomposed into additive and non-additive genetic effects, the environmental to shared and non-shared environmental effects. The heritability, in facts there's, I do mention this next time, last time, I'm sorry, I didn't mention it last time. But there's actually two heritability coefficients. I gave you this one last time, the heritability or total heritability sometimes called the broad sense heritability. Which is the proportion of variance that is attributable to all genetic factors, and it's usually denoted by an h. There's also something called the additive or narrow sense heritability. I'm going to call it the additive heritability or sometimes just a. And it's usually denoted a squared because it's a proportion of phenotypic variance that is associated with additive. Only the additive genetic effects, not the non additive genetic effects. A reasonable question to ask is, well, why do quantitative geneticists need two heritability coefficients. Well, there's several reasons for this. First, there's the conceptual reason. The Total Heritability indexes the contribution of all genetic effects to individual differences in the phenotype. Of course, the Additive He, Heritability is only indexing additive genetic contributions to individual differences in the phenotype. It turns out that, if you look at genetic mechanisms for parent/offspring resemblance in a quantitative system, only the additive genetic effects contribute to parent offspring resemblance. The non-additive genetic effects do not. So sometimes it is said that the heritable, or transmissible, from one generation to the next, quantitative genetic effects are additive genetic effects. Quantitative geneticists distinguish total heritability from additive heritability, because the additive heritability, is the genetic basis for parent offspring resemblance. And it actually becomes an important index for them to use in breeding studies. Because in breeding studies, you're trying to effect the distribution of the trait in the offspring generation. By manipulating who is in the parent generation. Or who mates in the parent generation. And it is only the additive genetic effects that will an impact on the breeding success in a quantitative system. So there is first conceptual distinction between the two. There's secondly, certainly for behavioral geneticists, a pragmatic or practical reason to distinguish between the two. I'm not going to really get too much into this because it really would get us very deeply into quantitative genetics. But it turns out that for, in humans it's very difficult to in humans estimate non-attitude contributions to variants. It's easier although, I'm not going to argue that it's easy, but it's easier to estimate additive genetic effects. So, a pragmatic approach here is. That people have taken, or biometricians have taken over the years. Because it's easier to estimate those additive genetic effects, let's focus on additive heritability rather than total heritability. Well that seems maybe potentially very misleading, right, because well, we're leaving out this very important part of the heritability. But there's a third reason for the distinction. And in fact there's, there's long been a debate within quantitative genetics about the degree to which there are additive genetic effects or not, and non additive genetic effects for quantitative traits. That debate is actually quite. Quite ver, quite very active right at the moment. And we'll come back to some of the reasons for that a little bit later. But most of the theoretical and empirical work would suggest that for most. I'm not going to argue all. But for most quantitative traits, the additive genetic effects will be much greater than the non-additive genetic effects. And its for that reason. Along with the practical reason, that at least initially what behavioral geneticist will do, will focus on the additive genetic variance. It's easier to estimate. And there's actually theoretical, empirical reason to expect that would be much much larger than the non-additive genetic effects. There's a lot of debate not only about additive versus non-additive genetic effects. But why even bother trying to estimate heritability at all. This is nice quote from an article. Just actually came out last year in very prominent genetics journal, Nature Reviews Genetics. Which argued that, the, if you read the article, and I give you the citation, you might go out and read it. It's a nice article. The, the point of the, one of the points of the article is, yes it's def-, it's difficult in humans to estimate this quantity called heritability, but none the less it's a very important concept or statistic in quanatative genetics. So let's talk about how biometricians try to go about estimating this quantity. The, essentially what biometricians do in trying to estimate. And I'm going to go through actually a little calculation with you on this. Although, I'd never ask yu to make these calculations. But I think if you go, if we go through one. You'll begin to understand what biometricians are doing when they're estimating heritability. In essence, the essence of trying to estimate bio-, heritability for biometricitions is to recognize that the contributions of these various variance components to the similarity between relatives. Differs for different types of relative pairs. So Additive Genetic Variance, Monozygotic twins share all of that because they have the same genome. Dizygotic twins only share half of that genetic variance and the adopted siblings that we talked about earlier aren't going to share any of those genetic factors. So there's differential contributions of added genetic effects to different types of relatives. So that the difference in similarity of monazidasc, dysodidiac twins should tell us something about the likely magnitude of additive genetic variance. Shared environmental variance, another thing that will be important in this course. Should con, all of those effects contribute to Monozygote twin similarity, to dizygotic twin similarity if they're reared together, but also to adopted sibling similarity. Non shared environmental variance, by definition is the basis for why individuals, growing up in the same home, differ from one another phenotypically. So those aren't going to contribute to the similarity of monozygotic twins, dizygotic twins, or adopted siblings. I've given some expectations here for non-additive genetic variance. But for the reasons I just touched on, again these are really, at least at the initial stages, and for the purpose of this course, we're not going to focus too much on this. so let's see how the biometricians can use information like this to actually try to generate a reasonable estimate of heritability. It's going to be the additive heritability. So, here's the MZ similarity is measured for quantitative trait by their phenotypic correlation. What is the, in the biometrical formulation here. What is that expected MZ correlation. Well, all of the additive genetic effects will contribute to their similarity. All of the shared environmental effects will. But, again, by definition none of the non-shared environmental effects will. The DZ twin similarity. The R sub DZ correlation. Half of the additive genetic effects, all of the shared environmental effects but of course again none of the no shared effects. We'll look what happens if I just take the difference of the MG correlation and subtract the dz correlation. I'm left with one half of the additive genetic effect. The C squared effects cancel out, because these contribute equally to both monozygotic and dizygotic twin similarity. That's the equal environmental similarity assumption we talked about last week. So, C squared isn't going to contribute to the difference. Not, nor will non-shared environmental effects. We take the difference there, we'll get again, no contribution of non-shared environmental. So, the difference between MZ and DZ twin correlations, corresponds to half the additive genetic effects. I told you that there is a very general pattern in the behavioral genetic literature. MZs are more similar than DZs. The MZ correlation is greater than the DZ correlation. By putting in this biometric formulation, what we can actually do is begin to quantify. That impression that we get just by looking at the correlations. And this is telling us how to quantify it. The difference corresponds to half the additive genetic effect. Therefore if we double the difference. We get an estimate of the additive genetic variance. In fact, this was first noted by a very famous. British quantitative genetics or genetics named Donald Falconer. He said that actually the study of twins could produce using the same kind of algebra. I'm not going to go through all the algebra here. This is not important. I just wanted to illustrate on of these calculations that Falconer did. That the, the study of twins could actually lead us to estimate, not only the additive genetic effects, as the difference between the two correlations times two, for the reasons I just went through, but also allow us to estimate the shared environmental effects. Now this might be intuitive here. But if you go through the algebra, it works out. That we can estimate this as twice the dz correlation minus the mz correlation, as well as the contribution of non-shared environmental effects. 1 minus the mz correlation, that's a little bit more intuitive, because again, non-shared environmental effects are those environmental effects that contribute to differences. Between individuals growing up in the same home. Let's go through a little, a couple of calculations on this, and I'm going to use the data that I calculated for studies that we've done here. It's data that we're already familiar with, and it's, it actually, is a good illustration of the calculations that a twin researcher would make. With data like this. This is height, again, MZ twins are much more similar in height than DZ twins. We presume that, that greater similarity, is due to their greater genetic similarity. We'd like to move beyond that simple impression that MZ's are more similar than DZ's, to actually quantify. The extent to which an egg factors are contributing here, we also had data for IQ; which is more relevant to this course. From this study I had done, in, the correlation for MZ is not as high for IQ, as it is for height. But again we get the same general pattern. What happens if we apply those Falconer formula. The added genetic variance is estimated as taking the difference in, in the two correlation and doubling it. And for height, the heritability estimate here is roughly 70%. Again, this is going to vary. It's a proportion between zero and a hundred. Her IQ is a little bit less. It's about 60%. What do, how do we interpret that? We say that, about, 60% of individual differences in IQ, appear to be associated with genetic differences among individuals, additive genetic differences. It turns out, just coincidentally, in this particular dataset, the estimate of shared environmental effects is just 20% in both cases. Non-shared environmental effects, 8 about 10% here, 20% there. And note that these do add up to 100% as they should. So, what the biometricians are giving us here, is a way to begin to quantify these underlying sources of individual differences. And, and interpret I'll just focus on IQ here, because it's the a behavioral trait, one that we'll be interested in, in this course. What, this would say is that, it looks like roughly 60% of the variance in IQ is associated with genetic factors. 20% to the twins common rearing, and 20% to environmental factors two twins don't share. It doesn't tell you what those genetic or environmental factors are but it begins to partition them into different types of categories. Now, you remember that we also had adopted sibling data, not only for height, and they're less similar than the dizygotic twins, not surprisingly for height. But also, for IQ, they're less similar. But we can put the adopted sibling in to the biometric model. Here I just added, what we'd expect the adopted sibling correlation to be in this additive genetic, shared environmental, and Non-shared environmental framework, or again ACE. They don't share genetics, but they do share a rearing environment. They don't share the non shared environment, again by definition. Even though they're reared together. So actually the expected adopted sibling correlation, should be a direct estimate of the importance of the shared environment. Because, it doesn't reflect genetics, or the non shared environment. And if we add them in here, actually what it does, is it nicely confirms what we saw here. The estimates here, are very close to the estimates coming out of the twin studies. Roughly 20% of the variance for both heighth. an IQ, from this particular set of data, appear to be not only from the twin studies, but also from the studies of adopted siblings, appear to be associated with the common [xx] of twins and siblings. Twin researchers generate a lot of estimates of A, C, and E. Here's an article that was published about ten years ago. And again this rather prominent journal, Nature Reviews Genetics. And what's depicted here, it's actually a very large study, twin study, from the Netherlands. These are reared together twins. And what they've applied is Faulkner's model. The ACE model. Essentially just using the formula that I just gave you. But we don't need to get hung up so much on the formula. What we're mostly interested in is the results of those formula. And hopefully you can see the various phenotypes. They have quite a few different phenotypes that they've applied these formula too. Some of, most of them up here are physical characteristics like your cholesterol levels, or maybe blood pressure is one of those. And down here are various behavioral traits. The estimates of added genetic variance. Are denoted in purple, here. These are the A estimates. Shared environmental variants are the green estimates, non-shared environmental estimates are in beige, these are the E estimates. And we begin to see some general trends. And they're actually very consistent with the general trends I noted before when we were just qualitatively. Comparing the correlation of MZ and DZ twins. Now that we're really using the quantitative estimates. The first thing is that for most of the traits, added genetic factors A are important. And for a lot of them they count, they, they differ a little bit from trait to trait. But for a lot of them they account for roughly half or maybe even more of the variance and the trait. The second thing to note is that for many of the traits, c does not seem to matter much. Both for the physical and for psychological traits. There's a couple of exceptions to that. Birth weight is one up here. These are the estimates for the female twins. And these are the estimates. For the male twins, birth weight is one where, probably the common, sharing the common entry uterine environment, leads to important effects, and so you get a large c estimate there. The other one is religion. And it's not whether or not your religion, religious, but rather whether or not you're Protestant versus Muslim versus Jewish. And that not surprisingly, you get a very, very strong shared environmental factor. So the second thing we begin to see when displayed data like this. Is the shared environment for many traits doesn't seem to matter. That's kind of a paradoxical observation, but it's one that we'll talk about quite a bit throughout the remainder of this course. Finally, there's always beige effects. There's always the non-shared environmental effects. Those are always important. So, I said this before, that we qualitatively saw certain general patterns, when we looked at the correlations of MZ and DZ twins. MZ twins were consistently more similar than DZ twins. Genetic factors appeared to be important. MZ twins were never perfectly similar. The environment is also important. The correlations for twins for physical traits, the pattern looked pretty similar as it did for psychological traits. Now, when we put this in a biometrical formulation, what we've gained is not only these qualitative impressions but, actually, we quantify them. So for most traits, show moderate to large a squared estimates, 50, 60, 70%. Most traits show moderate e squared estimates. Those are the non shared environmental factors. 30, 40, 50%. Most traits, not all of them, don't show much c squared estimate at all. In the AC and E estimates for physical traits are kind of in the same ball park as those for psychological traits. So hopefully through this illustration you begin to appreciate the value of generating or doing these biometrical analysis. Now it would be terribly misleading if I didn't note that a lot of assumptions go along with generating these estimates. And in the case of the Falconer of the ACE model that's applied to rear together twin data. These were the major assumptions that were made and I'll make them explicit here. We've already talked a lot about this. The equal environmental similarity assumption. The Faulkner model doesn't entertain non-additive genetic factors, both for pragmatic and for the theoretical empirical reasons I gave you before. It also and it's probably not intuitive, there's no reason why it would be intuitive why this assumption is made, but it is an assumption in the model. That there, for the trait you're looking at there's no what quantitive geneticist calls assortative mating. Like marrying like. And finally there's no gene-environment interaction or gene environment correlation. In general, we can't really expect all these assumptions to be true. So one of the ways of thinking about the estimates that come out of the ACE or Falconer Model, is that they're approximations. They're at best kind of ballpark estimates of the quantities that we are interested in. What we, can we do to improve the heritability estimates? Well there are biometrical or quantitative geneticists. The had put a lot of thought and effort into trying to improve. To move beyond these assumptions. One is if we begin to add in other relative pairs, we can begin to relax some of the assumptions. And it's kind of what I did when I added in the adopted siblings. When I added in the adopted siblings. I not only were, was confirming what I was seeing, with the MZ and DZ twins, but I was also, it provided me with an opportunity to begin to relax some of the assumptions of that Faulkner Model. We can use more elaborate statistical models. We're not going to do either of that in this course, really. What for this course what I'd like you to recognize is, is maybe a conclusion that I've come to over the years is that if you're dealing with humans it is difficult to estimate heritability. And so we need to take the heritability estimates maybe with a gain of salt. Maybe recognize that nobody's going to be able to come along and tell you that the heritability of IQ is 63.5%. Maybe at best, what we're able to do is kind of give us approximation of how important genetic factors are. Why are we only able to give an approximation? Because of the assumptions that need to be made, untestable assumptions in some cases, that need to be made to apply the biometrical. Next time, we'll begin to talk about how behavioral geneticists and quantitative geneticists interpret heritability, why they think it's useful to use a heritability coefficient, despite the limitation, or the, in, in est, in trying to get an estimate. [BLANK_AUDIO]
