0:01

Welcome back to Introduction to Genetics and Evolution.

Â In the previous video we were looking at

Â this dichotomy between genetics and environment.

Â And what we did in that context was trying to figure out whether or

Â not there's a genetic component to particular trait differences you see, or

Â whether there's an environmental component to trait differences we see.

Â Now what we want to really so is to actually get this part.

Â We want to say how much do each contribute to particular traits of interest.

Â We want to quantify how much they contribute.

Â And again, when we're inferring whether genetics or environments contribute,

Â typically the answer is very often both are contributing.

Â In that regard, it's not really that satisfying to just say, yes,

Â there's a genetic component, or yes, there's an environmental component.

Â It's much more satisfying to actually infer their relative contributions.

Â To say for a particular trait, this is something that 90% of the variation you

Â see is genetic, or 90% of the variation you see is environmental.

Â Well, this comes to the concept that we'll refer to as heritability.

Â I'll define that in just a moment but first let me go through a couple of quick

Â mathematical concepts that will be relevant to this lecture.

Â Let's talk about mean and variance, please.

Â And I apologize for

Â those of you who already have a lot of statistics background,

Â I just need to go over this.

Â Now most traits you look at tend to be variable,

Â that not everybody has exactly the same trait value.

Â So you can use height as an example there.

Â Now, if a trait is continuously variable, all right?

Â Meaning that you have all these different steps, so something like height.

Â You can be 5'9" tall, 5'10" tall, 5'11" tall, 5'11.5" tall.

Â Then we can calculate a mean, and we can calculate a variance.

Â Now, many of you are familiar with variance in the context of just thinking

Â of it as the spread of values.

Â And I can depict this.

Â Let's say you're looking at height in the classroom.

Â So let's say this is the height in the classroom.

Â This is saying 5'0" to 6'2", this is 5'0" to 6'2".

Â What is the mean?

Â 1:57

Well, in both of these classrooms,

Â it looks like the mean is right below 5'7", okay?

Â In contrast, which one has more variance?

Â And again, if we think of variance just as spread,

Â we see here the graph on the left has a lot more variance in height

Â than the one here on the right where basically everybody is 5'7".

Â Well making this more quantitative, the mean is simply the numerical average,

Â that if you have three numbers, one, two and three, the average is two.

Â You sum them all together and you divide by the total number of values.

Â The variance is a spread, or

Â basically how spread out individual measures are from the mean.

Â The calculation for it is this,

Â the summation of all the individual measures, minus the mean, and for

Â each one of those squared, divided by the total number of measures.

Â Okay, that's the formula for the variance.

Â So if you had ten individuals all with height 69 inches, right?

Â So now, let's imagine that's their height, everybody has height 69 inches, and

Â there's ten of them, what is the mean going to be?

Â 3:03

Well in fact, in this case, there's absolutely no spread whatsoever,

Â because we said everybody has exactly the same height.

Â So the variance would actually be zero in that example.

Â Let me give you a few others, here are two sets of measures.

Â And let's say these are again heights of people in a classroom, height in inches.

Â And I have the formula here in case you want to refer back to it.

Â So in classroom one, 63, 65, 67, 67, 69, 71.

Â Those are the heights you see.

Â For classroom number two, 65, 66, 67, 67, 68, 69.

Â Which one has greater variance?

Â Is it classroom number one, classroom number two, or are they equal?

Â 3:54

Okay, well, I think eyeballing this, this is a pretty easy problem.

Â Looking at the spread here, they're both perfectly symmetric, right, but

Â this one goes further out.

Â This one is much more clumped together.

Â So the answer is number one definitely has more variance than number two.

Â Well let's try this out numerically.

Â 4:14

So if we get the height in inches, the means for both are 67.

Â That's just adding all the numbers together and

Â dividing by the number of measures.

Â The variance, in this case, comes out to 6.66 for classroom number one.

Â And this is taking each individual measure minus the mean, and then squaring it,

Â adding all of those together and then dividing it by the total, so this is 6.

Â This comes to 6.66.

Â For those of you interested in sampling variance, now you can put that in there.

Â 4:39

For the class number two comes up to 1.66.

Â So clearly there's more variance in classroom number one

Â than classroom number two.

Â Well variance, and don't worry about the math for this right now, we'll come back

Â to the math later, variance, think of it, again, just as the spread that you see.

Â As the variance is larger there's more spread,

Â as there's less spread the variance is smaller, okay?

Â So what causes this variance in traits like height?

Â Well let's use this example right here.

Â Let's say here on the y-axis we'll get number of offspring

Â that have a particular height and on the x-axis we're looking at height.

Â 5:11

Such that this would be short at this end, and this will be tall at this end, okay?

Â So we see here, in this particular case, there's some variance in the phenotype,

Â the phenotype being height.

Â Now we have some individuals that are on the tall end,

Â some individuals that are intermediate, some individuals that are short.

Â Now with this example,

Â we're looking at two alleles at a single gene that are controlling height.

Â We're assuming there's no dominance to it, and there's no effect to the environment.

Â That's why these are perfect lines.

Â That if you're aa, then you're exactly that height always.

Â If you're Aa, there's more of you and you're exactly that height.

Â If you're AA, then you're exactly that height.

Â So in this case there's no effect to the environment and

Â there's some variance there among the individuals.

Â That variance, in this case, is all genetic, right?

Â Because we said there's no effect to the environment, so

Â all the variance is genetic.

Â 6:04

This is still 2 alleles at a single gene controlling height,

Â Aand there's no still no effect of environment.

Â But we see a bigger difference in height between some of the individuals.

Â In this case,

Â the lower graph here has more genetic variance than the upper graph.

Â Both of them still have no environmental variance.

Â But the lower one has more genetic variance because you see there's bigger

Â difference in phenotype among individuals with no environmental partner and

Â it's purely controlled genetically.

Â It's controlled by your genotype that the A gene.

Â 6:36

Now what would happen if we said, well, there's a little bit of environmental

Â variance here, there's a little bit of mush?

Â Well, we might see something more like this.

Â In this case, AA individuals are still intermediate, aa are on average taller,

Â AA are on average taller.

Â But we have some effect of the environment here too,

Â where some AA individuals might be almost as big as a Aa individual.

Â Some aa individuals might be as short as Aa.

Â But what we've done here is we've added some environmental variance,

Â some effect of the environment.

Â There's still a genetic variance here, because there's still a difference among

Â the genotypes on average, but there's also some environmental variance.

Â This is probably the more typical scenario where you have this mix of

Â genetics and environment.

Â 7:19

Now the formula that we use for this is very simple.

Â Vp, which is the phenotypic variance, so you calculate

Â the variance in height just like we did before, in the beginning of this video.

Â And we say that's a sum of that fraction of the variance that's genetic

Â with that fraction of the variance that's environmental.

Â It's a very simplistic formula, that the overall phenotypic variance has

Â a genetic component and it has an environmental component,okay?

Â Now, how do we calculate this?

Â Well, that's the big question.

Â I'm gonna show you in this video one mean,

Â and that's using an F2 cross between some strains that are isogenic.

Â In the next several videos, you'll actually see other means for calculating

Â heritability, and specifically, what fraction is genetic versus phenotypic.

Â 8:04

Now, let's say that you're looking at genetic variation in the F2 of a cross.

Â And let's say there's 6 genes for height.

Â Let's start with the very artificial scenario that we know these 6 genes

Â are involved, and you've got AABBCC, just like the example we used awhile back.

Â So these are some 6' tall people and

Â this is the exact gene type that's causing that height.

Â And let's say they have kids with these ones that are 5' tall, okay?

Â How much genetic variance is there in the tall parents?

Â 8:34

Well we're saying there is none, because we have their actual genotype there and

Â they're exactly the same.

Â In this case right here we're saying there's absolutely no genetic variance

Â in the short parents either.

Â What about the offspring?

Â They're all heterozygous.

Â Is there any genetic variance?

Â 8:49

The answer is actually no,

Â because every one of the offspring has exactly the same genotype.

Â Even though they're heterozygous, even though they have two different alleles,

Â there is still no genetic variance in these F1.

Â In the F2, however, you'll have a lot of variance, some of which will be genetic,

Â because you'll start to get some individuals that are AA,

Â some individuals that are aa, etc.

Â And if you're unlinked, then there's many possibilities and

Â you saw this before with the slide I used earlier.

Â So let's do this cross.

Â Again, we're saying there's no genetic variance in the parentals,

Â in this parental, in the tall parents or the short parents.

Â Between the parents, yes, sure there's genetic variance, but

Â we're not looking at that.

Â We're looking within this parent, within this parent, or within the F1s.

Â There's no genetic variance.

Â 9:34

When we see this genetic variance in the F2, right,

Â we see that there's this massive increase in genetic variance in here.

Â We can use that, we can leverage it.

Â Let me show you how.

Â Let's say, for example, in actual height among the tall people,

Â among the 6' tall people, there is no phenotypic variance.

Â This is important now,

Â I'm saying phenotypic variance, no phenotypic variance there.

Â Remember phenotypic variance comes from genetic variance and

Â environmental variance.

Â Since we already knew there was no genetic variance there, if there's no phenotypic

Â variance, then there can be no environmental variance, okay?

Â So Vp is 0, Vg is 0, and Ve is 0.

Â This is true for all three of those.

Â Now, let's add another step here.

Â 10:16

Let's say there is a little bit of environmental variance.

Â That's okay, I mean, we can say that maybe all these people aren't exactly 6' 0" or

Â these people aren't exactly 5' 0".

Â But let's say we know they have this particular set of genotypes.

Â In this case there's still no genetic variance but

Â there is some environmental variance.

Â You note the environmental variance should be about the same for all three.

Â Okay, we're assuming that these are all grown in, say, the same garden, or

Â if they're people, they're obviously not grown in a garden,

Â but you know what I mean.

Â Now what'll happen is in the F2,

Â even though you had a little bit of environmental variance here but no genetic

Â variance, in the F2 you'll have genetic variance and environmental variance.

Â Well we can leverage this, because up here the phenotypic variance which this,

Â you can measure.

Â 11:00

You can measure the phenotypic variance in the F1's or the parents, right.

Â You can measure it just the way I was showing you with height,

Â where it's the difference between individual measures

Â minus the mean squared, divided by the total number assayed.

Â You can measure the phenotypic variance,

Â in this case you're getting an estimate of Ve.

Â 11:18

Over here, you can again measure the phenotypic variance, and

Â you're getting Vg plus Ve.

Â So all you have to do is subtract this phenotypic variance

Â minus that phenotypic variance and you get Vg, right?

Â If you take this phenotypic variance, which is Vg plus Ve,

Â subtract from it this phenotypic range which is just Ve, you get Vg, right?

Â Very simple.

Â Well again, these are the components we have, and

Â we want to know how much is genetic versus environmental?

Â How much is that contributing to the overall phenotypic variance?

Â Well the fraction of the total phenotypic variance

Â that is genetic is called heritability.

Â So heritability is called (Vg/Vp) or

Â you can think of it as ((Vg/(Vg+Ve)) because that's just synonymous with Vp.

Â So this ranges from 0, there's absolutely no genetic component to 1,

Â when there's all genetic component.

Â So you can say something, for example, is 90% of the variance is genetic, or

Â 10% of the variance is genetic, using this very simple formula.

Â So let's try this out.

Â Here are some examples.

Â Let's say you manually calculate the variance in the F1s to be 5.

Â So here, this number's equal to 5.

Â We manually calculate the phenotypic variance here in the F2s, and

Â you calculate that to be 25, okay?

Â 12:35

So what is the heritability?

Â Well I have the formula right here.

Â Heritability is Vg/(Vg+Ve).

Â Well we know Ve, right, Ve is 5.

Â And we're assuming the same Ve here as over here, we're assuming it's the same.

Â So we're assuming that environment is basically the same in the F1 as it was in

Â the F2, right?

Â So the genetic variance must be what?

Â Well if Ve was 5, Vg must be 20.

Â So the heritability in this case, heritability is often abbreviated

Â h squared, is equal to Vg which is 20/Vp, and we'll use

Â this one right here, cuz we're measuring this is in the context of the F2's, 25.

Â So the answer in this case would be 80% or 0.80.

Â Now this may seem like an artificial scenario because what's happening here is

Â you're starting with lines that you know have no genetic variance.

Â Now in terms of human height, sure, you'd never apply this.

Â However, this is something that is quite commonly used in the context of say,

Â crops, where you have this pure breeding tall corn crossed with pure breeding short

Â corn, you want to look at the heritability of corn height or

Â something along those lines.

Â The same with model organisms such as Drosophila, fruit flies, things like that.

Â So this is used quite a bit but it's not used the in the context of,

Â say, human height, or anything dealing with humans.

Â But how do we deal with things like humans?

Â