Wow, all variation is lost.

We'll come back to this, actually, very shortly.

But you see that the individual step sizes here is very large.

Again, in each of these case, these are eight different simulations,

each with population size four and starting the allele frequency at 0.5.

So with those examples in mind, can we solve, mathematically, how

big the individual steps are that result from genetic drift in a single generation.

On average, the answer is yes.

So we can use the variance.

Now recall we used the variance before when we were

studying heritability a couple of lectures back.

We look at the variance in allele frequency due to one

generation of genetic drift.

So looking at how much of a spread is there.

The answer to that is pq divided by 2N.

Where p and q are the two allele frequencies and N is the population size.

We use 2N because we tend to work with diploid organisms.

Now, how do we use this to actually look at average changes?

Well, we can look at the standard deviation.

The standard deviation of this would be an estimate

of the average allele frequency change in one generation.

In fact, mathematically, it would actually be a slight overestimate, but

it still gives us an idea for illustration purposes.

So, how do we get the standard deviation from the variance?

Well, the standard deviation is always the square root of the variance.

So we have this formula here for

the variance, we take the square root of that, as illustrated here, and that gives

us the average of the frequency change from one generation of genetic drift.

So let's apply this to examples that I just showed you,

the figures from a couple of slides back.

When we had a population size of four,

we had starting allele frequencies of 0.5 and 0.5.

The average change based on this formula should be about 0.18.

What these means by the average change is that if you start with an allele frequency

of 0.5, it's likely that you will go up to about 0.68 or

likely that you might go down to 0.32.

That's sort of an average change.

The change could be more than that you could go to 0.70, you could go to 0.62,

so maybe is larger, maybe smaller of a change, it also could be up or

it could be down.

We don't know the direction of genetic drift from one generation.

This gives you an idea of the average step size, 'kay?

Now notice, for this one is 0.18.

If a population size is 40, the average changes is quite a bit smaller,

as we witnessed.

In this case,

the average change should be only an allele frequency change of about 0.06.

If the population size is 400,

the average change in one generation of genetic drift is 0.02.

Now, you notice with those very small ones, like the population size of 400,

that's why in the example when we're looking at a population size of 400,

no allele was ever lost or fixed.

We always still had variation in the population.

Because individual steps are very small, and

even over a hundred generations, we still retained variation in that population.

In contrast, when we looked at the very small population, population size of four.

We lost all variation very quickly,

because the step sizes are very big, there's very likely to get to 100% or 0%.

Okay, so what does it take home messages from this lecture as a whole?

So the take home messages from this video, drift is strongest in small populations,

drift is neither predictable in direction, nor

exactly replicable in degree in one generation.

That you saw with all those different populations even when we started it over

and did it again, they didn't all follow the exact same track.

They all have the same on average change allele frequency but

some went up, some went down, some had a little bit more than average,

some had a little bit less than average at times.

It's not exactly replicable in degree, and it's not predictable in one generation.

Very important to end on there.

And finally, drift can change big changes in allele frequency over time.

We'll pick up on this in the next video.

Thank you.