3:41

So, it's random indirection over one generation,

Â whether you're going to increase in frequency, or decrease the frequency.

Â So assuming that there is more than one allele, so assuming you have

Â at least two alleles, any allele is about equally likely to increase or

Â decrease in frequency after one generation of sampling error or genetic drift.

Â So for example, if the allele frequency of big A, assuming there's two alleles,

Â big A and little a.

Â If the allele frequency of big A is 0.6, you're about equally likely to have

Â a frequency above 0.6 or below 0.6 in the next generation.

Â However, it's very unlikely you're going to have exactly 0.6 again,

Â because there is a decent chance you're going to have some non-representation.

Â Even if you have a very large sample,

Â it might end up being 0.603 or something like that.

Â So allele frequencies tend to drift due to this sampling error, and

Â this is where the term genetic drift came from.

Â I'm going to show you what would happen in the context of this.

Â Imagine tossing a coin ten times this is similar to having P equals 0.5.

Â You may get five heads from these tosses.

Â Right?

Â So that would be exactly what's expected in the sense of the average, right?

Â Since you're equally likely to get heads or tails.

Â Now getting more than five heads or

Â getting fewer than five heads is equally likely.

Â This shows you the distribution that you expect the probabilities.

Â I'm probably getting exactly five heads is actually less than a quarter.

Â Your probability of having ten heads is extremely low, probability of having zero

Â heads is extremely low, but you're about equally likely to have slightly more or

Â slightly less than five heads when you toss the coin.

Â Okay, in fact, actually the probability of getting ten heads is about one

Â in a thousand, so very unlikely unless it's a weighted coin.

Â Well, the same concept applies to populations.

Â So if the original population has allele frequency of big A 0.6,

Â we see below what happened in one generation of genetic drift.

Â The probability of having it greater than 0.6 versus

Â less than 0.6 is about the same.

Â And this is the case if you have 10 diploid offspring.

Â 5:39

Okay, now let's see what happens as we look at this over

Â multiple generations briefly, but just looking at the individual steps.

Â So this magnitude change compounds as it relates to the population size.

Â Now, regular changes are going to occur if the population size is smaller.

Â You'll have greater individual deviations in allele frequency per generation

Â as the population is smaller.

Â So let's look at three different population sizes.

Â Let's look at population size 400.

Â You're starting in this case, this is looking at generations on the x-axis and

Â allele frequency on the y-axis.

Â You're starting at 0.5.

Â And what's happened here is we're starting one, two,

Â three, four, five, six, seven, about eight different populations at 0.5.

Â And this shows random changes over all eight population.

Â After about a hundred generations we see there's a few

Â that are kind of close to 0.5.

Â Some of them are higher, and some of them are lower.

Â So we have this genetic drift that's compounded over time.

Â This shows this little green figure shows the approximate average size of

Â a change in one generation in each population.

Â Notice what happens if we reduce this.

Â Instead of 400, what if we looked at a population of size 40?

Â What we see in this case, much bigger changes, we have several alleles that have

Â gone all the way to 100% or 0% in some of these populations, and

Â some are still segregating, but again, you're equally likely to go up or

Â down on an individual generation, and the individual step size now is much bigger.

Â You get bigger random changes in allele frequency with smaller population sizes.

Â All right?

Â Let's do the same thing.

Â This was with population size of 40.

Â Let's look at it in the extreme with population size four.

Â 7:20

Wow, all variation is lost.

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

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

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

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

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

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

Â On average, the answer is yes.

Â So we can use the variance.

Â Now recall we used the variance before when we were

Â studying heritability a couple of lectures back.

Â We look at the variance in allele frequency due to one

Â generation of genetic drift.

Â So looking at how much of a spread is there.

Â The answer to that is pq divided by 2N.

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

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

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

Â Well, we can look at the standard deviation.

Â The standard deviation of this would be an estimate

Â of the average allele frequency change in one generation.

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

Â it still gives us an idea for illustration purposes.

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

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

Â So we have this formula here for

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

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

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

Â the figures from a couple of slides back.

Â When we had a population size of four,

Â we had starting allele frequencies of 0.5 and 0.5.

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

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

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

Â likely that you might go down to 0.32.

Â That's sort of an average change.

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

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

Â it could be down.

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

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

Â Now notice, for this one is 0.18.

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

Â as we witnessed.

Â In this case,

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

Â If the population size is 400,

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

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

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

Â no allele was ever lost or fixed.

Â We always still had variation in the population.

Â Because individual steps are very small, and

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

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

Â We lost all variation very quickly,

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

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

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

Â drift is neither predictable in direction, nor

Â exactly replicable in degree in one generation.

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

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

Â They all have the same on average change allele frequency but

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

Â some had a little bit less than average at times.

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

Â Very important to end on there.

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

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

Â Thank you.

Â