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Hello welcome back to Introduction to Genetics and Evolution.

Â In this short video I'd like to actually talk about

Â measuring effects of gene flow and how we basically model effects of gene

Â flow among populations whether they be human or otherwise.

Â As I mentioned in the very last video, gene flow is why we don't see

Â bigger differences or bigger FST values among human populations.

Â And in fact, gene flow is referred to as the great homogenizing force in evolution.

Â Some people call it the great retarding force in evolution.

Â Now, what is gene flow?

Â Gene flow is basically just movement among populations where you go

Â there and you reproduce.

Â It's different from dispersal in that you actually go to a different place and

Â you reproduce there.

Â Such that it's not like you disperse, you go some place and you come right back and

Â you keep breeding in the same place.

Â But you actually have to be going to the other place and

Â actually breeding over there.

Â Leaving your offspring over there relative to say where you were born.

Â Now, gene flow makes populations' allele frequencies converge.

Â Basically, it makes divergence either get either stop happening or even undoing it.

Â So if you imagine this population here where in the left side we have all these

Â little black alleles, on the right side we have all these white alleles, over time,

Â if you have a couple of black ones, some of the white ones go there.

Â And there it's just random who's being selected here and

Â taken over there, randomly some are selected from there and

Â coming back, overtime you'd have this fairly intermingled population.

Â And the differences that you saw in the beginning are gone.

Â You could think of it almost like taking a little bit of paint from two buckets.

Â Maybe you have red paint bucket and a blue paint bucket.

Â And you use a syringe, you pull some up here and put it in there,

Â use a syringe from there and pull some up and put it back, okay?

Â Now, how does gene flow happen?

Â Well again, organisms or gametes move to a new location and

Â they reproduce there, as you see with some of these examples.

Â Nice thing is the dandelion.

Â I always like to think of that, because we see these just blowing around in

Â different places and that more dandelions cropping up in other areas.

Â Now, the math assumes that it's random with respect to genotype.

Â Right? We're not assuming that particular

Â genotypes are more likely to migrate or less likely to migrate.

Â Now, let me introduce a couple of general models for gene flow.

Â 2:10

So here are some models of gene flow.

Â The first one I shall introduce to you is referred to as the continent-island model.

Â So imagine we have a very large continent which has a huge population size that

Â we can approximate as almost infinite.

Â We have a very small recipient population that actually's receiving

Â some migrants from the continent.

Â We're assuming in this case that the effect of the continent on the island is

Â huge, but the effect of the island back on the continent is so

Â negligible we don't even have to consider it mathematically.

Â So that's referred to as the continent-island model.

Â Another general category of models are island models, and

Â you can see this depicted here,

Â where there's a lot of different islands exchanging migrants with each other.

Â You may have them like this, where they're all exchanging with each other or

Â you may have something more like this a stepping stone model where

Â they don't all exchange with each other but they do by way of other islands.

Â We're not really going to talk about the stepping stone model,

Â I just wanted to show you what it looked like.

Â We'll introduce just a general continent-island model and

Â a general atom model.

Â The outcomes of these are just slightly different from each another.

Â 3:11

In terms of the Continent-island model, let's say for example, the red in this

Â graph so the x axis here is generation, the y axis is allele frequencies.

Â The red here is depicting the allele frequency in the continent which

Â we'll say is 0.5.

Â The blue is depicting the allele frequency on the island,

Â which we'll say is 0.9 for big a.

Â What we see happening, and this is with a very low migration rate, this just means

Â that 1% of the individuals on the island are recent arrivals from the continent.

Â Then we see this decay of allele frequency down to the continental value.

Â 3:42

Okay. We're assuming in this case again,

Â there's an effect of the continent on the island.

Â But we're assuming the island's effect on the continent is so

Â negligible we don't even have to consider it mathematically.

Â But in this case I've just modeled 500 generations.

Â And we see that by the end basically,

Â the island looks just like the continent in terms of allele frequencies.

Â This probably happens quite a bit.

Â Let me show you a slight different ones, a totally different example.

Â Here's the island model.

Â Let's imagine we have four islands exchanging genes with each other,

Â same sort of figures.

Â This is going 500 generations on the x axis and

Â the y axis indicates allele frequencies.

Â Now, let's say the island has four different allele frequencies, 0.9, 0.65,

Â 0.35, and 0.1.

Â So then you can imagine maybe these are some of the Galapagos Islands exchanging

Â alleles with each other.

Â And again, with even still a fairly low migration rate we see they all converge on

Â the same allele frequency.

Â Importantly, the allele frequency they converge on,

Â assuming that this is symmetric migration everybody's receiving and

Â sending out the same proportion of migrants.

Â 4:40

The equilibrium allele frequency or the allele frequency on which they converge

Â upon is the mean of all those islands.

Â So if you take the mean of all these numbers, that would be 0.5.

Â And you see by 500 generations, they're all pretty much at 0.5.

Â And what are the relevant variables?

Â Essentially what exactly affects how fast we see this convergence?

Â In the continent-island model, the island arriving at the continental value or

Â in the island model of all of them coming to the same allele frequencies.

Â How fast do the become similar?

Â Well there's two parameters.

Â 5:11

First one is migration rate, how many migrants move?

Â So in the previous examples I showed you is about 1%.

Â If you have more migrants they converge even faster

Â if you have fewer migrants it would converge even slower.

Â Of course, more migration leads to bigger changes in allele frequency.

Â The other thing is how different the allele frequencies are?

Â That if you have allele frequencies that are very different,

Â you see bigger changes per generation.

Â Because again you're converging on the mean, so if you're starting further up,

Â you'll take bigger steps in because you're having migrants that are even less

Â representative of what was already there in your population.

Â Obviously, another parameter is gonna be the number of generations, but

Â my question in this issue was what affects the speed of convergence?

Â But the number of generations is obviously important, too.

Â That is you have even low levels of migration for a very long period of time,

Â you can erase all the divergence.

Â Now, importantly there are some assumptions here.

Â The assumptions include that migration rates are symmetric.

Â They're independent of genotype and we're assuming there's no difference in fitness.

Â We're assuming that the migrants are not somehow less fit or something like that,

Â especially with regard to their genotypes that are arriving.

Â Let me show you a couple of applications.

Â 6:18

Now, Glass and Li, in a classic study back in the 1950s,

Â measured European gene flow into African-Americans.

Â And what they did is they got these PTC allele frequencies from Europeans,

Â West Africans, and African Americans and from that,

Â they did some very simple math which we won't go over in this case.

Â And we were able to estimate from this,

Â a per generation contribution of about 3.58%.

Â Some of you may not be familiar with PTC, but PTC is something that particular

Â individuals can taste very strongly while other individuals cannot.

Â It seems to have a very simple genetic basis.

Â And you use these sort of test papers like this handsome individual's using.

Â Uses test papers, see if you can taste it.

Â So it's a very easy thing to test out there, but

Â from this they're able to look at the little frequencies in this populations and

Â estimate the per generation migration rate, which is pretty cool.

Â Given the number of generations since they've estimated this is over about ten

Â generations.

Â Given this number of generations they estimate about 31%

Â of the African American genetic makeup

Â comes ultimately from European ancestors which is potentially somewhat surprising.

Â