0:00

Hello welcome back to Introduction to Genetics and Evolution.

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

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

flow among populations whether they be human or otherwise.

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

bigger differences or bigger FST values among human populations.

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

Some people call it the great retarding force in evolution.

Now, what is gene flow?

Gene flow is basically just movement among populations where you go

there and you reproduce.

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

you reproduce there.

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

you keep breeding in the same place.

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

actually breeding over there.

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

Now, gene flow makes populations' allele frequencies converge.

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

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

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

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

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

taken over there, randomly some are selected from there and

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

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

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

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

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

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

Now, how does gene flow happen?

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

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

Nice thing is the dandelion.

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

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

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

Right? We're not assuming that particular

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

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

2:10

So here are some models of gene flow.

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

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

we can approximate as almost infinite.

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

some migrants from the continent.

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

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

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

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

Another general category of models are island models, and

you can see this depicted here,

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

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

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

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

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

I just wanted to show you what it looked like.

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

a general atom model.

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

3:11

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

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

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

we'll say is 0.5.

The blue is depicting the allele frequency on the island,

which we'll say is 0.9 for big a.

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

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

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

3:42

Okay. We're assuming in this case again,

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

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

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

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

And we see that by the end basically,

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

This probably happens quite a bit.

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

Here's the island model.

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

same sort of figures.

This is going 500 generations on the x axis and

the y axis indicates allele frequencies.

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

0.35, and 0.1.

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

alleles with each other.

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

the same allele frequency.

Importantly, the allele frequency they converge on,

assuming that this is symmetric migration everybody's receiving and

sending out the same proportion of migrants.

4:40

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

upon is the mean of all those islands.

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

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

And what are the relevant variables?

Essentially what exactly affects how fast we see this convergence?

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

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

How fast do the become similar?

Well there's two parameters.

5:11

First one is migration rate, how many migrants move?

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

If you have more migrants they converge even faster

if you have fewer migrants it would converge even slower.

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

The other thing is how different the allele frequencies are?

That if you have allele frequencies that are very different,

you see bigger changes per generation.

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

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

representative of what was already there in your population.

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

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

But the number of generations is obviously important, too.

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

you can erase all the divergence.

Now, importantly there are some assumptions here.

The assumptions include that migration rates are symmetric.

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

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

especially with regard to their genotypes that are arriving.

Let me show you a couple of applications.

6:18

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

measured European gene flow into African-Americans.

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

West Africans, and African Americans and from that,

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

And we were able to estimate from this,

a per generation contribution of about 3.58%.

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

individuals can taste very strongly while other individuals cannot.

It seems to have a very simple genetic basis.

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

Uses test papers, see if you can taste it.

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

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

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

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

generations.

Given this number of generations they estimate about 31%

of the African American genetic makeup

comes ultimately from European ancestors which is potentially somewhat surprising.