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Welcome back to introduction to genetics and evolution.

In the previous videos we talked about the process of recombination and

specifically the sub-process of crossing over.

We talked about using the fraction of

recombinant offspring to figure out how far apart genes were.

In this video we'll talk about how to leverage that calculation to generate

a map using three or more genes.

And basically to figure out the order genes are along a chromosome

without having to get its full DNA sequence.

So what if you have three genes?

Let's say that you have three genes, A, B and C.

And let's say you know the phase of these genes where

all the capitals came from one pair, all the lower cases came from another pair.

You have the heterozygote, so it's big A little a, big B little b, Big C little c.

But in this phase as depicted here, and you're crossing it to the little a,

little b, little c.

Just like what we did in the previous video as a test cross.

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Okay, now you know the parental phase is ABC, capitals or all lowercase's.

But what is the linear order?

Now what you don't know is, is this the order?

Is B between A and C, or is it this order where A is between B and C,

or is it this order where C is between A and B?

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Now these top two individuals are definitely parental, right?

Because they have the full combination.

Capital A, capital B, capital C and lowercase a and lowercase b and

lowercase c.

These other ones all have some sort of recombination event that's

happened in there.

We don't know the details.

Let's put some numbers in there to see what happened.

Here are some numbers.

Maybe you scored either molecular markers or phenotypic markers and

you get these sorts of numbers here.

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Now, the top two, the parental types, are always gonna be the most abundant.

You will nearly always see that.

At worst they'll be equal to the others, but more typically they will be more

abundant if you're looking at genes along the same chromosome.

We have a bunch of much rarer types going down.

Now what I'd like to do is I'd like to dissect the problem.

Rather than trying to look at A, B, and C simultaneously, let's just ignore C for

a minute and just look at A and B, okay?

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The next one is actually parental.

This is important.

The next one is parental-like.

They're still big A, big B, and little a, little b, even though we know the C is out

of phase with the others with respect to the parents, but

again, we're breaking down the problem just to look at A and B.

Okay.

And the bottom one here as recombinant.

Big A, little b, and little a and big B are together.

So when we add these up, what fraction are recombinant.

Well, it's 15 plus 13 plus one plus one so it adds up to 30.

That's a total of 30.

The total here is 1,000 if you add up all those numbers together.

So, our recombination fraction, in this case, would be 3%, or 0.03.

So that is the recombination distance between A and B.

Okay? So we calculate that,

that's between A and B.

Three centimorgans apart, or .03 recombination fractions.

What about between A and C, between B and C?

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Well, we can repeat the same process, let's go ahead and

do that, between A and C which ones are recombinant.

This would be recombinant between A and C.

This would be recombinant between A and C.

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This would be recombinant, and this would be recombinant between A and C.

The bottom one would actually be parental for A and C.

Because you see the capital A and capital C are together.

Or lowercase a and lowercase c are together.

So, between A and C, we have 18 and 13 is 31.

31 and 15.

It's 46.

46 over 1,000.

Okay.

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What about between B and C?

Which ones are recombinant?

Which ones are parental?

I'll change the color of my diagram here.

Between B and C, this would be parental, this would be parental.

This would be recombinant.

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This would be recombinant, cuz again big B, little c, little b, big C.

This would be recombinant, this would be recombinant.

So in this case we have 20/1000 would be recombinant between B and C.

So let's put all these numbers together.

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So, we can, from this, figure out the layer or order genes, right?

What should happen is the distance from, from one at one end to the middle plus

from the middle to the other end, should be about the same as the total distance.

Imagine that you're going from, say New York to Florida.

So you have three points, New York, Washington D.C. and Florida.

If you add the distance from New York to Washington D.C., and

distance from Washington D.C.

to Florida, that should be about the same as the distance from New York to Florida.

So in this case, we can do that.

We can say, because of this A and C must be on the outside.

So you have to have A at one end, C at the other end, and

therefore necessarily, B will be in the middle.

So this would be the correct order.

Right? Because here we have,

distance from A to B is about three, distance from B to C is about two.

The total of the two is close to five, it would round up to five.

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So now you may be wondering why don't AB + BC,

why don't those two distances add up exactly right?

Why doesn't it add up exactly to 4.6?

Well the reason is something you actually noticed when

we were calculating these numbers.

Is that we have two things that we're calling parental, but

they're actually recombinant.

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Here in the bottom two, this individual and this individual,

we are counting as parental for A and C, but in fact they are double crossovers.

So not only should they be counted, but they should be counted twice, but

we didn't do that.

So this is why it doesn't quite add up exactly.

We'll come back to this in just a second, but

first let me emphasize a different point.

When you're trying to figure out the linear order of genes

there's a few tricks you can use.

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First, if all the loci are linked at some level and

I don't mean completely linked, but I mean they're on, for example,

the same chromosome and reasonable close together.

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The largest two, the combinations which are the most abundant.

So that's just what we saw last time with capital A,

capital B, capital C lowercase a, lowercase b, lowercase c.

Those will always be the original non-recombinant parentals.

So that will help you determine the phase.

The smallest two, basically the numbers that are the least frequent,

so this is what we saw in the previous slide of capital A and little b capital C.

Or lowercase a big B little c.

Those would be the double crossover.

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Well again, double crossovers, there were basically two things happening together.

So in this case we have the little a, big B, little c as a double crossover gamete.

So imagine that you have a 1% chance of recombination between A and B and

a 1% chance of recombination between B and C.

Then what would happen is you could actually multiply these two probabilities

so it'd be a 0.01% chance of a double crossover.

Essentially, you're taking a rare thing and

multiplying by the probability of another rare thing to get this double

crossover class, it'll always be the rarest class from any particular cross.

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And again, you can identify which marker's in the middle

because it'll be that rarest class.

The alleles at two markers will be parental relative to each other,

while the allele at the third will be recombinant.

So, we could have immediately looked at the previous slide and said oh,

I see that little a, big B, little c is the least frequent Category,

therefore this must be the double recombinant.

If you notice, the double recombinant,

you immediately know that this one must be the one that's in the middle.

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The parental group would be the most abundant group, so clearly in this case,

the most abundant group is capital A, capital B, capital C, and lowercase a,

lowercase b, lowercase c.

That establishes your phase already, so we know that the person who we're measuring

recombination, and would look something like this.

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So what we said is that this would necessarily be

the double recombinant class.

Given that, when we look at it, A and

B are in the same phase relative to the parents, C is in a different phase.

A and B are in the same phase relative to the parent, C is in a different phase.

So this case we can infer, the order is actually A, C, B,

and then we can calculate the distance between these pairs of genes.

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What would that mean?

Well there's a couple of possibilities here.

Now it could mean that A and B are reasonably close together,

and C is really far away on the same chromosome, right?

Just because you have recombination fraction of 50% doesn't

necessarily mean they're on different chromosomes.

Could also mean they are on different chromosomes.

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Right? So you could add this or

this is on one chromosome, this is another chromosome.

You can have this, or you could even have this other order.

Basically, one point I just wanna toss out there for you is that above about 40%

map distances are very inaccurate and maybe basically, 50%.

So, I wouldn't ever trust, when you're determining an order of genes,

any map distance you see that's more than 40%.

Because, at that point, you really just have no information.

So if you have something like this,

where A and B is 11%, B and C is 49, or even 43%, or something like that.

A and C is 50%, or even 45%.

Basically, you don't know how far apart these are.

You just know that A and B are linked.

So all the information you have in this case, is that A and B are nearby,

and you have no idea where C is.

C could be really far out this way on the chromosome, it could be really far out

that way on the chromosome, or it could be on a different chromosome.

I just want to emphasize that because some people use these numbers as though

they have this absolute precision to them but we're actually measuring rare events.

So when you get something on the order of 49%, or

really anything above about 40%, don't have too much faith in that number.