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MICHAEL HEMANN: OK.
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So let's think about two markers.
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One of them is called M1 and the other one is called M2.
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So not only can we look at the distance
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between a marker and a phenotype,
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but we could just look at the distance
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between two markers using the same kind of analysis.
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So in doing this, we determine that M1 and M2 are linked
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on the same chromosome, and they're somewhere around 30
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centimorgans apart.
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So we have these two markers and we have our wingless gene.
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And we want to simply ask, where is wingless
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relative to these two markers?
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Now we could do this by just looking
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at pairwise interactions and pairwise crosses.
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So wingless in M1, wingless in M2, and figure it out that way.
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But we can do it another way that is somewhat faster,
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an interesting way I think that tells us a little bit more
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about meiosis, and that is by doing what's
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called a three-factor cross.
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Here, the three factors are going
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to be M1 and M2 and wingless.
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OK, so let's do this cross.
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So we're going to start with two true-breeding flies
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as we almost always do.
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And this one is going to be wingless minus M1A and M2A.
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And they're true-breeding, so M1A and M2A.
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Now I've drawn them all on the same chromosome,
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but we don't know what the order is.
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It could be wingless M1A M2A.
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It could be M1A wingless M2A.
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That's what we're trying to figure out.
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We're trying to figure out the order.
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And we're going to cross with the male,
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and the male is wingless plus M1B
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So it's the B version of the M1 allele.
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And M2B wingless plus M1B M2B.
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Again, these are both true-breeding flies.
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And I just want to remind you all that true-breeding does not
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mean wildtype.
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Breeding just means they are homozygous at all
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of their loci.
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So it essentially allows us to concoct an F1 constellation
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of genotypes that is going to be informative in our cross.
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So we're using this parental line
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to generate an F1 where the meiosis is going
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to be actually interesting.
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OK.
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So the F1 for this cross is going
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to be heterozygous at all of these loci.
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So wingless minus M1A M2A.
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Wingless plus M1B M2B F1.
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And so this is going to be the organism-- this
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is going to be the female where all the action happens,
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where we actually see meiosis and we
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can look at the distances between all of these things.
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OK.
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So let's draw this female again at the top.
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So we have female wingless minus M1A M2A, wingless plus M1B M2B.
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And we'll cross with a male that is homozygous
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for M1A M2A M1A and M2A.
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And so we're going to look at just the meiotic of products
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that are generated by the females.
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So the gametes from the female.
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I mean, importantly, we can see by phenotype
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all of the offspring.
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So just looking at the flies, we can
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see whether the wingless are not,
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and then we can look at the marker status
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and see are they AA or AB.
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So these are things that fall under the general constellation
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of phenotypes that we can see, but in this case,
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we're just going to look at the gametes.
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So we can have wingless minus M1A M2A or wingless minus--
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or wingless plus M1B M2B.
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So these you'll recognize this the parental,
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these are nonrecombinant.
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And then we can get all of the possible recombinant.
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So we can get wingless minus M1A M2B and wingless plus M1B M2A.
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We can get wingless minus M1B M2A and wingless plus M1A M2B.
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Or we can get wingless minus M1B M2B and wingless plus M1A M2A.
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So there are eight total possible gametes that
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are coming from this cross.
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Now you'll notice the way that I've drawn them is in pairs.
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And we actually call these pairs reciprocal pairs.
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Because essentially, they are the two recombination products
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you would get from crossing-over events.
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So in each of these cases, I have
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all of the markers represented.
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In this case here, we have essentially M2A and M2B
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that have flipped from one chromosome to the other.
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And so we see the two recombination products
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that would be generated from that recombination event.
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And so we can put in numbers.
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And let's say we have 60 flies, 68 flies, 20 flies, 22 flies,
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12 flies, 10 flies, three flies, five flies.
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These are experimental numbers.
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You did a cross and you're just counting flies.
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What you'd expect in theory is that in a given reciprocal
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pair, the numbers would be identical.
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And if you counted enough flies, they would be.
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But you can already see here with the numbers
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that we've generated that they're
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very similar to one another.
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60 and 68, 20 and 22, 12 and 10, 3 and 5.
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OK.
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So we have a total of 128 of these.
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We have 42 of these, we have 22 of these,
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and we have eight of those.
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And we're going to call this pair number 1, pair number 2,
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and pair number 3.
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So the way that the three-factor cross works is we're
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going to look at the rarest class of reciprocal pairs.
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And we're going to say that the rarest class is the result
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of a double-crossover.
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Now we talked about double-crossovers last week.
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And you'd expect that a single-crossover
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is going to be more likely than a double-crossover.
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