 back, everyone. Also, if you're watching it on YouTube, today, we will be talking about phenotypes, quantitative trait, loci, genome-wide association, and then fine mapping of QTLs. And as an encore, I will tell you guys about my PhD project that I did. So it's a new method I developed. And I wanted to show you guys the method because I'm really proud of it. And I like the method a lot. And I think it will be relatively new. But before you can understand the new method that I made, which I spent four years on, you have to understand what quantitative trait loci are. So let's get into it. The solution we already did. So phenotypes, we talked about this. Here we see some examples of phenotypes, right? So a phenotype is, for example, the amount of cannabis that you get from a cannabis plant, but also the quality. For example, another phenotype, which is relatively important economically, is, for example, mildew, right? So if your plant is susceptible to mildew or not, so the susceptibility to a pathogen is also a phenotype. And of course, if we are talking about things like food, then we have a lot of different phenotypes in food, like what is the texture, what is the taste, what is the content of, for example, certain sugars. So and like I told you guys before, just as a reminder, phenotypes are defined into two groups. So you have the whole universe of phenotypes. And every phenotype that there is can, of course, be measured or be quantified in a qualitative way, right? So the qualitative way is a subjective way of saying this phenotype is good, or this phenotype is bad, or I give this phenotype a five or a seven, right? So because you're not using the international system of units, like in a quantitative trade, it is really easy to kind of give a number or give a score to something, right? So the world of qualitative trades is much bigger than the world of quantitative trades, although quantitative trades grow, like the more machines that we get that can measure new phenotypes, the more quantitative phenotypes we can extract from an organism. Besides that, I told you guys already in like one of the first lectures that phenotypes are divided in Mendelian phenotypes, where there's one genetic locus. And for me, always the best example for this is the air wax thing, like dry air wax versus wet air wax. There's a single gene in the genome, which controls the type of air wax that you have. However, the most interesting phenotypes are the complex phenotypes. So complex phenotypes means that there are two or more regions in the genome, or two or more genes, which are involved in this phenotype. So there is a complex interplay. For me, the standard kind of complex phenotype, when I talk about complex phenotype, is things like obesity, right? Obesity is a very complex phenotype. There's literally like 50 to 100 genes that we have already identified, which are more or less involved in obesity. And all of these genes, of course, are interacting in some way with the environment, right? Having a certain gene doesn't mean that you become obese. You only, this gene only has its effect when certain environmental conditions are met. So just a reminder. So when we talk about phenotypes, and we talk about phenotypes, and we want to figure out if a phenotype is something that we can find a gene for, right? Because phenotypes can be Mendelian or complex, but we want to know if we can find a locus for a certain phenotype. Then first things first, we have to make sure that this phenotype is heritable, right? So heritability means that the phenotype of your parent is transferred to the offspring, right? So that there is a relationship between how the parent looks and how the offspring look, right? So we can think about, for example, code color and cows, right? Code color and cows is heritable because if you have a black and white cow and you made it with another black and white cow, then the offspring will be black and white cows, right? So there is a heritability. And heritability is measured as the fraction of the phenotypic variance or variability that we can attribute to genetic variation. So when we talk about genetics, this is more or less the core formula that we use, right? So that we say that a phenotype is defined or the variance in a phenotype that we see is defined as a part which is caused by the genetics and a part which is caused by the environment. So from this formula, we can already see that heritability is not something which is static, which a lot of people kind of say to you, right? They say that the heritability of human stature is 80 percent. But you can see that there are two parts to this formula, right? So if the environment changes and has a higher contribution because of some effect, right? Because of global warming, some heritabilities will go down and other heritabilities will go up, right? So that's what I'm trying to say is that heritability can change even without any genetic changes because of the environmental part, right? So it's a balance. So the variation that we see in things like human height is partly caused by genetic, partly caused by the environment. So when we want to estimate heritability, we can of course not directly estimate this in a way, right? So we have here more or less the same formula, but now instead of saying that a phenotype is made up of a genetic component plus an environmental component, when we talk about variance, right? So because we are talking about differences in phenotypes, we can say that the variance of a phenotype is caused by the variance in the genetics plus the variance in the environmental, and then we have to add this term for the genetic and environmental interaction, right? Because genetics and environment are not two separate things. There is also genetics which responds to the environment, right? So that's this part which is two times the covariance between the genetics and the environment, right? But normally in experiments, when we do animal experiments or plant experiments, we can control this part. So we can set this cough, so the covariance of the genetics and the environment to zero, right? Because we can make sure that for example, there is no variance in the environment. So if there is no variance in the environment and every plant in our experiments has the same environment, that means that more or less the variation in the environment kind of drops out, but it also means that the covariance is not there, right? So if we want to estimate heritability, then we have two types of heritability. The first type of heritability is called the broad sense heritability. And the broad sense heritability is just when we say, okay, so we control the covariance, right? So we are not allowing the genetics and the environment to interact with each other. And then what we say is that the broad sense heritability is defined as h square, so capital h square. And that is defined as the variance that we see coming from the genome divided by the variance that we see in the phenotype as a total, right? So we are just estimating the three components saying that, well, we estimate the variance in the phenotype, the variance in the genetics. If we know these two, then we of course also know the variance in the environment when we set this third term, the covariance to zero. So broad sense heritability is more or less a summary of all of the genetic effects coming from the genome. The other way that people define heritability is when we look at the additive variance, so the variance which is caused by additive alleles. So what do we mean by additive alleles? There will be more slides about additivity, but what we mean by additive alleles is that if you have the AA gene or type, then you have a certain mean or a certain median to your population, right? So now when we have individuals which have a single B allele and an A allele, we have an increase. So this increase is seen from the A to the B, right? So in this case, having a B allele on a certain marker in the genome will increase your phenotypic value. Having two B alleles will again increase your your phenotypic value by the same step, right? So when you would draw a straight line, then the increase from AA to AB is the same as the increase from AB to BB. So if we now define heritability as narrow sense heritability, then we have defined that as when we look at every marker that we have in the genome and we look at all of these additive effects, when we add all of these effects up, then we have the narrow sense heritability, right? So that is only the variance caused by additive alleles. So we ignore things like dominance. We ignore things like over dominance or under dominance. And we just define saying that heritability, now written with a small age, because it's the narrow sense heritability, is the variance of the additive alleles divided by the total variance in the phenotypes. So based on this, there are two schools of thought, right? So there are two ways that we can kind of estimate heritability of a phenotype. So the first one is the school of thought, which is from Siebel, right? Which is the analysis of correlations using regression. So it's using regression analysis, which we talked about a lot last week, to figure out how much of the variance that we observe in our phenotype is caused by additive alleles or which is caused by genetic alleles in total. And then we have the other school of thought. I don't want to talk too much more about regression, but we also have the school of thought from Ronald Fisher, which is that it is actually not, you should not look at the correlations between the phenotype of the parent and the phenotype of the offspring, but you should do more an analysis of variance, right? So how does this work? So imagine that we have a parent distribution, right? So these, this is the parent generation. So we see here the normal distribution, which is the phenotype distribution of the parents, right? So the lowest parents has a phenotype of zero, the highest parent has a phenotype of 10, and the average parent has a phenotype value of five. So now what we are going to do is we're now going to select parents, right? So we're going to select parents and the parents that we're going to select is again, a nice normal distribution. So we're not going to take only two individuals, but we're going to take like 50 individuals from our whole population. But we are going to select these individuals in such a way that instead of having a mean of five, we now are going to select parents which have a mean of seven and a half, right? And we are going to mate these selected individuals, so the selected parents, to random individuals from the parent generation, right? So we're going to put some selective pressure on the next generation. And now what we can see when we look at the next generation, right? Now we can see that the next generation is bigger than the parent generation because we have selected some parents, right? So there is the pressure that we put on, right? So the selection differential, which in our case is two and a half, right? Because we select individuals which are two and a half units larger than the mean. And then we have, when we then look at the mean of the offspring, we can see what the response was to this selection. And then broad sense heritability is just defined as the response divided by the selection differential, right? So in this case, our response is six. So the response is one unit increase, but we applied a pressure of two and a half units, one and a half unit. Sorry, because it's seven. So there's two units of pressure, right? Selection pressure. There is one unit of response, which means that in this case, the heritability of this phenotype, the broad sense heritability is 50%, one divided by two. And these are relatively easy experiments to do in plans, right? Or in cows or in others. So if you want to estimate, get an estimate of your heritability, then the only thing that you have to do is do kind of a selection experiment where you first measure a whole population of cows that have a certain milk production, then you select cows, which have a high milk production, you then breed these cows to random bulls from your whole population. And then you look in the offspring that you get to see what their milk production is. And then you can calculate the heritability of the milk production. So the broad sense heritability. So analysis of variants is the experiment where we take sires and their progeny with random dams. Children get half of their genes from their father, half of their genes from their mother. And then we can just analyze this using this linear model. So what we say is that the phenotype that we observe is caused by the father and some error. And then we can compute the heritability by comparing the variance that is explained by the father to the total variance, right? Because for every individual, we know its phenotype value, we know who his father was. And now what we can see is we can see how much of the variance we can assign to the father part of this model, right? So that is another way of estimating heritability. So we just take sires and random dams. And then we just do this regression model. And of course here the variance explained by the father term is only half of the heritability, right? Because the other half of the mother we don't have. So there's two ways of estimating heritability. One is by selecting parents. Another is by just using more or less an ANOVA. And in this ANOVA, we just fit the effect of father on the phenotype. And then this is half of the heritability that we see. So in total we might see a variance of 100 liters of milk, but of this we can assign to the father 25 liters of milk, right? So that means that the ratio between what is explained by the father and what we see in the total population is 25 over 100, so 25 percent. And then we multiply that by two, since you only get half of your genome from your father. So in this case again 50 percent heritable. So of course heritable traits are passed from one generation to the next. This passing happens to via DNA and the molecule that encodes genetic information. And the nice thing about DNA is that it's able to pass information, but it also allows for modification and mutation, right? So it's not that you are 50 percent your father, 50 percent your mother. No, there is also some random variance in the genome, which is unique to you. And of course there's also things like recombination, right? So the idea of life is that you take parents and that you generate semi-random offspring genotypes from the parents that are there. So how does this happen? Well this happens because of DNA crossovers, right? Because DNA recombines. So if you take a gamete, so when the DNA is replicated in the S phase, this is step A, right? So we have DNA, DNA is replicated, so we now have two strands of, so we have, so we have chromosome one, right? So we have the chromosome one from the mother, we have chromosome one from the father. What happens is that this gets duplicated into the cell, right? And then we have, for example, let me explain this better. So when we make sperm cells, right? So just think about the father, right? So the father has chromosome one from its mother and it has chromosome one from its father, right? So what happens when you start producing sperm? Well, first you have one copy of chromosome one, or you have, yeah, you have two copies of chromosome one, one from your father, one from your mother. So in the first phase, in the S phase, what happens is that every chromosome that you have gets copied, right? So you now have a cell which has two copies of chromosome one from the father and two copies of chromosome one from the mother. Then you have meiosis one, and meiosis one is where homologous recombination occurs. So what happens now inside of the cell? Had these cell, the cell starts to divide, but it doesn't start to divide. Let me actually block some of this shit in chat. Where's the band? There's band. Another one. Where's the other one here? So first things first, right? We have a cell which has one copy of each chromosome, of which has two copies of each chromosome. It gets duplicated. So now it has four copies of each chromosome. So two copies from the father chromosome, two copies from the mother chromosome. Then in the next step, the cell is being divided into two cells, which means that you have the spindles which are created, which attach to the chromosomes. But these spindles are not perfect. So they won't always pull the whole father chromosome into one cell and they won't always pull the mother chromosome into one cell. So they attach and this attachment is more or less random. So what happens is that you get two copies of the same chromosome, right? So one from the father and one from the father, which has this little blue piece from the mother. In the other cell line, right? Because the cell divided into what we see is we get one copy of the chromosome, which is exactly identical to the original maternal copy. But here we see that in this chromosome, this little piece of the father is attached to the mother chromosome, right? Then in the next step of sperm creation, what happens is that again the cell divides. So this cell now divides and now what we see is that we get one chromosome, which we get one copy of chromosome, one inside of the sperm cell, which is a combination of a little piece of the mother, large piece of the father, one of them, which is exactly like the original father. We see that there's one piece which has a little piece from the father, big piece from the mother, and one which has the big piece from the mother. And of course, when I say mother, I mean the mother of the one that is producing the sperm, right? So in the end we start off with one cell, which has two copies of each chromosome, and in the end we end up with four different sperms. Can you use a laser pointer? I should be able to. You can see my mouse, right? Where's the laser pointer thing here? Normal, slight shorter. Let me see, there should be a laser pointer thingy here, right? That's all the way at the end. Laser pointer, laser pointer. Oh, you can see the mouse. Good. Let me just go back to here. All right, good. All right, so what happens? So when sperm is created, we start off with one cell, which has one copy from the father, one copy from the mother. Inside of this cell, this DNA is copied. This is called replication or S phase. In the next phase, spindles attach from the side of the cell to the chromosomes that just got copied, and they get pulled apart. But this pulling apart is not perfect. So what happens is that you get a combination of one chromosome has large part father, little piece mother, and the other one gets the large part or gets the whole father chromosome, right? So blue is the father, no blue is the mother, red is the father. In the other one, because it pulls these things apart, and these spindles attach kind of randomly to one of the four copies that is there. So you have this piece of DNA which is exchanged. In the next step, which is called meiosis two, we go from having a deep fluid cell to a monopluid cell. So what happens again is, again, we have the spindle formation, it pulls it out and it pulls this one cell into two cells. So we end up from the beginning of one cell with two copies of each chromosome to having four sperm cells, each sperm cell carrying one copy of chromosome one. Some of them are exactly identical to the original chromosome that you got from your father or the chromosome that you got from your mother, but some of them will have a recombination. So where the spindle didn't attach to the exact same chromosome, but to the other one. So it pulled them apart, but the recombination happens here in the middle, right? It doesn't happen here in the C phase, it happens in the meiosis one phase. How does this work in the exact phases? So again, here we have the same picture, right? So we have pro phase one, meta phase one, ana phase one, and then telephase one. So this is the first part in the diagram, right? So this is the first step here where we have the homologous recombination taking place, right? So we have the centromere with the spindles and the spindles get attached to this points at the genome where they are connected, they are then pulled apart. And what we end up with is having two copies of each chromosome inside of the cell, but now with this little recombination here, right? So this is just zooming in what exactly happens here in B, right? So this is the slide for meiosis one, and of course, we also have meiosis two, which is also in more detail. I just want to show you guys this because the important part here is that if you start off with one cell with two copies from each chromosome, you end up with four sperm cells. Some of these sperm cells will have a complete exact copy of the original chromosomes, but more or less half of them won't. They will have an exchange of genetic material from one chromosome with the other chromosome that is there, right? So just some additional slides to more or less show you in detail what happens. So how can we now measure this, right? Because in the end, we need to have a ability to measure which part of the genome came from which, right? So because in genetics, we always talk about big A, small A, two big As, two small As. So the way that you can measure this is multiple. But originally in the 1980s, when we started figuring this out, what we did is we just used restriction enzymes, right? So we have a restriction fragment length polymorphism, which means that we first take the DNA from an individual, right? And then we digest this by restriction enzymes. So the restriction fragments are separated according to their length by gel electrophoresis. And of course, we have to label the DNA. We have to have to have a labeled DNA probe, right? So what happens is that this is, for example, big A is the chromosome that you got from your father, small A is the chromosome that you got from your mother. So here the little triangles are the sites at which the restriction enzyme can cut the DNA, right? So if we, if we would fragment this first big A piece, we get a small piece from the beginning to the first cut side, we get another piece from this fragment to that fragment, right? Then we get another fragment here and we get a fragment at the end. So in total, we divide the whole length of the chromosome into one, two, three, four fragments. If we look at the allele, which is small A, it now has a non-functional cleavage site, which means that the enzyme cannot cut here because a mutation has occurred in the DNA. So the sequence has slightly changed. And because the sequence has slightly changed, what happens is that the enzyme is unable to cut the DNA. So when we use the enzyme to cut the small A allele, we now get only one fragment here. This becomes a whole fragment, right? So this part here from the first up until the third is just one fragment because the enzyme cannot cut here. And then we get another fragment at the end. So for this, for the big A, for the big A chromosome, we cut it up in four fragments. The small A chromosome gets cut up in three fragments. Then we have a DNA probe. So we pull out this part of the DNA and we wash away all the other parts. And so what we get is we get a very short fragment for the big A allele. Well, we get a very long fragment for the small A allele. So if we then bring this onto a DNA gel to separate by electrophoresis, then what we see is that there are three different types of individuals that we can distinguish, right? So when we see only one band on the on the gel, and this is the big band, we can now infer that this individual had two AA alleles. When we see two bands on the gel, one big, one small, then we know that this individual was a heterozygous, right? So this individual had one chromosome from the parental strain and from the father parental strain and the other chromosome from the maternal parental strain. Of course, we can also have like only a short fragment visible on the gel. When we only have the short fragment visible, we know that this individual has two copies of the large A chromosome, right? So using these DNA probes, we can pull out part of the of the genome. And of course, these fragments are, so here we have a single marker on the genome and this marker can have a short fragment if we are big A, and it is as a long fragment when we are small A. So we can then infer which two chromosomes each individual has. So we just put like three individuals on a gel. If we see that there's only a large band, we know this individual was small a small a. If we see a very short fragment, then we know that this individual is AA. If we see two bands on the gel, then we have big A small a. So this is one way to look at the genome. Of course, we don't have to use the cleavage of the DNA. One other way that we can do it is use these RFL-Ps, which, so these RFL-Ps can also be done when we have a variable number of tandem repeats. So everywhere in the genome, we have these little sequences which are repeated over and over. So for example, TC, right? So some individuals have TC 10 times in their genome. Other individuals have TC only four times. So again, we do the same thing, right? So we have our cleavage side, then we have our repeated sequence, which is different for every or not for every individual for the two parentals that we start off with. And then based on the length of the fragment, have we conceded that when you have multiple repeats or like 10 repeats, then your fragment is larger than when you only have four repeats, right? Because this this this repeat here takes up 20 base pairs. Well, this repeat here takes up only eight base pairs. So now we end up in the same situation that when we put these fragments on a gel, right? So we take an individual, we cut the piece of DNA, then we use the DNA probe to extract the fragment, and then we get the same situation where we can, based on the length of the fragment, infer how many of these repeated sequences there were. So these are called VNTRs, variable number of tandem repeats. And that is because the tandem repeats comes from these are generally like AT, and then some individuals have 10 ATs, other individuals have only four. And then of course, if we cut the DNA with a variable number of tandem repeats in the middle, then this has an effect on the length of the little piece of DNA, right? So this is just cutting the DNA, pulling out pieces, and then looking at the length of the pieces. And based on the length of the pieces, and the length of the pieces that we saw in the parents, we can then infer if this individual has the maternal homozygous, the paternal homozygous, or if this individual is a mix. So if it is a heterozygous individual. Nowadays, we use snips, right? So we look at single nucleotide polymorphisms, which is a single base pair in the DNA. So some individuals carry an A, another individual might carry a T, right? So now what we do is we can use something like a snip chip, which looks like this. And we measure hundreds, perhaps even thousands of these little individual base pairs at the same time, right? So there's many techniques to kind of identify single nucleotide polymorphisms. But the most common one is to just use snip chips. So it's a variation in a single nucleotide at a very specific position in the genome. And we can measure those using snip chips, using sometimes 200,000 snips for a single individual when we put this individual on the snip chip. So for each snip that we are having on the chip, it says this individual is AAAT or TT. So a snip chip is an array containing these immobilized allele-specific oligonucleotide probes, and it is very similar to a microarray, right? But instead of having one probe for a snip, it actually has two probes. So one probe targeting the A, one probe targeting the T. If this probe is on and this probe is off, you know it was AA. If this probe is on and this one is off, then it was TT. And if both probes are on, you know that it has a 1A and 1T, right? This happens due to fluorescent dyes. And have we have a detection system that records and interprets hybridization signals? So the first paper using these original random fragmented length polymorphisms, right, was published in 1989 and was published by Lander and Wotstein. So they are credited with inventing QTL mapping, quantitative trade locus mapping. So what they did is they they made hundreds of these DNA probes targeting different positions in the genome and then they took two animals, which were different, right? So you have, for example, an Arabidopsis from Colombia. You have an Arabidopsis plant from Germany. You cross these two together. And now, hey, you get all kinds of children. And for each of these children, you can now, at each position in the genome, measure if it got their genome from the one parent or it got the genome from the other parent, right? So the basics of quantitative trade locus mapping is to associate a phenotype with a genetic marker and you require three things, right? You require a population, right? So individuals that have been crossed in a certain way to make sure that these genomes of the two parentals mix. Furthermore, you need to have markers like SNPs or RFLP markers or these variable number of tandem repeats. And of course, you need to measure a phenotype or multiple phenotypes. So how do we make these populations, right? So the first population that was kind of used is the back cross population, right? So we have a mouse, for example, which has an unknown genotype. And we cross this with a known homozygous background. So here we have the standard laboratory mouse, which is an inbred mouse, which means that this mouse is homozygous at each point of the genome. And we just say, well, this individual, at every point in the genome, we say it is big A. Now we cross this mouse with another mouse, which we caught in the wild. And we don't know at each position in genome what this mouse has, right? So here we're just looking at a single marker. But at this first marker, the first parent, we have no idea because it's just a mouse that we caught in the wild. And here we have our standard laboratory mouse, which we say by default, since it is a homozygous mouse, because we've inbred for multiple generations. And we can say that every marker that this mouse has is AA. So when we cross these two mice together, then of course, the offspring will be a question mark, right? Because because it will always get one chromosome from the father, and it will always get one chromosome from the mother, right? And since this animal is AA, it cannot recombine, right? So it cannot introduce recombinations because of the fact that if even because the whole DNA genome is AA, perhaps I should make a little drawing of that to make you guys understand better. But when we now have the F1 population, so the F1 population has two chromosomes, at each marker of the genome, when we would measure it, we would say that one part is an AA, and the other part we don't know because we've got that from this wild white mouse. What we then do is we take this F1 individual, multiple of them, of course, not just one. And then we cross this individual to the laboratory mouse again, right? So it can be the same mouse, but it can also be another mouse because these mice are homozygous across their whole genome. So if you have a parent, then the offspring will have the exact same genotype when we only read the laboratory mice, right? So they're always more or less the same. But now what happens when we cross this A question mark mouse with this AA mouse? Now we end up with, at a certain marker, when we do this cross like 100 times, right? We end up with 75% of the animals being AA, so similar to the mouse that is our laboratory mouse, but 25% of the animals will have the A question mark, right? So we can draw the diagram if you want to show this is the inheritance. But what happens is we get now a population and every individual of this population will look slightly different. We'll look as a mix between the white mouse and the black mouse, but some of the animals will have more markers which are black than other mice, right? So every mouse in this population gets a unique combination of the two original parental strains. So of course these crosses have a certain amount of disadvantage. Here we cannot investigate additive and dominance effects because of the fact that we only have homozygous AA and a question mark individuals or a question mark at a certain point. I do want to draw this because I do think that it's important for you guys to understand how this works and I think by drawing it, it might be a little bit better for you guys to understand. So it's not drawing time yet. It's not going to be your puffer fish, but I just want to draw this genetically, right? So what we do, right, is we have our genome. So let me go to draw. Let me make sure that I have white. So we have one chromosome, right? So when we call this P1, so parent one, that's a very big pen actually, slightly smaller one, right? So we have parent one, right? So parent one has two chromosomes of which we know nothing about, right? Because it is, so it has two chromosomes, right? So if I measure a certain marker, oh, when I measure a certain marker here, right, then this individual has as a genotype question mark, question mark. At the next marker here, it also has question mark, question mark, right? So now we take parent two and parent two, let's draw this in a different color and let's draw this. Now let's make the chromosome still white, right? So again, it has one chromosome, two chromosomes. We measure it at the first marker and we call this AA because it is our standard laboratory mouse. The same thing holds for the second one. We call this AA, right? So now when we cross this two, and let's actually do use a color here for the markers. So an A marker is colored red and these ones are just colored white, right? So then we have the genome. So now when we cross these, what we get is because there cannot be any recombination, right? Because it doesn't matter which part of the chromosome you pull in, if you pull in this part combined with this part, right? So even if there would be a recombination, it would not change the chromosome that you get. Same thing here, right? So for this mouse, if you take an offspring mouse, we get an individual which looks like this. So on the one chromosome, it has two white markers. And on the other chromosome, it has two red markers, right? So now what starts happening, if we cross this individual again with another individual, which is the laboratory mouse, right? So that again has the two red markers here, like this. So now there are different possibilities in the offspring, right? Because when this individual generates gametes, right? So this individual here, the F1 individual, right? And this is the P2 individual again. This F1 individual can have a recombination, right? So what could happen is we have chromosome 1, chromosome 2, right? And here we have the two markers and we have the two red markers. So now what might happen is we might get a gamete from this individual, which looks like this, right? So it takes a little piece of the first chromosome, right? And then recombines to the other one. So we have the first marker being white and then the second marker is going to be red. Another possibility is that you get the other chromosome, right? So it starts off with a little red, with a red marker. So it starts off with a red marker, right? So you get this gamete, right? So in the first meiosis phase, what happens is that this part is copied, then it switches to the other because the spindles didn't detach correct, right? So you get a white gamete. Of course, you can also just get the standard ones. So you could also get a gamete, which looks like this, right? So which is exactly a copy of the original one. And you can get a gamete, which looks like this, right? So there are four different possible gametes that this F1 individual can generate, right? So this is one, then we have two, then we have three, and then we have four, right? And for this individual, this cannot, this doesn't matter, right? If you take here and no matter where you cross in the genome, right, no matter which part you pull in, you will always get one gamete. Let me go back and you always get a gamete, which looks like this, right? So it's a gamete, and this gamete has two red alleles, right? So now when I start generating offspring, right? So from these two individuals cross together, because this one can recombine, right? It has four different gametes that it can produce. In the end, we get, because we only have two markers, we get four different types of offspring. So the first type of offspring is the one which has the first gamete, right? So it's, let me just draw two of them, and then add the red bars for, right? So it's gamete, first gamete from the first F1. And it of course always gets the red gamete, because that's the only one that P2 can produce, right? Of course we can draw the other possibilities as well. So let me just draw the chromosomes first. This is kind of hard to draw exactly straight lines. But when we take the second gamete from the F1 individual, right, what happens is that we get a red allele here, and of course we always get two red alleles on the second allele which you get from the P2. So this one always looks like this. So when we look at the fourth, then of course we have a red marker here, a red marker here, and then we get a white marker here, and a white marker here, right? So here we have four offspring, right? So now if we look at the first marker, only at the first marker, right, and we do the test using this restriction link polymorphisms, then what we see is that individual one is called small a, or not a, let's use question mark. So at the first marker, so at m1, it is question mark big a. This individual is actually a a at the first marker. This individual is again question mark a. This individual is again a a, right? If we look at the second marker, right, we now see a different story because now the individual one is a a. The second one is question mark a. This one is question mark a, and this one is a a, right? So now we're not going to just generate four offspring. We're going to generate a hundred or a thousand, right? And we're not having two markers, but we're having like 50 or a hundred markers on a chromosome, right? So you can imagine that there's a lot of combinations that now start becoming possible, right? But the F1 individuals, they have no choice. They always get one of these, one of those, and even if they would recombine, it would not matter for the F1, right? Because these one can only produce two gametes or actually only one gamete. So this one always produces a gamete, which is called, which looks like this, right? So is that clear that there's a there's a difference here, right? That that by by by having this this individual here, which has two different chromosomes, it now can start generating different gametes. And these different gametes, because we cross them with the red one, and we know that one of the DNA strands will always be red, red, but the other one can have a recombination. And this recombination can happen anywhere in the genome, right? So if we have a chromosome, then the recombination can happen exactly at the beginning. It can happen a little bit later, it can happen here, it can happen here. So anywhere in the genome it can break, and it can switch from one chromosome to the other. It can even do something where you would have a couple of white markers, then there's a couple of red markers. And then you have a double recombination because it actually recombined back and it pulled in the last part from from the this chromosome again, right? So at each position in the genome, the gamete that is being produced can have a different structure. I hope that that's clear because that's very fundamental. Recombination is one of the hardest parts of genetics to understand. But once you wrap your head around what's happening with the production of the sperm and the egg cells, then it kind of directly clicks, right? Why we do that? So in genetics, we always show these patterns, right? So we always show these cross diagrams. But here what we we only look at a single marker, right? And at a single marker, in this case, the individuals at this marker can be AA, 75% of the individuals will be AA, 25% of the individuals will be a question mark. But of course, at the next marker, the same individual can have a different genotype because of the fact how these gametes interact with each other. Good. So there's some disadvantages like you cannot look at additive and dominance effects because you do not have the question mark question mark in the in the last generation. And you have a low effect size because you only have half of the additive effect, right? If we look at the additive effect thing, which came all the way in the beginning right here, we only have these two groups occurring in our population. So we only can see if the AB individuals or the A question mark individuals are higher or lower than the AA individuals. But we cannot know if we can draw a straight line, if the increase from AA to A question mark is the same from a question mark to question mark question mark, right? So that is the back cross. So the back cross is generating F1 individuals. We don't generate one individual with multiple of these. And then every one of these individuals gets crossed back to a mouse where we know the genotype and then all of these hundred offsprings at each marker in the genome, they will have their own unique genotype based on the recombination in the gametes of this F1 individual. Another cross is the F2 cross. So now we do the same thing as we did before. So we take a male, we take a female mouse, we take a male mouse, we cross them, we generate offspring. But now, instead of taking these individuals and crossing them back to the first parent, we now cross them to each other, right? So in this case, what would happen if we would look at the drawing again, right? So now we don't have one individual, let me actually switch there. So now we don't have one individual which is recombining. We actually, instead of crossing it with P2, we now cross this F1 individual with an F1 individual, right? So instead of happening here, what we see is we now cross an F1 with an F1. So now we have two recombinations happening, right? So because this individual can generate four distinct gametes when we have two markers, but this individual can do the same thing, right? Because they have two different sides of the genome. So in the F2 cross, this is what we do. So we cross the offspring from the F1 with themselves or not so much with themselves or with another animal that we have, right? And then we generate offspring and these offspring can be males and females, but now these individuals can have an AA genotype occurring 25% of the time. They can have an AB which happens 50% of the time or they can have a BB which happens 25% of the time, right? The standard Mendelian inheritance which you would normally write down in a Mendelian inheritance diagram, right? So that's why we did the inheritance diagrams all the way back, because that's where this is based on. So an F2 cross is the same as a back cross, but instead of taking an F1 individual and mating it back to one of the parents, you take two F1 individuals which both can generate recombinations and then you cross them together to generate the F2 and then you start at each marker in the genome, you start genotyping them. We also have things which are called recombinant inbred lines in which we create an F2 population, right? So we create an F1. So we have the two alleles from the father, from the mother. We generate them, then we get the F1. So every F1 individual has two exact copies, one from the father, one from the mother, right? So one from the father, one from the mother. We have many of these individuals. Then we create the F2. So the F2 looks like this, right? So there's a recombination here on this chromosome. There's a recombination here on the chromosome that you get, right? Because we cross an F1 with an F1. This is more or less how a chromosome can look. Of course, every individual has its own unique breakpoints because it was made by a sperm cell and an egg cell which had recombinations altogether. And of course, we generate multiple of these, right? So we generate like 50 to 100 animals, right? So 50 animals get or one animal gets crossed to another animal. One animal gets crossed to another animal. So what we now do is now we start stabilizing the genome. So we made an F1 individual with an F1 individual. We generate F2 individuals. And now we take a male F2 and a female F2, cross them together. But from now on, every generation, the offspring of this pairing is only allowed to pair with itself. So in every generation, we lose part of the variance, right? So after doing like 20 generations, what happens is that at each position in the genome, because of recombination, we cannot introduce new variants, right? So when an individual becomes homozygous at a location, then all of its offspring in this funnel will have this location homozygous. And of course, every generation, half of the genome will become homozygous because we take, we start off with individuals which are more or less fully heterozygous. We then take the F1 individual where half of the genome is heterozygous, half of the genome is more or less, well, not half of the genome, but most of the genome is hetero, some parts are homozygous. And then when we start inbreeding them, then we end up with something which is called a recombinant inbred line. So a recombinant inbred line has as an advantage that we have the genotype frequencies of AA being 50%. The BB individual, at every marker when we look across our population, we see that 50% of the animals are BB. And so we have the best split into two groups. So the advantage is that we have the effect size, so we have the full additive effect, but we don't have any information about additivity and dominance. And in mice we need around 20 generations to start off with F2 individuals to generate individuals which are fully inbred and which are homozygous at each point in the genome, but every individual in this funnel will be the same. So if I cross a BXD1 with a BXD1, it ends up having the exact same genome because of the markers being there at every marker you measure the exact same thing. So these are the three most used crosses in genetics to study genetics. So just as a summary, we have the back cross which is quick and easy to set up. It has a relatively low resolution because it's only one individual or one generation in which recombination occurs and only in half of the individuals because the fathers generally come from the standard mouse lines. So there is no information about additive and dominance effects. When we look at the F2, it is not too complex to make an F2, right? You just have to make random F1 individuals with random F1 individuals. We can look at additive versus dominance effects. We have medium resolution low power and we have the recombinant inbred line which is most power to detect the effects because we can look at the full additive effect because we compare AA to BB and not AA to AB like in the back cross. And this is really good resolution depending on the size of our population. And again, the drawback of the recombinant inbred line is because individuals can only be AA or BB at a certain locus. We cannot know if an effect or if a locus is controlling our phenotype in an additive way or in a dominant way. We can only see that there is a difference but we don't know how the heterozygous looks. Besides that nowadays, we do a lot of more complex crosses where we don't start with two inbred founders where for example the new crosses that people are making are starting with eight different inbred founders. So you take eight different inbred mice and then what they did is they crossed these mice together the same way as that you would normally generate a recombinant inbred line but in mice this is called the collaborative cross. So they started off with eight inbred mouse strains, crossed them together and then generate a population which is at each marker is a mix of these eight inbred founders. We also have the magic lines which are the same thing in Arabidopsis taliana. So starting with eight inbred founders they use the crossing scheme to make this population that again at each marker each individual is as either as one of the eight original chromosomes, well not one of the eight, but anyway so and the problem here is that when we look at complex crosses it is still not a solved issue. We cannot analyze these crosses without any doubt because we're still, for our for example we can analyze it using RQTL2 but still there's a lot of work to be done to make this software work with eight inbred founders compared to two inbred founders. Good, so now we're kind of ready to start or so now I'm kind of ready to start explaining you guys what linkage analysis is where we associate a phenotype with a genetic marker, a genotype at a certain marker. So this comes into two flavors, we have QTL mapping and we have genome-wide association and of course this analysis only works when phenotypes are heritable, right? If a phenotype is not heritable because it's totally driven by the environment then of course we will never find any region in the genome which is controlling our phenotype. Good, so I've been talking a lot, I hope that it was clear with the drawing of the gametes of the F1 to kind of have you guys know. The thing is try doing it at home, right? So at home take a piece of paper, take two inbred founders where you say okay so this one has two chromosomes which are completely bred, this one has two chromosomes which are completely white and then cross them together on paper and then when you have two different chromosomes, right, so oh wait a second, drawing time, right? So when you have two different chromosomes, right? At this point you now have to start drawing all the possible gametes, right? So if you have two markers there are four possible gametes, if you have three markers then of course there are two to the power of three, so eight different gametes, if you have four markers you have two to the power of four, so 16 different gametes that come out but just do it for the F2 population, right? Where you cross an F1 individual with an F1 individual and then generate all the possible offspring for that or by mice. Yeah, yeah and then start doing it at home, I wouldn't advise that but it's a lot of work keeping mice and crossing them in the exact same way especially because mice tend to run wild and cross with anyone that they want. Buy some snakes, yeah that will keep the mouse under control. Good, I will do a quick break, we'll be back in like five to ten minutes so if you're watching this on YouTube, see you on the flip side and if you're watching it on Twitch then you can just continue watching but for now this is the end of part two.