Assume that a recessive autosomal disorder occurs in 1 of 10,000 individuals (0.0001) in the general population and that in this population about 2 percent (0.02) of the individuals are carriers for the disorder. Estimate the probability of this disorder occurring in the offspring of a marriage between first cousins. Compare this probability to the population at large.

Video transcript

Hi, everyone. Let's look at our next problem. It says the co ancestry coefficient is the probability that one randomly selected from A and another randomly selected away from B are identical by descent. The probability of typical co ancestries between grandfather, granddaughter or grandmother, grandson is and one way to think about what this means and how to think this through is if we want to think about the co ancestry coefficient of identical twins And we might be tempted to say, Oh, it would be 100%. But we're thinking about a single alley and we're saying a random alleyway from person a to random away from person B, what's the probability that they're identical based on descent from a common ancestor? Identical twins do have all the same D N A but half their DNA comes from their mom, half their DNA from their dad. So if you randomly picked an alil from twin A and then an Aloe from twin B, their ancestry coefficient will be one half because you might pick um, a little from twin A and then maternal alot from twin A and then also the material alot from twin B. But you're just as likely to pick the paternal alot from twin B. So that's kind of how to think through what that means. And identical twins pretty straightforward situation. But there's actually a formula for calculating that ancestry coefficient for more complex relationships. And I'm gonna go ahead and post that here. And this is the equation based on the method of calculating this known as path linking. And it says the co ancestry coefficient data of and be individuals, A and B is equal to one half to the anti power where N is the number of individuals in the path linking A and B through a common ancestor and then you some together or add up over all the ancestors if there are multiple common ancestors. So let's think about with a grandparent and grandchild. So our individual A as a grandparent individual, B is a grandchild. And if we draw the path linking them together through common ancestry, well, here's our grandparents. A and then there's parent will call them X and then grandchild be. And if we were to draw the path we go from A to X to be, and that would be the ancestry at that alley that we might be looking for a common goal. And if we look at that the path between them here, we just follow the arrows and the number of individuals in this path and It's going to equal three. So when we look at our ancestry coefficient here, then we've got the ancestry coefficient of A and B. In this case, grandparent grandchild equals one half to the 10th power, which in this case is three And that's going to give us 1/8 as our ancestry coefficient. So highlight that and then we look at our answer choices. We see that choice C is 12.5% or 1/8. Now, if you'd like to see an example of how to use this equation and maybe more complex situation, keep watching and I'll just post another scenario where we can just see how to use this equation. Um Let's imagine the case of where we have um individuals, A and B being full siblings. In this case, we have individuals A and B and we do have in this case to common ancestors, their parents, X and Y, we're going to call it. Now, let's say we want to look at the paths connecting them through a common ancestor. Well, okay, here's their dad, X and the path connecting would be A two X and an X to be. And that pathway which will highlight in blue here Would have three individuals good. So three individuals for that first pathway for the first common ancestor, but their mom is also their common ancestor. So the pathway is going to be A to Y to be. So when we highlight that second path, we also get 123 individuals. So we have two paths linking them to their common ancestor. And so we have, we have, we know that if we have multiple common ancestors, we add up each path for each common ancestor. So in this case, The ancestry coefficient for A&B is going to be 1/2 To the 3rd power for that first pathway. And then we add another one half to the third power for the second pathway. That'll be 1/8 plus 1/8 which will equal 1/ to 8 equals 1/4. So that would be an example of how to get the ancestry coefficient for full siblings of 1/4. So just how you kind of see to do those different paths with that equation. But again, our question asked us the probability of typical co ancestries between a grandparent and a grandchild. And that's choice c 12.5% or 1/8. See you in the next video.