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Man: Hey look. It's our friend Gregor Mendel. The super monk who discovered the basic principles of genetics. Hopefully you remember all of these, both parents contribute one version of each of their genes called an allele to their offspring and some of those alleles are dominant or always expressed while others are recessive and only expressed when they're not paired with a dominant one. Oh! And here's our old friend Chucky D. He lets me call him that. All this information that Mendel figured out would have been, really, quite interesting to him because Darwin spent his whole life defending his ideas of natural selection as the primary force for evolution. Darwin had no idea how traits were passed on to their offspring. Even though these two guys were living and working at the same time. With Mendel and Darwin died not knowing how their ideas fit together. Today we're going to introduce them and their ideas to one another through the science of population genetics which demonstrates how genetics and evolution influence each other. I have good news, it involves a lot of math. (instrumental music) Population genetics on the surface is not a complicated idea, it's the study of how populations of a species change genetically overtime leading to species evolving. Let's start up by defining what a population is. It's simply a group of individuals of a species that can interbreed. Because we have a whole bunch of fancy genetic testing gadgets and because unlike Darwin we know a whole lot about heredity. We can now study the genetic change in populations over just a couple of generations. This is really exciting and really fun because it's basically like scientific instant gratification. I can now observe evolution happening within my lifetime. You know, just cross that off the bucket list. Now, part of population genetics or pop-gen and now we've got fancy abbreviations for everything now, involves the study of factors that cause changes and what's called allele frequency. Which is just how often certain alleles turn up within a population. Those changes are at the heart of how and why evolution happens. There are several factors that change allele frequency within a population. Just like Fast and Furious movies, there are five of them. Unlike Fast and Furious movies, they're actually very, very important and are the basic reason why all complex life on earth exists. The main selective pressure is simply natural selection itself, Darwin's sweet little baby which he spent a lot of his career defending from haters. Obviously we know these natural selection makes the alleles that make animals the strongest and most virile and least likely to die more frequent in the population. Most selective pressures are environmental ones like food supply, predators or parasites. At the population level, one of the most important evolutionary forces is sexual selection. Population genetics gets its special attention particularly when it comes to what's called non-random mating which is a lifestyle that I encourage in all of my students, do not mate randomly. Sexual selection is the idea that certain individuals will be more attractive mates than others because of specific traits. This means they'll be chosen to have more sex and therefore offspring. The pop-gen spend on things if that sexual selection means mating isn't random. There are specific traits that are preferred even though they may not make the animals technically more fit for survival. Sexual selection changes a genetic make up of a population because the alleles of the most successful maters are going to show up more often in the gene-pool. Maters are going to mate. Another important factor here, and another thing that Darwin wished he had understood is mutation. Sometimes when eggs and sperm are formed through meiosis, a mistake happens in the copying process of DNA, that errors in the DNA could result in the death or deformation of offspring. But not all mutations are harmful. Sometimes these mistakes can create new alleles that benefit the individual by making it better at finding food or avoiding predators or finding a mate. These good errors and the alleles they made are then passed to the next generation and into the population. Fourth, we have genetic drift which is when an alleles frequency changes due to random chance. A chance that's greater if the population is small. Those happens much more quickly if the population gets knocked way back by a tornado or something. Genetic drift does not cause individuals to be more fit, just different. Finally, when it comes to allele game changers you got to respect the gene flow which is when individuals with different genes find their way into a population and spread their alleles all over the place. Immigration and emigration are good examples of this. As with genetic drift, its effects are most easily seen in small populations. Again, our factors: Natural selection; alleles for fitter organisms become more frequent. Sexual selection; alleles for more sexually attractive organisms become more frequent. Mutation; new alleles popping up due to mistakes in DNA. Genetic drift; changes an allele frequency due to random chance. Gene flow; changes in allele frequency due to mixing with new genetically different populations. Now that you know all that, in order to explain specifically how these processes influence populations we're going to have to completely forget about them. This is what's called the Hardy-Weinberg principle. Godfrey Hardy and Wilhelm Weinberg were two scientists in 1908 who independently at the same time came up with the exact same equation that describes how under the right circumstances Mendelian Genetics works at the scale of a whole population. But those right circumstances assume that none of the factors I just mentioned are at play. Hardy and Weinberg simple equation shows us the frequency with which you could expect to find different alleles within a hypothetical population that's not evolving. This weird hypothetical state is called the Hardy Weinberg-Equilibrium in which the frequency of alleles in a population remains constant from generation to generation. To make sure that happens no funny stuff is allowed to go on. To it, the Hardy-Weinberg Equilibrium requires no natural selection. Which means that no alleles are more beneficial than any other. So the better alleles will not be selected within a population. No sexual selection. Which means that mating within the population must be completely random. No individual can have a better chance of getting it on than any other. No mutations. Because mutations modify the gene-pool. Hardy-Weinberg demands a gigantic population size because the smaller the population, the more likely you are to get genetic drift. Finally, no gene flow. That means that nobody can bring over their hot cousin from the next island over because that would significantly mess with the allele frequencies. If you know what I mean. Clearly, no fun and lots of rules. Hardy and Weinberg, they figured the set at the exact same time. It can't be that complicated because it wasn't some kind of stroke of like Einsteinian inspiration. They just figured out a thing that was pretty simple. The question is can we do the same thing right now? Can we figure it out on our own? What we're looking for is the relationship between the phenotype and the actual frequency of the genes in the population. How do we proceed from here? Alas! Earwax. The consistency of earwax is a Mendelian trait. Wet earwax is a big W because it's dominant and dry earwax is recessive so it's a little w. It's called the frequency of the dominant wet allele on the population p, and the frequency of the recessive dry allele q, which is you've never noticed, q is kind of a backwards p. Since there's only two alleles for this gene in the entire population, p + q = 1 If the frequency of p is 75%, the only other thing it could be is q, so that's going to be 25% which is 1. Imagine we'd go to this hypothetical no fun Hardy-Weinberg island and there are a hundred people and we poked every single one of them in a year and 9 of them have dry earwax. That's 9/100 or 9% or 0.09. You know math. This is not q, it's not the frequency of the little w, it's the frequency of ww, homozygous ww. This is the expressed phenotype, it's not the genotype. We don't know that yet. We know the frequency of ww. But you know that there's going to be a bunch of other w alleles hanging around in heterozygous pairs. How do we figure out where those are? How many of those there are? Well, I have no idea. I now am stuck, I do not know. I am lost. When I'm stuck at situations like this what I do is I go back to what I do know and what I know is that the frequency of big W plus the frequency of little w = 1. But that's in the entire population. In each individual we want to know their genotype, so 2 different alleles. What's happening, if this is happening twice in every individual. What we need to do is square it. When we square that equation, if you remember algebra at all, you get p^2 + 2pq + q^2 = 1. That my friends is what Hardy and Weinberg did and it is the Hardy-Weinberg equation. P^2 is the odds of it being a ww. This 2pq here is the heterozygotes and the q^2 is the homozygous recessive. Good news, we know ww, we know the homozygous recessive, it's .009 so we already have that information. We know what q^2 is, it's .09 and in order to get what q is we just take the square root of that, that was a horrible square root symbol, which is .30 or 30%. 30% frequency of the q allele in the population. Then we just use the simplest equation in the world to figure out what p is, that's minus 1 and that's .70. Now, using our Hardy-Weinberg equation we can go beyond the frequency of the alleles and actually talk about the frequency of the genotypes. The frequency of the ww homozygous dominant is the p^2. We have p so we just have to square this, and that equals 0.49 or 49% of the population is homozygous dominant. Now the match gets even easier because we know p and q. To figure out how many heterozygotes there are, we just do 2 times p which is .7 times .3 which is q, and that equals 0.42 which is math that I did before hand. No, I didn't just know that. 9% of the population homozygous recessive, 49% homozygous dominant and 42% heterozygous, displaying what earwax but with that little w in there as well. What's awesome about all of these is that we could see Mendel's ideas at work in a big population. When things aren't lining up with this equation, we know that there are one of those five factors at work, probably more than one. Like for example, a bunch of hot surfers moved to the island, they all happen to have dry earwax and they start spreading their hot surfer genes all over the place. (instrumental music) None random mating, it always goes out the window whenever the hot surfers get involved.