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Hey look it's our friend gregor mendel the super monk who discovered the basic principles of genetics hopefully you remember of this 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 Fred Chuckie 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 but 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 both Mendel and Darwin died not knowing how their ideas fit together so 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 and I have good news it involves a lot of math population genetics on the surface is not a complicated idea it's the study of how populations of a species change genetically over time leading to species evolving so let's start out by defining what a population is it's simply a group of individuals of a species that can interbreed and 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 like fun because it's it's basically like scientific instant gratification I can now observe evolution happening within my lifetime so eazy-e's cross that off the old 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 in what's called allele frequency which is just how often certain alleles turn up within a population and those changes are at the heart of how and why evolution happens so there are several factors that change allele frequency within a population it does like fast and furious movies there are five of them and 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 this natural selection makes the alleles that make animals their strongest and most virile Island least likely to die more frequent in the population now most selective pressures are environmental ones like food supply predators or parasites but at the population level one of the most important evolutionary forces is sexual selection and population genetics gives it 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 more offspring the pop gen spin on things that 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 so sexual selection changes a genetic makeup of a population because the alleles of the most successful mater's are going to show up more often in the gene pool we'll mater's going to make 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 bad 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 and this 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've 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 and 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 in allele frequency due to random chance and 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 in will held 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 population remains constant from generation to generation and 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 party Weinberg demands a gigantic population size because the smaller the population the more likely you are to get genetic drift and 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 so clearly no fun and lots of rules Hardy and Weinberg they figured this out of the exact same time so it can't be that complicated because it wasn't some kind of stroke of like Einstein Ian's inspiration they just they're 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 well we're looking for as the relationship between the phenotype and the actual frequency of the genes in the population so how do we proceed from here alas earwax the consistency of earwax is a Mendelian trait wet earwax is Big W because it's dominant and dry earwax is recessive so it's a little W now let's call the frequency of the dominant wet allele in 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 are only two alleles for this gene in the entire population P plus Q is going to equal one so three Qin C of P is 75% the only other thing it could be is Q so that's to be 25% which is one so imagine we go to this hypothetical no-phone hardy-weinberg island and there are a hundred people and we poke every single one of them the year and nine of them have dry earwax so that's nine over a hundred or 9% or 0.09 you know math but this is not Q it's not the frequency of the little W it's the frequency of W W homozygous w W so 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 and heterozygous pairs so how do we figure out where those are how many of those there are well I have no idea right now and stuck I do not know I am lost I'm stuck in 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 equals one but that's in the entire population and each individual we want to know their genotype so two different alleles so what's happening is this is happening twice and every individual so what we need to do is square it and when we square that equation if you remember algebra at all you get P squared plus 2pq I'm such excellent handwriting plus Q squared equals one and that my friends is what Hardy and Weinberg did and it is the hardy-weinberg equation so P squared is the odds of it being a WW this - PQ here is the heterozygotes and the Q squared is the homozygous recessive well good news we know W W we know the homozygous recessive is point zero zero nine so we already have that information so we know what Q squared is it's point zero nine and in order to get what Q is we just take the square root of that I was a horrible square root symbol which is point three zero or 30% 30% frequency of the Q allele in the population and then we just use the simplest equation in the world to figure out what P is this -1 and that's point seven zero now using our hardy-weinberg equation we can go beyond the frequency of the alleles and actually talk about the frequency of the genotypes so the frequency of the WW homozygous dominant is the p squared so we have P so we have to square this and that equals 0.49 or 49 percent of the population is homozygous dominant and now the math gets even easier because we know P and Q so to figure out how many heterozygotes there are we just do two times P which is 0.7 times 0.3 which is Q and that equals 0.4 - which is math that I did beforehand no I didn't just know that so nine percent of the population homozygous recessives 49 percent homozygous dominant and 42 percent heterozygous displaying wet earwax but with that little W in there as well it's awesome about all this is that we can see Mendel's ideas at work in a big population and 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 move to the island they all happen to have dry earwax and they start spreading their hot surfer genes all over the place non-random mating it always goes out the window whenever the hot surfers get involved
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