okay so in this video we're going to see how we can measure and see if a population is actually evolving and we'll be using the Hardy weidenberg theorem or the Hardy weidenberg equations in order to do that so as a quick refresher let's talk about this population of deer here and uh basically when we think about a population uh there are five mechanisms or five ways for this deer population to evolve or to change over time so there's five things that may cause the alal frequencies to change over the generations because if you remember evolution is a change in AO frequencies over time so when we think about the five things that may cause this to happen we have natural selection sexual sexual selection mutations genetic drift and gene flow so um Hardy Weinberg is how we're going to calculate and see did the Alo frequencies actually change from one generation to the next so uh basically for a population to be in Hardy Weinberg equilibrium like uh sometimes it's phrase like that it'll say something like a population is in Hardy Weinberg or population in Hardy Weinberg equilibrium like what does that mean right well equilibrium means like balanced or staying the same so here if a population is in Hardy Weinberg equilibrium that means it's not evolving from one generation to the next which means its Al frequencies are not changing so if we remember those five fact like fact not factors five mechanisms of change the five reasons why alal frequencies would change we need to make sure that none of them are occurring so in order for a population to be in Hardy weberg it basically has to have no natural selection occurring random mating there can be no sexual selection no new mutations or no mutations um at least in whatever Gene you are uh like studying or tracking basically right needs to have a large population size so that any random events don't change the alal frequencies so like the bottleneck effect or the founder effect really have a large impact if we're talking about a small population size so by having a large population if um okay for example if you had like there's a snow leopard population uh maybe Siberia that's like very at risk for extinction like 40 individuals left in the planet in that population so if there's an avalanche that kills like 35 of those snow leopards or something um there's only five survivors like that's an example of the bottleneck effect like a small population was greatly reduced for at least one generation but if you look at like humans with seven billion people on the planet and four or 35 die in an avalanche it's not going to change the alal frequencies of that human population so a large population size helps us kind of um negate the effects of genetic drift and then lastly there can be no migration or no gene flow no individual carrying alals into or out of the population so um when we look at this evolution is a change in alal frequencies over time so we need a formula to calculate or find those alal frequencies so we can see is the population evolving so one of the formulas we'll use is p+ Q equal 1 and P is going to stand for the frequency of the dominant Al like in the gene pool so if you had all of the alals what percent of the gene pool would be the dominant Al then you have q and Q represents the frequency of the recess of Al like how often does that recess of Alo uh found in the gene pool and then from there once we know the frequency how often those two alals are like show up in the Generation Well then in the next year did they stay the same or did they change so let's go ahead and see so here we have our deer population and I see two different phenotypes and by looking at this the orange-ish phenotype is the recessive phenotype now if I see an orange deer I know it's a um what's it called genotype is homozygous recessive if that is the recessive phenotype now if I see a brown deer though I don't know if it's homozygous dominant or if it's heterozygous so with the brown deer you could have some that are homozygous dominant or some that are heterozygous so my sweet students when you or anyone watching this video when you are solving for alal frequencies you're going to want to start with the recessive Al solve for Q first because you know by looking at a recessive phenotype you are sure of the genotype so if I see an orange deer I know they are little a little a homozygous recessive if I see a round deer I don't know could be homozygous dominant could be heterozygous so we always want to solve for Q first and then we can solve for p okay so um here in this deer population we have 24 deer and they 48 alals are found within this population because they're diploids and they have two alals for each gene um and then here if you count all of these deer you can see that there are 2 24 dominant alal and 24 recessive alals which that would make the frequency of the dominant Al 50% 24 divided 48 is 50% or 0.5 and then it'd be the same for the um recessive a Leo for Q it would be 24 divid 48 is 0.5 okay so now though let's go ahead and see a second formula that we use and this one is p ^2 + 2 PQ + Q ^2 = 1 now when you see this equals 1 that's also like equals 100% so over here in p + Q equals 1 it's the frequency or the percent of the dominant Alo in the gene pool and the frequency or percent of the recessive a Le in the gene pool is going to equal 100% of the gene pool or one okay so uh p s is actually like representing our homozygous dominant individuals uh in a population 2 PQ is going to represent our heterozygous individuals in a population and then q^2 is going to represent the homozygous recessive individuals in a population so if I added up all of the deer I found I added up the homozygous dominant the heterozygous and the homozygous recessive that would be 100% of my population which is the one okay so uh it is important to remember that these two formulas p+ Q = 1 one is for Al frequencies in a gene pool whereas this formula is for individuals or genotypes in a population so if I were to tell you I have like 16% of the population is homozygous recessive I just gave you q^2 basically so this formula is used for if they're talking about a percent of a population the individuals if it tells you a certain number of genotypes so that is when we use this and really it'll get a lot easier the more practice you have with solving um like word problems about uh Hardy Weinberg situations okay so let's go ahead and apply this I'm going to do two examples of how we can work uh through these two formulas to see if p and Q or the Alo frequencies are changing from one generation to the next then I'll have a whole another video just showing different ways to solve the problems okay so here I have this steer population and let's pretend that natural selection is occurring and the orange fur phenotype is selected against so here I have some orange deer who have low Fitness they do not survive long enough to get to reproduce so now the Brown Deer um are the ones who have higher Fitness and get to reproduce have Offspring and I see that the next generation of deer um have a little bit more brown deer compared to Orange Deer uh because the brown was a high Fitness compared to Orange low Fitness so now visually I can see okay natural selection occurred the population changed over time but now we're going to actually calculate those alal frequencies to confirm yes the population did evolve or maybe it didn't so let's go ahead and see so from now this is the here we go here we go so from just looking at our deer just looking at the phenotypes can we solve for p and Q like when you see these deer do you see all of the dominant and recessive alals in the gene pool no right but what we do know for sure is that when I am looking at a recessive phenotype oops so there's our two formulas when I'm looking at a recessive phenotype so here the orange fur was the recessive phenotype I do know that they are homozygous recessive so from just that that gives me some information it does not directly give me Q though it doesn't give me Q because how do I know like I can't count like what if this deer right here was heterozygous and I I can't see that recessive alil in that heterozygote so if I know and I can visually see or the problem tells me um the number of home homozygous recessive individuals based on that recessive phenotype I basically have q sared so uh if we remember Q2 is equal sorry I'm trying to clear off the ink um q^ SAR is equal to um the number of homozygous recessive individuals so here uh we have q^2 and we can get to Q from here though right like we can take q^2 and then take take the square root of it to solve for Q then if you get Q then you can solve for p and then you can answer anything so we always want to try to solve for Q first because then we can find P then we can find p^2 2 PQ and then Q squ is what we're starting with so now let's go ahead and see how we'll do this so let me move my face okay so I here I have four deer out of the 24 that have this recessive phenotype so these four deer um I'm sorry I still have the pen on oh man so sorry um so if I look at the four deer I have a q s remember uh q^ s or 2pq or p^ squ are dealing with like the number of individuals in a population so there are four individuals with this recessive phenotype so they're homozygous recessive for their genotype and there's four of them out of the 20 4 total in this population so that tells me that my q^ sared is17 or 177% of the population is homozygous recessive now all I need to do is to take the square root of this 17 OR7 uh and that's going to give me Q so here Q is going to be equal to 41 now because I have the formula p + Q = 1 I can calculate P I can take 41 and subtract it from both sides so 1 minus 041 and now I have P equal 0.59 okay okay so now in our original population our alal frequencies were 0. five and 0.5 and then natural selection occurred though okay okay and in our next generation p was 0.59 and Q was 041 so what we see is we see the dominant Al increasing in the population and the recess of a decreasing you can think of this as kind of like directional selection for natural selection so we can see that dominant phenotype is being favored all right and then uh our question now is did this population evolve and the answer would be yes we did have a change in a Leo frequencies from one generation to the next okay so we're going to go go through the same kind of logic here but with a different premise of sexual selection and then um there are so many different ways you can get asked about Hardy Weinberg so instead of making a super long video I'll make a next video of solving um more styles of Hardy weberg questions so let's go ahead and look here with sexual selection so let's say that we have this population of deer and you can tell that the orange deer the males have a little bit shorter antlers than the Brown Deer so as these females are choosing their mates or maybe the males are competing for the females and it's the males with a longer antlers who get to reproduce um and have Offspring um then we can see that the next generation of uh deer the next um like yeah generation's Offspring will inherit the alal for larger antlers so with this um male antlers with larger ant sorry the m deer with larger antlers have high Fitness because Fitness is based on reproductive success so if they're the ones who are Ming they are also the ones passing their traits or their genes or their alals onto the Next Generation so here we have the Next Generation and we have more of the deer are going to carry those Al for larger antlers okay so let's go ahead and find p and Q and see if sexual selection shifted the Alo frequencies in in this gene pool so here I have U my deer and we have eight deer in this population originally now just looking at their phenotypes I can see that four of the deer are homozygous recessive so that's going to help me find my Q squared because Q squared is when you have individuals so here I'm going to take my here's my two formulas and I have q^ squared I can find from this setup so now I can uh go ahead and take q^2 a half of the population four out of eight um have this recessive homozygous phenotype and then I find uh the square root of this q^2 and I find that Q is 71 now because p + Q = 1 I know that my P is 0 29 now let's go ahead and take into account the Next Generation though and let's go ahead and see with these Offspring so here um I still have those deer that were orange they didn't necessarily die but they also didn't reproduce I but this one female right here reproduced okay okay so here though if I look at my four uh individuals that are uh homozygous recessive that is my q^ squar four out of the whole population so 4 / 14 is going to give me a q^2 of. 29 which is telling me that 29% of the population has the homozygous recessive phenotype now I can find my Q by taking the square root of. 29 and I find Q is equal to .53 well p + Q = 1 so now I know that P is 47 so now if we look at our first generation Our p was. 29 and our Q was 71 then after sexual selection played a role we find that in the second generation our p is 47 and our Q is. 53 oops did our population evolve yeah the AL frequencies changed all right all right so that is my intro on Hardy Weinberg and then my next video will be a lot more different uh styles of questions and how you can solve them okay great job