Applying the Hardy-Weinberg equation

so let's stick with this idea the simplification that there's a gene for eye color and it only comes with two variants as it has the dominant variant which is which codes for brown eye color and it has the recessive variant which codes for blue eye color so if you have any of if either one of your alleles is this capital B you're going to have brown eyes the only way to have blue eyes is to have a lowercase is to have is to be homozygous for the recessive allele now let's say that in a population it's a large population one that meets all of the the hardy-weinberg equilibrium assumptions let's say that you were to observe that nine percent of this population has blue eyes so now we're talking about the phenotype you can actually observe that they have blue eyes so based on this can we figure out can we figure out P which is the frequency of the dominant allele can we figure this out and can we figure out Q which is the frequency of the recessive allele can we figure that out as well and I encourage you to pause this video and figure and based on what we solve the hardy-weinberg equation can we figure these things out given this information well let's revisit the hardy-weinberg equation we've worked it out in previous video but I'll rewrite it right now says the allele frequency for the dominant the the dominant allele frequency squared plus two times the dominant allele frequency times the recessive allele frequency plus the recessive allele frequency squared is equal to one and we saw that this just comes from the idea that P plus Q is going to be equal to one this is a 100 percent chance if you were to randomly pick a gene that it's one of these two one of these two variants now when you see nine percent has blue eyes what does that mean well in or only way to have blue eyes is if your genotype is homozygous recessive because if you have a capital B in here then you're going to have brown eyes so we can say that nine percent also has this genotype or you could say that the frequency in the population of this genotype is nine percent but we've already seen that's exactly that's exactly what this term right here is that's this Q squared term this is the probability one way to think about it of getting of this is the Q of course is the frequency of the recessive allele now this is the you could view this as the probability of getting two of the recessive alleles is going to be if you're in your population it's going to be nine percent so we could say Q squared is equal to nine percent or another way to think about it this term right over here is 9 percent or 0.09 0.09 that's what this nine percent has this genotype that's what this tells us right over here so then we can solve for Q if Q squared I'll write it as a decimal 0.09 that means that Q is going to be the square root of 0.09 which is equal to 0.3 so just like that we were able to figure out the allele frequency of the recessive allele 30% and I could write that as a percentage 0.3 or 30% if you were looking at the genes in the population 30% express our code code for the recessive allele are the are the recessive variant and so based on that we can figure out what percentage code for the dominant vary the rest of the rest of the genes must code for the dominant cuz we're assuming there's only two of them P plus Q equal 100% or P plus P plus Q is equal to 1 so this must be 70% so just based on that we can all we can we can kind of dig a little bit deeper here so what is P squared P squared is going to be 70% squared or 0.7 squared so this right over here is 0.7 squared which is 0.49 so one way to think about it is based on this and once again a lot of simple equation but these really neat ideas are starting to pop out of it based on just this information we're now able to say that 49 percent of the population is going to be is going to have a genotype of capital B capital B they're going to be homozygous dominant and then we can figure out this right over here 2 times P times Q that's going to be 2 times 0.7 times zero point seven times zero point three times zero point three so let's see that's going to be two times two times point two one so this is going to be this right over here is going to be zero point four two or another way to think about it is forty two percent of this population is going to have the genotype upper case B and lower case B and you see they all add up 49 percent plus forty two percent is ninety one percent plus nine percent all adds up to one all adds up to one hundred percent so you get a little bit of information here and based on what we know about allele frequency is making a few assumptions we're able to get a lot more knowledge about this population and this because this is actually very useful in real life when people think about say a recessive allele that might cause some type of a disease based on based on the incidence of that disease people can start to think about well what percentage of the population is a carrier say they're they're heterozygotes for that disease so this is actually very useful in real life