Example Hardy-Weinberg Problems

okay so in this video what we're going to look at is um are are a few examples of how we can solve hardy-weinberg problems so let's go ahead and start with a population of butterflies where pink wings is going to be the recessive trait while purple wings is dominant so if we have a population of 600 butterflies and 54 of them have pink wings so just from this information we can really think more deeply about what is given to us here i know that 54 out of 600 of these butterflies are homozygous recessive so i would know their genotype as well as their phenotype now out of that 600 though 600 minus 54 i would have the dominant phenotype so 546 butterflies have the dominant phenotype but let's go ahead and look at a few of the questions that we're going to answer with these butterflies so first we'll we'll calculate and figure out well how many alleles are in the gene pool and once we know how many alleles in the gene pool what is the frequency of the recessive allele the frequency of the dominant allele well how many of these butterflies are homozygous dominant and then how many are heterozygous okay so let's just start with this first easy question so if we have 600 butterflies and each butterfly is a diploid organism meaning that they have two copies for each gene they have two alleles so here you would take your 600 times two so in this gene pool for 600 butterflies you would have 1200 alleles now in that gene pool though what is the frequency of the recessive allele like out of that 1200 what percent is a recessive allele and then what percent is the dominant allele so for that we we're going to use the formula um we have two formulas to choose from but really we are looking for p and q so q is the recessive allele frequency and p is the dominant allele frequency but what we're given in our problem is they've told us the number of recessive phenotype individuals so in the setup they have given us q squared q squared is your homozygous recessive individuals so now can we get from q squared to p or q yes so with that we're going to take our q squared is equal to 54 divided by 600 and that gives us 0.09 so now this tells us that 9 of this butterfly population is homozygous recessive but now if we take the square root of both sides we find that q is equal to the square root of .09 which puts q at point three so then if we use the formula p plus q equals 1 what we find is um p is going to equal 0.7 so to answer our question what is the frequency of the recessive allele q is equal to 0.3 and that tells us that 30 of this gene pool 30 of those 1200 alleles are recessive alleles then the 0.7 tells us that 70 of those 1200 70 of the gene pool uh for wing color is the dominant allele for this population okay so now uh what percent of this butterfly population is homozygous dominant okay so now a common mistake i see from students but you want to try and avoid this mistake is where they will take 600 and then they just subtract the 54 that are recessive phenotypes and like oh the rest are dominant so that's going to be you know 546 butterflies out of 600 would be dominant or homozygous dominant but that's not true because the dominant phenotype is both homozygous dominant individuals and heterozygous individuals so now let's go ahead and refresh your memory about this formula so in this formula p squared represents the frequency of the homozygous dominant individuals in that population two p q is the heterozygotes so now what i'm gonna do is i'm gonna they're asking for p squared but i already calculated p earlier so now i'm gonna take my point seven and i'm going to square it and that'll tell me that 49 of this population of butterflies um is homozygous dominant for wing color okay so i also i don't think i've said it out loud yet is when you are solving hardy-weinberg problems you always want to solve for q first so earlier here on this previous slide we solved for q first and then you can find p and then from there you can answer any part of this formula as well okay so let's go ahead and answer the next uh part e of this question it says what percent of the butterfly population is heterozygous okay okay so that's going to be the middle section of this formula and we already know p and q so we're going to take our p and our q um and go 2 times 0.7 times 0.3 and that's going to tell us 42 of this population is heterozygous now if you were curious about the percent of the population that was um homozygous recessive that is your 54 divided by 600. right that's your 16 percent we started with oh not 16 uh nine percent that we started with okay uh so now let's go ahead and look at our next question oh so in a population of 350 horses 16 express the recessive phenotype how many horses are are homozygous dominant okay okay so we want to think to ourselves we know the total population size and we know 16 have the recessive phenotype so we always want to solve for q first and let's see how we can get to q from what's given well what i see here at that 16 percent that is the 16 of individual horses in a population so that is um q squared now if it said 16 of the gene pool was the recessive allele that would be just straight up q but here it's 16 of a population and that's individual so that is going to be our q squared and just like uh oh and then the question is asking for though well how many are homozygous dominant so we're given q squared and we got to get over to solving for p squared okay so we're going to solve for q first so if q squared is equal to the point 16 then we take our square root and we find that q is 0.4 then we can solve for p because p plus q is 1 and that tells us that p is 0.6 so if it asks us how many are homozygous dominant we need that p squared so we're going to take our 0.6 and square it so 36 of these horses um are uh homozygous dominant so uh what i need to do though this is asking not for a percent 36 percent it's asking for how many horses so that is our next step will then be to take the 0.36 times the population of 350 and that will tell us that 126 horses are homozygous dominant okay um so now if 84 of a population express the dominant phenotype what is the frequency of the dominant allele okay okay so now the question is asking us uh for the frequency of the dominant allele which is p but what did they give us right they say 84 of the population express the dominant phenotype so we're talking about dominant phenotype and we're looking for dominant allele but we still need to solve for q first q is the frequency of the recessive allele so here in our question they are asking for p the frequency of the dominant allele but what they gave us was the percent of the population that is dominant for their phenotype so they told us p squared and 2pq because both of these genotypes will lead to this dominant phenotype so now uh we still need to solve for q first to be able to get to p uh because what you cannot do which i've seen this mistake a lot is p squared is not equal to 0.84 really we need to really remember that 0.84 that dominant phenotype is made out of or composed of the homozygous dominant as well as the heterozygous individuals so try not to make that mistake okay so now though uh what i have here if um the p squared and 2p 2pq is 84 or 0.84 then i'm only really looking for q squared um and that one means like 100 so here if i subtract 0.84 from each side i find that q squared is equal to 0.16 or 16 percent of the population how's that recessive phenotype so then i solve for my q it's 0.4 but the question was asking for p and therefore our frequency of the dominant allele is 0.6 so our final answer here for this question would be 0.6 okay so let's go ahead this is my last question um another way to kind of present the information and ask a different question it says in leopard geckos yellow skin with brown spots is dominant to white skin with with brown spots now i made this up i really don't know okay so it says determine the genotypic frequencies okay okay so let's see we are given numbers of individuals with the total population and we want to solve for q first so what we're going to do is we're going to think about the recessive phenotype and if i look at the question white skin with brown spots is the recessive phenotype so now i know that my q squared is equal to the 572 divided by the total population that tells me how much of the population the frequency of homozygous recessive individuals now be very careful even when i was making this powerpoint i took 572 and i divided it by a hundred or 1789 and luckily i caught my mistake but i always make that mistake when i'm making answer keys and stuff so remember you're finding like i have this many recessive individuals out of the total population okay so be careful there so now when i calculate this q squared i find that 24 of the population is homozygous recessive uh for this white skin with brown spot phenotype now i need to solve for q so i find that q is equal to 0.49 now once i know q then i can solve for p and p is equal to 0.51 so we got to our p and our q but in reality the question was asking us to determine the genotypic frequencies now when they're when they ask that they're asking for out of the total population how often what does the homozygous dominant genotype show up how often does the heterozygous phenotype show up i'm sorry genotype uh and then how often is the um homozygous recessive genotype like what is the breakdown within that total population so here homozygous dominance is going to be represented by our p squared so i'll take p squared and i find that 26 of this gecko population is homozygous dominant then i find in the heterozygotes that 2pq represents the frequency of heterozygotes in a population so if i calculate that out we find about 50 percent um and there is slight rounding errors i hear um they're not errors but like there's going to be rounding issues so depending on how many like decimal places you leave in your calculator could lead to slight differences in our answers but as long as you're close it should be okay and acceptable um and then for our homozygous recessive is what we originally calculated with our q squared so we find uh that's 24 of the population and you can check this because p squared plus 2pq plus q squared should equal 1. so point two six plus point five plus point two four adds up to one or a hundred percent of our population okay so those are just a few ways you may experience hardy-weinberg problems and uh yeah great job

Channel: HeyNowScience

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Length: 13min 35sec (815 seconds)

Published: Tue Mar 02 2021