So I know, Hardy Weinberg is probably your favorite topic, because it's just so much fun to do. So hopefully, you won't have too much to review, but for most people, most people do not really like Hardy Weinberg. So let's delve in. So Hardy Weinberg, what is it? All it is a formula, and this formula looks at the frequencies, so how frequent different alleles and genotypes are in a population at a specific time. Right? So you're looking at a population of fish, and some fish are brown and some fish are blue. What are the frequencies of those brown and blue alleles in that population? We can measure this in two ways using two formulas. First, is the allelic frequency, and that's measuring the frequency of the alleles. And so that formula is here, p+q=1, where p allele represents dominant, and the q allele represents recessive, which makes sense. You add all the dominant, you add all the recessive, that's going to total the number of alleles in the population. Now, you may be asking, well, we've gone over a lot in genetics and we realize that not all alleles are dominant and recessive. Does Hardy Weinberg take that into account? It does. So if you have more alleles than just dominant and recessive, then you can actually add those in, too. So you add the dominant, you add the recessive, and you add any other type of allele that you may have in these sort of weird genetic cases that we've talked about, and all of them will add up to equal one. But for simplicity's sake, we're just going to focus on p+q=1, because that's probably what you're familiar with. And so, the allelic frequency is looking at the gene pool of the population, and that is the sum of alleles, so p+q, in the breeding members of the population. These are the alleles that can be passed on at that specific time.

Then, we have genotypic frequencies, and these are looking at genotypes. Right? So either homozygous or heterozygous. And so this formula is here, p2+2pq+q2=1. So, p2 represents dominant homozygotes, 2pq represents heterozygotes, and q2 represents recessive homozygotes. Using this formula, we can calculate the frequency of heterozygotes in the population, the frequency of dominant homozygotes, and it's a great way to measure frequencies. Now, Hardy Weinberg requires a bunch of assumptions, which we'll talk about on the next page. But before we get to them, I just want to say that because of all these assumptions we're about to go over, Hardy Weinberg says that the genes, the alleles, and the genotype frequencies, so whatever these numbers are, do not change, underline this, from one generation to the next. So if you get a question that says something like, assuming Hardy Weinberg Equilibrium, here's p and q for this generation. What's p and q for the next generation? Well, assuming Hardy Weinberg, they're exactly the same. All the alleles get passed on to the next generation, according to Hardy Weinberg. And so, all the frequencies that you calculate using the genotypic formula or the allelic formula do not change.

This, for example, usually, some of the easier questions will give you the value for p or the value for q, then ask you to solve any of the other questions. But sometimes, professors use weird wordings, hopefully making a point. This question says, "A recessive disease has a frequency of 1 in 1100 in the population. Assuming Hardy Weinberg, calculate all these values." This is difficult because it doesn't tell you directly what p is or q is or 2pq is. It mentions a recessive disease and gives its frequency. Now let's say, Hardy Weinberg is at work here, assuming we use the formulas above, calculate all these values. Because we know this is for a recessive disease, only 1 per 1100 in the population have it, so this is q squared. It's a homozygous. So if you put that into the formula, you get this, which enables us to find q by taking the square root. Now, we solve for p using p+q=1, and we can fill in the rest of the formula values for 2pq, etc. This formulae approach allows us to calculate p squared, 2pq, q squared, and p based only on the information about recessive disease frequency.

Now, let's move on to the really important part of Hardy Weinberg, the assumptions. Hardy Weinberg exists in an ideal world. What does this ideal world mean? I have abbreviated it to Samir. You may know someone named Samir, but each one of these letters represents an assumption for Hardy Weinberg. 'S' stands for no selection, which means all genotypes and alleles have equal viability. 'A' stands for no new alleles, indicating that there are no mutations creating new alleles. 'M' stands for no migration, meaning individuals are neither coming into nor leaving the population. 'I' signifies an infinitely large population where no genetic drift occurs. Finally, 'R' for random mating, where mates are completely chosen at random. If we look back, no selection, no new alleles, no mutation, no migration, infinite population, and always random mating highlight that this is not reality. There is always selection, mutations, changing populations due to migration, finite populations, and mating influenced by genes and alleles. Thus, we use Hardy Weinberg to estimate allele and genotype frequencies in ideal situations. However, these five Samir assumptions are seldom met in any natural population. So, make sure you understand those formulas, how to calculate the values with those formulas, and memorize these five assumptions, because they are likely to be on a quiz or test. With that, let's now move on.