# I don't get Hardy Weinberg equation :( watch

1. P+q= 1
Allele frequency

p2+2pq+q2=1
Gene frequency ^?

Can someone do me a worked out example?
2. (Original post by Hazel99)
P+q= 1
Allele frequency

p2+2pq+q2=1
Gene frequency ^?

Can someone do me a worked out example?
okay so this only works if you have a gene with 2 alleles and if 1 is dominant over the other. Let's say the dominant allele is "A" and the recessive allele is "a". Now let's assume that in a population, 62% of the alleles for this gene are dominant, that would obviously mean that 38% of the remaining alleles in the population are the recessive type. So if we say p=A and q=a, then p=0.62 and q=0.38. Now let's assume that this gene codes for freckles, and not having freckles is the dominant trait. This means that having freckles is the recessive trait. Therefore, if you have freckles, the only genotype you can have is "aa" (homozygous recessive).

Now, the second equation you've listed expresses all the possible combinations of alleles that you can have. You can either have AA, Aa, aA (the same as Aa) or aa. If you've ever studied statistics, you'll also know that the probability of one event happening OR another event happening is found by ADDING the probabilities of each event happening individually. For example if the probability of it raining one day is 0.2 and the probability of it snowing one is 0.1, then the probability of it raining OR snowing is 0.3. On the other hand, the probability of one event happening AND another event happening at the same time is found by MULTIPLYING the probabilities together, e.g. the probability of it raining AND snowing at the same time is 0.02 (much less likely). The equation is basically saying that you can inherit AA OR Aa OR aA OR aa hence why they're added together. But it is 100% likely that you'll inherit one of those genotypes, so the sum is 1. (also notes that the values of p and q are squared because when you inherit a dominant allele from your father for example and a dominant allele from your mother then the probability of inheriting them both is found by multiplying the probability of inheriting each on individually by eachother, I'll explain this better in a sec).

Now going back to our example, because 38% of the alleles in the population are recessive, the probability of inheriting a recessive allele from your father AND from your mother is 0.38x0.38 (because as I said before, the probability of 2 events occurring together is found by multiplying together the probabilities of each event happening individually). So that way, you can use the equation above to find out the probability that someone in a population will have freckles or not. In this case, the probability of them having freckles is 0.14, and therefore the probability of them not having freckles is 1-0.14 = 0.86. So if you had a population of 100 people, you'd expect 86 of them to not have freckles and 14 of them to have freckles.

A harder example would be if they made you work that out in reverse. So let's say that having dimples is a dominant trait, and that not having dimples is a recessive trait. So DD and Dd will mean you have dimples and dd will mean you don't have dimples. If 64% of the population have dimples, what % of them are heterozygous? Would you be able to do that for me?
3. (Original post by AortaStudyMore)
okay so this only works if you have a gene with 2 alleles and if 1 is dominant over the other. Let's say the dominant allele is "A" and the recessive allele is "a". Now let's assume that in a population, 62% of the alleles for this gene are dominant, that would obviously mean that 38% of the remaining alleles in the population are the recessive type. So if we say p=A and q=a, then p=0.62 and q=0.38. Now let's assume that this gene codes for freckles, and not having freckles is the dominant trait. This means that having freckles is the recessive trait. Therefore, if you have freckles, the only genotype you can have is "aa" (homozygous recessive).

Now, the second equation you've listed expresses all the possible combinations of alleles that you can have. You can either have AA, Aa, aA (the same as Aa) or aa. If you've ever studied statistics, you'll also know that the probability of one event happening OR another event happening is found by ADDING the probabilities of each event happening individually. For example if the probability of it raining one day is 0.2 and the probability of it snowing one is 0.1, then the probability of it raining OR snowing is 0.3. On the other hand, the probability of one event happening AND another event happening at the same time is found by MULTIPLYING the probabilities together, e.g. the probability of it raining AND snowing at the same time is 0.02 (much less likely). The equation is basically saying that you can inherit AA OR Aa OR aA OR aa hence why they're added together. But it is 100% likely that you'll inherit one of those genotypes, so the sum is 1. (also notes that the values of p and q are squared because when you inherit a dominant allele from your father for example and a dominant allele from your mother then the probability of inheriting them both is found by multiplying the probability of inheriting each on individually by eachother, I'll explain this better in a sec).

Now going back to our example, because 38% of the alleles in the population are recessive, the probability of inheriting a recessive allele from your father AND from your mother is 0.38x0.38 (because as I said before, the probability of 2 events occurring together is found by multiplying together the probabilities of each event happening individually). So that way, you can use the equation above to find out the probability that someone in a population will have freckles or not. In this case, the probability of them having freckles is 0.14, and therefore the probability of them not having freckles is 1-0.14 = 0.86. So if you had a population of 100 people, you'd expect 86 of them to not have freckles and 14 of them to have freckles.

A harder example would be if they made you work that out in reverse. So let's say that having dimples is a dominant trait, and that not having dimples is a recessive trait. So DD and Dd will mean you have dimples and dd will mean you don't have dimples. If 64% of the population have dimples, what % of them are heterozygous? Would you be able to do that for me?
Ugh not sure

Do you have to square root something :/
4. (Original post by Hazel99)
Ugh not sure

Do you have to square root something :/
okay so dd=0.36, which means d=0.6. Therefore D=0.4, so the proportion of heterozygotes is 2 x 0.4 x 0.6 = 0.48 = 48%.

Let me explain:

The proportion of heterozygotes is the 2Dd part of the Hardy Weinberg equation. If DD + 2Dd + dd = 1, and the proportion of people with dimples is DD + 2Dd = 0.64, then you know that dd = 1 - 0.64 = 0.36 (I've just rearranged the HW equation to get that answer). d therefore = the square root of 0.36, which conveniantly is a square number, so q=0.6 (square root of 0.36). So this means that the proportion of recessive alleles is 0.6, and therefore the proportion of dominant alleles is 1 - 0.6 = 0.4. Now that we have these values, you simply do 2 x D x d, which is 2 x 0.4 x 0.6 = 0.48. Does that make sense? You can check that you're correct by rearranging the equation. If we're right, then DD should equal 1 - (0.48+0.36) = 0.16. We know that D=0.4, so DD=0.16, which agrees with the rearranged equation.

If there's anything you don't get then let me know!
5. (Original post by Hazel99)
Ugh not sure

Do you have to square root something :/
I see what you've done, you don't square the 0.36, the 0.36 = dd, this means that d x d = 0.36, so you have to square root the 0.36 to get an individual value for d. Just think of these letters as genotypes. Homozygous recessive is dd (ie d x d), homozygous dominant is DD (ie D x D) and hererozygous is 2Dd. The rest is all maths, just algebra. Another key thing to remember is that if someone has a dominant trait then they can be either homozygous dominant (DD) or heterozygous (2Dd). It is essential to remember that. It'll help you answer the question.

Do you want another question to try and answer?
6. (Original post by AortaStudyMore)
I see what you've done, you don't square the 0.36, the 0.36 = dd, this means that d x d = 0.36, so you have to square root the 0.36 to get an individual value for d. Just think of these letters as genotypes. Homozygous recessive is dd (ie d x d), homozygous dominant is DD (ie D x D) and hererozygous is 2Dd. The rest is all maths, just algebra. Another key thing to remember is that if someone has a dominant trait then they can be either homozygous dominant (DD) or heterozygous (2Dd). It is essential to remember that. It'll help you answer the question.

Do you want another question to try and answer?
Yeah sure
7. (Original post by Hazel99)
Yeah sure
Okay, let's say that in a population, people either have pointy noses or not. Pointy is dominant (P) and not-pointy is recessive (p). If 31% of the population don't have pointy noses, then what % of the population are heterozygous?

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