### How To - Hard-Weinberg Equilibrium - 3. Lecture

Okay, this one is not a complete summary, but rather a How-To for Population Equilibrium.

Hard-Weinberg Equilibrium

The Hard-Weinberg-Principle is mostly used to count and calculate population,
but with the side note, that the population we want to work with, is an ideal population.

There is no evolution, no natural selection, we just look at the state the group of animals is like, at this very moment.

The HWE itself is simple, it looks like the binomic equation you probably got to know in high school.
Our population is a bunch of sheep, 1000 to be frank.
Of those sheep, 18 are black - black being recessive, the other 982 sheep are grey-ish.
Now I want to know how many of those are pure grey sheep and which are heterozygous grey-ish-black-ish sheeps .___.
Because we look at all possible constellations for 2 allele (p and q), there are 3 possible phenotypes:

(p + q) x (p + q) ==> p^2 (black) + q^2 (grey) + 2pq (grey-ish-black-ish BUT THEY LOOK FUCKING GREY)

Another thing that is important is, every individual of the population has to have one of the phenotypes, so the three constellations must add up to 1.

If you imagine the two genotypes, it is likely that one of them (q in our case) is dominant, and the other (p) is recessive.
Recessive genes only show as phenotype, if there is nothing that could dominate them (pp as phenotype). Being the weak is not always bad^^
In this case, it's our way into the equation.

Since (p^2) visible to us, we can derive (p) from by taking the square root of 18.
(To make this more detailed I divide it by 1000 and later multiply it all again)

Right now, we calculate the values for the allele only - there are 2 allele, we got (p) so we minus that from 1 and get (q), because the rest that is not (p) must be (q)

Now we are back to the total population - just fill in the formula and to finish off, multiply by 1000

Finally we have p^2 + 2pq , we only lack q^2 to complete our Hardy-Weinberg-Equation.

Square that shit and multiply!
To see if you did all right, add up all final numbers up. If they come only close to 1, it's fine - because of rounding inaccuracies.
If you went over the top though, you probably forgot to square root the recessive phenotypes in the beginning ._.

That's it. Now go to bed and count your sheep - color is not important if you are tired...