Hardy Weinberg

 This is the sort of thing I love when it comes to biology. Something I dabble in on the side is physics, and as such I love a good formula! The formula in question is as follows: p^2 + 2pq +q^2 = 1. This is the Hardy-Weinberg Theorem, and it states that allele and genotype frequencies in a population will remain constant from generation to generation (if other evolutionary influences are absent). This theorem is helpful in determining genotype frequencies when you only know the number of individuals with a trait within a population. 

This is shown in the problems given at the end of the first lecture on HWE2:

If in a population of 800 "dwarbs", 25 of them had black tongues (a recessive trait), then the frequency for dwarbs with the black tongued allele is 0.177. The frequency for the dominant allele would then be 0.823. 29.13% of the "dwarbs" would be heterozygous for the black tongue.

If the frequency for the delta-32 mutation (a recessive allele) in a town was 20% for the allele that causes it, then the percentage of the population that homozygous for this allele is 4%. As this allele confers immunity to HIV only to those who are homozygous for it, 32 % of the population is not immune but is capable of having children who are immune.

Here is my own made up version of a problem of this type:

Say for example you had 35 tressym with black wings (which are recessive) in a population of 400 tressym (a fantasy creature which looks like a cat with wings). 35 divided by 400 is 0.0875, or for our purposes 8.75%. This is the p^2 value in our theorem. if you get the square root of it you get the q value, which is 0.296. If we subtract that from one we get 0.704. So our frequency for the allele for black wings is 0.296, and our frequency for the allele for white wings is 0.704.