For example, given two alleles A and a, with P(A)=p and P(a)=q, where p+q=1 (mutually exclusive), the probability of AA=p^2, aa=q^2 and Aa=2pq...
That's true assuming random mating, no selection and no gene flow from other populations.
If you observe that the frequency of AA in reality is greater than p^2, that might mean allele A is being selected for, i.e. is increasing in frequency because its bearers have more kids.
If the frequency of Aa exceeds 2pq, well that's pretty weird. It might mean that AA's are mating with aa's more frequently than random chance predicts. Opposites attract?
Other formulas describe:
- fitness: fitness of AA= w = kids(AA) / kids(any genotype)
- effective population size
- genetic drift
- narrow sense heritability
- response to selection for a continuous (many gene controlled) trait (like height or IQ)
This is the beginning of a collection of the simplest math of various fields inspired by Yudkowsky: "But for people who can read calculus, and sometimes just plain algebra, the drop-dead basic mathematics of a field may not take that long to learn. And it's likely to change your outlook on life more than the math-free popularizations or the highly technical math."