What is the Hardy-Weinberg equilibrium and when is it used? With an example

The Hardy-Weinberg equilibrium is used to work out dominant and recessive allele ratios in a population regarding one gene. Dominant alleles are those which when at all present in the genotype develops a particular characteristic, whereas the recessive allele only 'shows' itself if no dominant allele of the gene is present. The law predicts that the frequency of alleles in a population will remain constant as long as certain rules are adhered to e.g. a very large population that has no mutation, migration or natural selection. It can be used for allelic frequencies using the equation P + q = 1 or for genotypic frequencies using: P^2 + 2Pq + q^2 = 1 For these equations, P = dominant allele and q = recessive allele. The two equations can be used interchangeably, as in, if you know the proportion of homozygous recessives in the population (q^2) you can work out the ratio of q (recessive allele) in the population by square rooting the homozygous recessive number. Example: The disease sickle-cell anemia is only present if an individual has a certain genotype and it results in deformation of red-blood cells at low oxygen levels. If the individual is dominant homozygous (SS) their blood is normal, but they have high risk of malarial infection. If they are homozygous recessive (ss) they often don’t survive because they have the sickle-cell trait. Heterozygotes (Ss) are at an advantage in some countries because they are only severely affected by sickle-cells at high altitudes (low oxygen) and they have some form of defence against malaria. Imagine 12% of a population is born with sickle-cell anemia (ss) what is the percentage that will be more resistant to malaria as they are heterozygous (Ss)? Answer: 12% = 0.12 = ss = q^2. To find q, you should square root 0.12 to get 0.35 (2d.p) and then since p= 1- q, p = 1- 0.35, which is equal to 0.65. To work out the heterozygote population you must do 2(0.35 x 0.65) = 0.455 = 45.5% of the population is heterozygote.