There are 2 types of populations:
1. Real population ( Influenced by non-random mating, mutations, selection, random genetic drift, gene flow and meiotic drive )
2. Basic idealized population 
- The population is large
- The influence of change can be ignored
- Mating is at random
- There is no migration in or out
- There are no new mutations
- There is no differential selection
- Each genotype has equal chance of survival and reproduction
Hardy–Weinberg principle is based on basic idealized population.
The Hardy-Weinberg principle states that in a large randomly breeding population, allelic frequencies will remain the same from generation to generation assuming that there is no mutation, gene migration, selection or genetic drift. 
In the simplest case of a single locus with two alleles: allele one is denoted A and allele two a and their frequencies are denoted by pand q; freq(A) = p; freq(a) = q; p + q = 1. If mating is random, then new individuals will have freq(AA) = p2 for the AA homozygotes in the population, freq(aa) = q2 for the aa homozygotes, and freq(Aa) = 2pq for the heterozygotes.
The formula is sometimes written as (p2) + (2pq) + (q2) = 1
or, (p+q)2 =1 0r, p+q = 1
The genotype frequencies in the parental generation are now: p2(AA), 2pq (Aa), and q2 (aa), respectively.
Gamete frequencies are
– For A: p2 + pq = p(p+q) = p(1) = p
– For a: q2 + pq = q(q+p) = q(1) = q
So, genotype frequencies in the next generation again will be p2 (AA), 2pq (Aa), and q2 (aa), respectively.
Once genotype frequencies can be explained by allele frequencies in the parental generation, they will not change anymore.
Genotype and allele frequencies are in equilibrium (so called Hardy-Weinberg equilibrium).
Application of Hardy-Weinberg equilibrium
If one knows the population frequency of an autosomal recessive disease, one can calculate the population frequency of carriers of this disease. 
The disease frequency is q2 . So the allele frequency is the square root of it, i.e. q, the frequency of the normal allele (1-q), and the carrier frequency is 2pq, or 2(1-q)q.
This is important knowledge for counselling family members of patients with autosomal recessive diseases.
For rare diseases p is almost 1. So 2pq ≈ 2q.
For lethal diseases, in which patients do not contribute to the next generation, all patients have two carrier parents. If the carrier frequency in the population is C, the frequency of carrier couples will be C2, and the frequency of the disease will be C2 /4.
As C2 /4 = q2, C2 = 4q2, and therefore C = 2q.
For frequent, non-lethal autosomal recessive disorders the carrier frequency remains 2pq.
• Note: Lethality is a violation of the conditions of the basic idealized population.
In order for a population to be considered in Hardy-Weinberg equilibrium, following steps can be done…
- Step 1: Determine the gene frequencies of the current generation.
- Step 2: Determine the expected genotype frequencies for the next generation.
- Step 3: Compare the expected frequency with the original population numbers.
Comparing the expected numbers with the actual numbers of each phenotype, population geneticists can determine if populations are either in equilibrium (or very close to it) or are experiencing disequilibrium of some sort .
3. Thompson & Thompson genetics in medicine. 6th ed.
Last revised: 12/12/2012