Balance H-W

Hard-weberger balance: standard definition ----
If a population meets the following conditions: 1. the population is extremely large. 2. mating among individual populations is random, that is, the chance of mating between each individual in the population and other individuals in the population is equal; 3. no mutation occurs. 4. there is no individual migration or genetic exchange between populations; 5. if there is no natural choice, the population's genetic frequency (including the genotype frequency) can remain stable for generations and maintain a balance. This is the law of genetic equilibrium, also known as the balance between the hard drive C-winberger and the hard drive.
In actual application --
For genetic analysis such as polymorphism, the data results should be analyzed first by using the hard-weberger equilibrium. Of course, if it is a case-control study, the case group may be associated with the disease because of this genetic polymorphism, it is likely that it does not conform to the hard-weberger balance. This is also a normal phenomenon, but the control group must comply with this balance in any case.

 

The hard-winberger equilibrium law, that is, the HW equilibrium, refers to a large and random mating population, gene frequencies and genotype frequencies remain unchanged without migration, mutation, and selection.
It is built on an ideal group model and has four assumptions: 1. unlimited groups; 2. random matching; 3. no mutation; 4. there is no impact on large-scale migration and selection factors. The conclusion is that the gene frequencies and genotype frequencies in the population remain unchanged during generation-by-generation transmission.
In fact, the conditions of this ideal population cannot be fully met, but after mathematical derivation, in a population, the gene frequency and the genotype frequency are constant in each generation, even if the population is not balanced, A new balance can be achieved by breeding a generation.
It is important to test the results of the sampling survey to assess whether the target group meets the HW balance, so as to assess the reliability of the Group survey data, especially in genetic epidemiological association studies.
The Chi-square statistic is usually used to measure the degree of coincidence between the observed value of the number of genotype and the expected value of the distribution of all genotype frequencies at the site in line with the HW balance. Generally, P = 0.05 is used as the Boundary Value of the significance level. P> 0.05 indicates that the survey population reaches the genetic balance, that is, the data in this survey is credible. Otherwise, when P <0.05, consider the following: 1. whether the population to be investigated is in a genetic balance; 2. whether there is an error in the techniques or standards of genetic markers (such as SNP) classification; 3. whether the random sampling requirement is met. In particular, pay attention to the last two points!

 

For example:

1. The actual number of three genotypes (o ):
AA---AB---BB
1787 3039 1303 total N = 6129

2. allele frequency
F (a) = (1787 + 3039/2)/6129 = 0.54 = P
F (B) = (1303 + 3039/2)/6129 = 0.46 = Q... And s (p, q) = 1

3. Expected genotype frequency:
Expected AA frequency: P2 = (0.54) 2 = 0.2916
Expected AB frequency: 2pq = 2x0.54x0.46 = 0.4968
Expected BB frequency: q2 = (0.46) 2 = 0.2116

4. Expect genotype (q ):
Expected AA: p2n = 0.2916x6129 = 1787.2
Expect AB: 2pqn = 0.4968x6129 = 3044.9
Expected BB: q2n = 0.2116x6129 = 1296.9

5, Chi-square value
X2 = (OAA-QAA) 2 [sq]/Qaa + (OAB-QAB) 2 [sq]/QAB + (OBB-QBB) 2 [sq]/qbb

Then calculate the P value based on X2 !!